< draft-mraihi-oath-hmac-otp   rfc4226.txt 
Internet Draft D. M'Raihi Network Working Group D. M'Raihi
Category: Informational VeriSign Request for Comments: 4226 VeriSign
Document: draft-mraihi-oath-hmac-otp-04.txt M. Bellare Category: Informational M. Bellare
Expires: April 2005 UCSD UCSD
F. Hoornaert F. Hoornaert
Vasco Vasco
D. Naccache D. Naccache
Gemplus Gemplus
O. Ranen O. Ranen
Aladdin Aladdin
October 2004 December 2005
HOTP: An HMAC-based One Time Password Algorithm
Status of this Memo HOTP: An HMAC-Based One-Time Password Algorithm
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Abstract Abstract
This document describes an algorithm to generate one-time password This document describes an algorithm to generate one-time password
values, based on HMAC [BCK1]. A security analysis of the algorithm values, based on Hashed Message Authentication Code (HMAC). A
is presented, and important parameters related to the secure security analysis of the algorithm is presented, and important
deployment of the algorithm are discussed. The proposed algorithm parameters related to the secure deployment of the algorithm are
can be used across a wide range of network applications ranging discussed. The proposed algorithm can be used across a wide range of
from remote VPN access, Wi-Fi network logon to transaction-oriented network applications ranging from remote Virtual Private Network
Web applications. (VPN) access, Wi-Fi network logon to transaction-oriented Web
applications.
This work is a joint effort by the OATH (Open AuTHentication) This work is a joint effort by the OATH (Open AuTHentication)
membership to specify an algorithm that can be freely distributed membership to specify an algorithm that can be freely distributed to
to the technical community. The authors believe that a common and the technical community. The authors believe that a common and
shared algorithm will facilitate adoption of two-factor shared algorithm will facilitate adoption of two-factor
authentication on the Internet by enabling interoperability across authentication on the Internet by enabling interoperability across
commercial and open-source implementations.
Table of Contents Table of Contents
1. Overview...................................................3 1. Overview ........................................................3
2. Introduction...............................................3 2. Introduction ....................................................3
3. Requirements Terminology...................................4 3. Requirements Terminology ........................................4
4. Algorithm Requirements.....................................4 4. Algorithm Requirements ..........................................4
5. HOTP Algorithm.............................................5 5. HOTP Algorithm ..................................................5
5.1 Notation and Symbols.......................................5 5.1. Notation and Symbols .......................................5
5.2 Description................................................5 5.2. Description ................................................6
5.3 Generating an HOTP value...................................6 5.3. Generating an HOTP Value ...................................6
5.4 Example of HOTP computation for Digit = 6..................7 5.4. Example of HOTP Computation for Digit = 6 ..................7
6. Security Considerations....................................7 6. Security Considerations .........................................8
6.1 Authentication Protocol Requirements.......................8 7. Security Requirements ...........................................9
6.2 Validation of HOTP values..................................8 7.1. Authentication Protocol Requirements .......................9
6.3 Bi-directional Authentication..............................9 7.2. Validation of HOTP Values .................................10
6.4 Throttling at the server...................................9 7.3. Throttling at the Server ..................................10
6.5 Resynchronization of the counter...........................9 7.4. Resynchronization of the Counter ..........................11
6.6 Management of Shared Secrets..............................10 7.5. Management of Shared Secrets ..............................11
7. HOTP Algorithm Security: Overview.........................12 8. Composite Shared Secrets .......................................14
8. Composite Shared Secrets..................................13 9. Bi-Directional Authentication ..................................14
9. IANA Considerations.......................................13 10. Conclusion ....................................................15
10. Conclusion................................................13 11. Acknowledgements ..............................................15
11. Acknowledgements..........................................13 12. Contributors ..................................................15
12. Contributors..............................................13 13. References ....................................................15
13. References................................................14 13.1. Normative References .....................................15
12.1 Normative...............................................14 13.2. Informative References ...................................16
12.2 Informative.............................................14 Appendix A - HOTP Algorithm Security: Detailed Analysis ...........17
14. Authors' Addresses........................................15 A.1. Definitions and Notations .................................17
15. Full Copyright Statement...................................15 A.2. The Idealized Algorithm: HOTP-IDEAL .......................17
16. Intellectual Property......................................16 A.3. Model of Security .........................................18
Appendix A - HOTP Algorithm Security: Detailed Analysis........16 A.4. Security of the Ideal Authentication Algorithm ............19
A.1 Definitions and Notations..................................16 A.4.1. From Bits to Digits ................................19
A.2 The idealized algorithm: HOTP-IDEAL........................17 A.4.2. Brute Force Attacks ................................21
A.3 Model of Security..........................................17 A.4.3. Brute force attacks are the best possible attacks ..22
A.4 Security of the ideal authentication algorithm.............19 A.5. Security Analysis of HOTP .................................23
A.4.1 From bits to digits......................................19 Appendix B - SHA-1 Attacks ........................................25
A.4.2 Brute force attacks......................................20 B.1. SHA-1 Status ..............................................25
A.4.3 Brute force attacks are the best possible attacks........21 B.2. HMAC-SHA-1 Status .........................................26
A.5 Security Analysis of HOTP..................................22 B.3. HOTP Status ...............................................26
Appendix B - SHA-1 Attacks.....................................23 Appendix C - HOTP Algorithm: Reference Implementation .............27
B.1 SHA-1 status...............................................23 Appendix D - HOTP Algorithm: Test Values ..........................32
B.2 HMAC-SHA-1 status..........................................24 Appendix E - Extensions ...........................................33
B.3 HOTP status................................................25 E.1. Number of Digits ..........................................33
Appendix C - HOTP Algorithm: Reference Implementation..........25 E.2. Alphanumeric Values .......................................33
Appendix D - HOTP Algorithm: Test Values.......................29 E.3. Sequence of HOTP values ...................................34
Appendix E - Extensions........................................29 E.4. A Counter-Based Resynchronization Method ..................34
E.1 Number of Digits..........................................30 E.5. Data Field ................................................35
E.2 Alpha-numeric Values......................................30
E.3 Sequence of HOTP values...................................30
E.4 A Counter-based Re-Synchronization Method.................31
E.5 Data Field................................................31
1. Overview 1. Overview
The document introduces first the context around the HOTP The document introduces first the context around an algorithm that
algorithm. In section 4, the algorithm requirements are listed and generates one-time password values based on HMAC [BCK1] and, thus, is
in section 5, the HOTP algorithm is described. Sections 6 and 7 named the HMAC-Based One-Time Password (HOTP) algorithm. In Section
focus on the algorithm security. Section 8 proposes some extensions 4, the algorithm requirements are listed and in Section 5, the HOTP
and improvements, and Section 9 concludes this document. The algorithm is described. Sections 6 and 7 focus on the algorithm
interested reader will find in the Appendix a detailed, full-fledge security. Section 8 proposes some extensions and improvements, and
analysis of the algorithm security: an idealized version of the Section 10 concludes this document. In Appendix A, the interested
algorithm is evaluated, and then the HOTP algorithm security is reader will find a detailed, full-fledged analysis of the algorithm
analyzed. security: an idealized version of the algorithm is evaluated, and
then the HOTP algorithm security is analyzed.
2. Introduction 2. Introduction
Today, deployment of two-factor authentication remains extremely Today, deployment of two-factor authentication remains extremely
limited in scope and scale. Despite increasingly higher levels of limited in scope and scale. Despite increasingly higher levels of
threats and attacks, most Internet applications still rely on weak threats and attacks, most Internet applications still rely on weak
authentication schemes for policing user access. The lack of authentication schemes for policing user access. The lack of
interoperability among hardware and software technology vendors has interoperability among hardware and software technology vendors has
been a limiting factor in the adoption of two-factor authentication been a limiting factor in the adoption of two-factor authentication
technology. In particular, the absence of open specifications has technology. In particular, the absence of open specifications has
led to solutions where hardware and software components are tightly led to solutions where hardware and software components are tightly
coupled through proprietary technology, resulting in high cost coupled through proprietary technology, resulting in high-cost
solutions, poor adoption and limited innovation. solutions, poor adoption, and limited innovation.
In the last two years, the rapid rise of network threats has In the last two years, the rapid rise of network threats has exposed
exposed the inadequacies of static passwords as the primary mean of the inadequacies of static passwords as the primary mean of
authentication on the Internet. At the same time, the current authentication on the Internet. At the same time, the current
approach that requires an end-user to carry an expensive, approach that requires an end user to carry an expensive, single-
single-function device that is only used to authenticate to the function device that is only used to authenticate to the network is
network is clearly not the right answer. For two factor clearly not the right answer. For two-factor authentication to
authentication to propagate on the Internet, it will have to be propagate on the Internet, it will have to be embedded in more
embedded in more flexible devices that can work across a wide range flexible devices that can work across a wide range of applications.
of applications.
The ability to embed this base technology while ensuring broad The ability to embed this base technology while ensuring broad
interoperability require that it be made freely available to the interoperability requires that it be made freely available to the
broad technical community of hardware and software developers. Only broad technical community of hardware and software developers. Only
an open system approach will ensure that basic two-factor an open-system approach will ensure that basic two-factor
authentication primitives can be built into the next-generation of authentication primitives can be built into the next generation of
consumer devices such USB mass storage devices, IP phones, and consumer devices such as USB mass storage devices, IP phones, and
personal digital assistants). personal digital assistants.
One Time Password is certainly one of the simplest and most popular One-Time Password is certainly one of the simplest and most popular
forms of two-factor authentication for securing network access. For forms of two-factor authentication for securing network access. For
example, in large enterprises, Virtual Private Network access often example, in large enterprises, Virtual Private Network access often
requires the use of One Time Password tokens for remote user requires the use of One-Time Password tokens for remote user
authentication. One Time Passwords are often preferred to stronger authentication. One-Time Passwords are often preferred to stronger
forms of authentication such as PKI or biometrics because an forms of authentication such as Public-Key Infrastructure (PKI) or
air-gap device does not require the installation of any client biometrics because an air-gap device does not require the
desktop software on the user machine, therefore allowing them to installation of any client desktop software on the user machine,
roam across multiple machines including home computers, kiosks and therefore allowing them to roam across multiple machines including
This draft proposes a simple One Time Password algorithm that can home computers, kiosks, and personal digital assistants.
be implemented by any hardware manufacturer or software developer
to create interoperable authentication devices and software agents. This document proposes a simple One-Time Password algorithm that can
The algorithm is event-based so that it can be embedded in high be implemented by any hardware manufacturer or software developer to
volume devices such as Java smart cards, USB dongles and GSM SIM create interoperable authentication devices and software agents. The
cards. The presented algorithm is made freely available to the algorithm is event-based so that it can be embedded in high-volume
developer community under the terms and conditions of the IETF devices such as Java smart cards, USB dongles, and GSM SIM cards.
Intellectual Property Rights [RFC3668]. The presented algorithm is made freely available to the developer
community under the terms and conditions of the IETF Intellectual
Property Rights [RFC3979].
The authors of this document are members of the Open AuTHentication The authors of this document are members of the Open AuTHentication
initiative [OATH]. The initiative was created in 2004 to facilitate initiative [OATH]. The initiative was created in 2004 to facilitate
collaboration among strong authentication technology providers. collaboration among strong authentication technology providers.
3. Requirements Terminology 3. Requirements Terminology
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
this document are to be interpreted as described in RFC 2119. document are to be interpreted as described in [RFC2119].
4. Algorithm Requirements 4. Algorithm Requirements
This section presents the main requirements that drove this This section presents the main requirements that drove this algorithm
algorithm design. A lot of emphasis was placed on end-consumer design. A lot of emphasis was placed on end-consumer usability as
usability as well as the ability for the algorithm to be well as the ability for the algorithm to be implemented by low-cost
implemented by low cost hardware that may provide minimal user hardware that may provide minimal user interface capabilities. In
interface capabilities. In particular, the ability to embed the particular, the ability to embed the algorithm into high-volume SIM
algorithm into high volume SIM and Java cards was a fundamental and Java cards was a fundamental prerequisite.
pre-requisite.
R1 - The algorithm MUST be sequence or counter-based: One of the R1 - The algorithm MUST be sequence- or counter-based: one of the
goals is to have the HOTP algorithm embedded in high volume devices goals is to have the HOTP algorithm embedded in high-volume devices
such as Java smart cards, USB dongles and GSM SIM cards. such as Java smart cards, USB dongles, and GSM SIM cards.
R2 - The algorithm SHOULD be economical to implement in hardware by R2 - The algorithm SHOULD be economical to implement in hardware by
minimizing requirements on battery, number of buttons, minimizing requirements on battery, number of buttons, computational
computational horsepower, and size of LCD display. horsepower, and size of LCD display.
R3 - The algorithm MUST work with tokens that do not supports any R3 - The algorithm MUST work with tokens that do not support any
numeric input, but MAY also be used with more sophisticated devices numeric input, but MAY also be used with more sophisticated devices
such as secure PIN-pads. such as secure PIN-pads.
R4 - The value displayed on the token MUST be easily read and R4 - The value displayed on the token MUST be easily read and entered
entered by the user: This requires the HOTP value to be of by the user: This requires the HOTP value to be of reasonable length.
reasonable length. The HOTP value must be at least a 6-digit value.
It is also desirable that the HOTP value be 'numeric only' so that The HOTP value must be at least a 6-digit value. It is also
it can be easily entered on restricted devices such as phones. desirable that the HOTP value be 'numeric only' so that it can be
easily entered on restricted devices such as phones.
R5 - There MUST be user-friendly mechanisms available to R5 - There MUST be user-friendly mechanisms available to
resynchronize the counter. The sections 6.4 and 8.4 detail the resynchronize the counter. Section 7.4 and Appendix E.4 details the
resynchronization mechanism proposed in this draft. resynchronization mechanism proposed in this document
R6 - The algorithm MUST use a strong shared secret. The length of R6 - The algorithm MUST use a strong shared secret. The length of
the shared secret MUST be at least 128 bits. This draft RECOMMENDs the shared secret MUST be at least 128 bits. This document
a shared secret length of 160 bits. RECOMMENDs a shared secret length of 160 bits.
5. HOTP Algorithm 5. HOTP Algorithm
In this section, we introduce the notation and describe the HOTP In this section, we introduce the notation and describe the HOTP
algorithm basic blocks - the base function to compute an HMAC-SHA-1 algorithm basic blocks -- the base function to compute an HMAC-SHA-1
value and the truncation method to extract an HOTP value. value and the truncation method to extract an HOTP value.
5.1 Notation and Symbols 5.1. Notation and Symbols
A string always means a binary string, meaning a sequence of zeros A string always means a binary string, meaning a sequence of zeros
and ones. and ones.
If s is a string then |s| denotes its length. If s is a string, then |s| denotes its length.
If n is a number then |n| denotes its absolute value. If n is a number, then |n| denotes its absolute value.
If s is a string then s[i] denotes its i-th bit. We start numbering If s is a string, then s[i] denotes its i-th bit. We start numbering
the bits at 0, so s = s[0]s[1]..s[n-1] where n = |s| is the length the bits at 0, so s = s[0]s[1]...s[n-1] where n = |s| is the length
of s. of s.
Let StToNum (String to Number) denote the function which as input a Let StToNum (String to Number) denote the function that as input a
string s returns the number whose binary representation is s. string s returns the number whose binary representation is s. (For
(For example StToNum(110) = 6). example, StToNum(110) = 6.)
Here is a list of symbols used in this document. Here is a list of symbols used in this document.
Symbol Represents Symbol Represents
------------------------------------------------------------------- -------------------------------------------------------------------
C 8-byte counter value, the moving factor. This counter C 8-byte counter value, the moving factor. This counter
MUST be synchronized between the HOTP generator (client) MUST be synchronized between the HOTP generator (client)
and the HOTP validator (server); and the HOTP validator (server).
K shared secret between client and server; each HOTP K shared secret between client and server; each HOTP
generator has a different and unique secret K; generator has a different and unique secret K.
T throttling parameter: the server will refuse connections T throttling parameter: the server will refuse connections
from a user after T unsuccessful authentication attempts; from a user after T unsuccessful authentication attempts.
s resynchronization parameter: the server will attempt to s resynchronization parameter: the server will attempt to
verify a received authenticator across s consecutive verify a received authenticator across s consecutive
counter values; counter values.
Digit number of digits in an HOTP value; system parameter. Digit number of digits in an HOTP value; system parameter.
5.2 Description 5.2. Description
The HOTP algorithm is based on an increasing counter value and a The HOTP algorithm is based on an increasing counter value and a
static symmetric key known only to the token and the validation static symmetric key known only to the token and the validation
HMAC-SHA-1 algorithm, as defined in RFC 2104 [BCK2]. service. In order to create the HOTP value, we will use the HMAC-
SHA-1 algorithm, as defined in RFC 2104 [BCK2].
As the output of the HMAC-SHA1 calculation is 160 bits, we must As the output of the HMAC-SHA-1 calculation is 160 bits, we must
truncate this value to something that can be easily entered by a truncate this value to something that can be easily entered by a
user. user.
HOTP(K,C) = Truncate(HMAC-SHA-1(K,C)) HOTP(K,C) = Truncate(HMAC-SHA-1(K,C))
Where: Where:
- Truncate represents the function that converts an HMAC-SHA-1 - Truncate represents the function that converts an HMAC-SHA-1
value into an HOTP value as defined in Section 5.3. value into an HOTP value as defined in Section 5.3.
The Key (K), the Counter (C) and Data values are hashed high-order The Key (K), the Counter (C), and Data values are hashed high-order
byte first. byte first.
The HOTP values generated by the HOTP generator are treated as big The HOTP values generated by the HOTP generator are treated as big
endian. endian.
5.3 Generating an HOTP value 5.3. Generating an HOTP Value
We can describe the operations in 3 distinct steps: We can describe the operations in 3 distinct steps:
Step 1: Generate an HMAC-SHA-1 value Step 1: Generate an HMAC-SHA-1 value Let HS = HMAC-SHA-1(K,C) // HS
Let HS = HMAC-SHA-1(K,C) // HS is a 20 byte string is a 20-byte string
Step 2: Generate a 4-byte string (Dynamic Truncation) Step 2: Generate a 4-byte string (Dynamic Truncation)
Let Sbits = DT(HS) // DT, defined in Section 6.3.1 Let Sbits = DT(HS) // DT, defined below,
// returns a 31 bit string // returns a 31-bit string
Step 3: Compute an HOTP value Step 3: Compute an HOTP value
Let Snum = StToNum(S) // Convert S to a number in Let Snum = StToNum(Sbits) // Convert S to a number in
0...2^{31}-1 0...2^{31}-1
Return D = Snum mod 10^Digit // D is a number in the range Return D = Snum mod 10^Digit // D is a number in the range
0...10^{Digit}-1 0...10^{Digit}-1
The Truncate function performs Step 2 and Step 3, i.e. the dynamic The Truncate function performs Step 2 and Step 3, i.e., the dynamic
truncation and then the reduction modulo 10^Digit. The purpose of truncation and then the reduction modulo 10^Digit. The purpose of
the dynamic offset truncation technique is to extract a 4-byte the dynamic offset truncation technique is to extract a 4-byte
dynamic binary code from a 160-bit (20-byte) HMAC-SHA1 result. dynamic binary code from a 160-bit (20-byte) HMAC-SHA-1 result.
DT(String) // String = String[0]...String[19] DT(String) // String = String[0]...String[19]
Let OffsetBits be the low order four bits of String[19] Let OffsetBits be the low-order 4 bits of String[19]
Offset = StToNum(OffSetBits) // 0 <= OffSet <= 15 Offset = StToNum(OffsetBits) // 0 <= OffSet <= 15
Let P = String[OffSet]...String[OffSet+3] Let P = String[OffSet]...String[OffSet+3]
Return the Last 31 bits of P Return the Last 31 bits of P
The reason for masking the most significant bit of P is to avoid The reason for masking the most significant bit of P is to avoid
confusion about signed vs. unsigned modulo computations. Different confusion about signed vs. unsigned modulo computations. Different
processors perform these operations differently, and masking out processors perform these operations differently, and masking out the
the signed bit removes all ambiguity. signed bit removes all ambiguity.
Implementations MUST extract a 6-digit code at a minimum and Implementations MUST extract a 6-digit code at a minimum and possibly
possibly 7 and 8-digit code. Depending on security requirements, 7 and 8-digit code. Depending on security requirements, Digit = 7 or
Digit = 7 or more SHOULD be considered in order to extract a longer more SHOULD be considered in order to extract a longer HOTP value.
HOTP value.
The following paragraph is an example of using this technique for The following paragraph is an example of using this technique for
Digit = 6, i.e. that a 6-digit HOTP value is calculated from the Digit = 6, i.e., that a 6-digit HOTP value is calculated from the
HMAC value. HMAC value.
5.4 Example of HOTP computation for Digit = 6 5.4. Example of HOTP Computation for Digit = 6
The following code example describes the extraction of a dynamic The following code example describes the extraction of a dynamic
binary code given that hmac_result is a byte array with the binary code given that hmac_result is a byte array with the HMAC-
HMAC-SHA1 result: SHA-1 result:
int offset = hmac_result[19] & 0xf ; int offset = hmac_result[19] & 0xf ;
int bin_code = (hmac_result[offset] & 0x7f) << 24 int bin_code = (hmac_result[offset] & 0x7f) << 24
| (hmac_result[offset+1] & 0xff) << 16 | (hmac_result[offset+1] & 0xff) << 16
| (hmac_result[offset+2] & 0xff) << 8 | (hmac_result[offset+2] & 0xff) << 8
| (hmac_result[offset+3] & 0xff) ; | (hmac_result[offset+3] & 0xff) ;
SHA-1 HMAC Bytes (Example) SHA-1 HMAC Bytes (Example)
------------------------------------------------------------- -------------------------------------------------------------
skipping to change at line 343 skipping to change at page 8, line 4
------------------------------------------------------------- -------------------------------------------------------------
| Byte Number | | Byte Number |
------------------------------------------------------------- -------------------------------------------------------------
|00|01|02|03|04|05|06|07|08|09|10|11|12|13|14|15|16|17|18|19| |00|01|02|03|04|05|06|07|08|09|10|11|12|13|14|15|16|17|18|19|
------------------------------------------------------------- -------------------------------------------------------------
| Byte Value | | Byte Value |
------------------------------------------------------------- -------------------------------------------------------------
|1f|86|98|69|0e|02|ca|16|61|85|50|ef|7f|19|da|8e|94|5b|55|5a| |1f|86|98|69|0e|02|ca|16|61|85|50|ef|7f|19|da|8e|94|5b|55|5a|
-------------------------------***********----------------++| -------------------------------***********----------------++|
* The last byte (byte 19) has the hex value 0x5a. * The last byte (byte 19) has the hex value 0x5a.
* The value of the lower four bits is 0xa (the offset value). * The value of the lower 4 bits is 0xa (the offset value).
* The offset value is byte 10 (0xa). * The offset value is byte 10 (0xa).
* The value of the 4 bytes starting at byte 10 is 0x50ef7f19, * The value of the 4 bytes starting at byte 10 is 0x50ef7f19,
which is the dynamic binary code DBC1 which is the dynamic binary code DBC1.
* The MSB of DBC1 is 0x50 so DBC2 = DBC1 = 0x50ef7f19 * The MSB of DBC1 is 0x50 so DBC2 = DBC1 = 0x50ef7f19 .
* HOTP = DBC2 modulo 10^6 = 872921. * HOTP = DBC2 modulo 10^6 = 872921.
We treat the dynamic binary code as a 31-bit, unsigned, big-endian We treat the dynamic binary code as a 31-bit, unsigned, big-endian
integer; the first byte is masked with a 0x7f. integer; the first byte is masked with a 0x7f.
We then take this number modulo 1,000,000 (10^6) to generate the We then take this number modulo 1,000,000 (10^6) to generate the 6-
6-digit HOTP value 872921 decimal. digit HOTP value 872921 decimal.
6. Security Considerations 6. Security Considerations
Any One-Time Password algorithm is only as secure as the The conclusion of the security analysis detailed in the Appendix is
Therefore, this section discusses the critical security that, for all practical purposes, the outputs of the Dynamic
requirements that our choice of algorithm imposes on the Truncation (DT) on distinct counter inputs are uniformly and
authentication protocol and validation software. independently distributed 31-bit strings.
The security analysis then details the impact of the conversion from
a string to an integer and the final reduction modulo 10^Digit, where
Digit is the number of digits in an HOTP value.
The analysis demonstrates that these final steps introduce a
negligible bias, which does not impact the security of the HOTP
algorithm, in the sense that the best possible attack against the
HOTP function is the brute force attack.
Assuming an adversary is able to observe numerous protocol exchanges
and collect sequences of successful authentication values. This
adversary, trying to build a function F to generate HOTP values based
on his observations, will not have a significant advantage over a
random guess.
The logical conclusion is simply that the best strategy will once
again be to perform a brute force attack to enumerate and try all the
possible values.
Considering the security analysis in the Appendix of this document,
without loss of generality, we can approximate closely the security
of the HOTP algorithm by the following formula:
Sec = sv/10^Digit
Where:
- Sec is the probability of success of the adversary;
- s is the look-ahead synchronization window size;
- v is the number of verification attempts;
- Digit is the number of digits in HOTP values.
Obviously, we can play with s, T (the Throttling parameter that would
limit the number of attempts by an attacker), and Digit until
achieving a certain level of security, still preserving the system
usability.
7. Security Requirements
Any One-Time Password algorithm is only as secure as the application
and the authentication protocols that implement it. Therefore, this
section discusses the critical security requirements that our choice
of algorithm imposes on the authentication protocol and validation
software.
The parameters T and s discussed in this section have a significant The parameters T and s discussed in this section have a significant
impact on the security - further details in Section 7 elaborate on impact on the security -- further details in Section 6 elaborate on
the relations between these parameters and their impact on the the relations between these parameters and their impact on the system
system security. security.
It is also important to remark that the HOTP algorithm is not a It is also important to remark that the HOTP algorithm is not a
substitute for encryption and does not provide for the privacy of substitute for encryption and does not provide for the privacy of
data transmission. Other mechanisms should be used to defeat data transmission. Other mechanisms should be used to defeat attacks
aimed at breaking confidentiality and privacy of transactions.
6.1 Authentication Protocol Requirements 7.1. Authentication Protocol Requirements
We introduce in this section some requirements for a protocol P We introduce in this section some requirements for a protocol P
implementing HOTP as the authentication method between a prover and implementing HOTP as the authentication method between a prover and a
a verifier. verifier.
RP1 - P MUST be two-factor, i.e. something you know (secret code RP1 - P MUST support two-factor authentication, i.e., the
communication and verification of something you know (secret code
such as a Password, Pass phrase, PIN code, etc.) and something you such as a Password, Pass phrase, PIN code, etc.) and something you
have (token). The secret code is known only to the user and usually have (token). The secret code is known only to the user and usually
entered with the one-time password value for authentication purpose entered with the One-Time Password value for authentication purpose
(two-factor authentication). (two-factor authentication).
RP2 - P SHOULD NOT be vulnerable to brute force attacks. This RP2 - P SHOULD NOT be vulnerable to brute force attacks. This
implies that a throttling/lockout scheme is RECOMMENDED on the implies that a throttling/lockout scheme is RECOMMENDED on the
validation server side. validation server side.
RP3 - P SHOULD be implemented with respect to the state of the art RP3 - P SHOULD be implemented over a secure channel in order to
in terms of security, in order to avoid the usual attacks and risks protect users' privacy and avoid replay attacks.
associated with the transmission of sensitive data over a public
network (privacy, replay attacks, etc.)
6.2 Validation of HOTP values 7.2. Validation of HOTP Values
The HOTP client (hardware or software token) increments its counter The HOTP client (hardware or software token) increments its counter
and then calculates the next HOTP value HOTP-client. If the value and then calculates the next HOTP value HOTP client. If the value
received by the authentication server matches the value calculated received by the authentication server matches the value calculated by
by the client, then the HOTP value is validated. In this case, the the client, then the HOTP value is validated. In this case, the
server increments the counter value by one. server increments the counter value by one.
If the value received by the server does not match the value If the value received by the server does not match the value
calculated by the client, the server initiate the resynch protocol calculated by the client, the server initiate the resynch protocol
(look-ahead window) before it requests another pass. (look-ahead window) before it requests another pass.
If the resynch fails, the server asks then for another If the resynch fails, the server asks then for another
authentication pass of the protocol to take place, until the authentication pass of the protocol to take place, until the
maximum number of authorized attempts is reached. maximum number of authorized attempts is reached.
If and when the maximum number of authorized attempts is reached, If and when the maximum number of authorized attempts is reached, the
the server SHOULD lock out the account and initiate a procedure to server SHOULD lock out the account and initiate a procedure to inform
inform the user. the user.
6.3 Bi-directional Authentication
Interestingly enough, the HOTP client could also be used to
authenticate the validation server, claiming that it is a genuine
entity knowing the shared secret.
Since the HOTP client and the server are synchronized and share the
same secret (or a method to recompute it) a simple 3-pass protocol
could be put in place:
1- The end user enter the TokenID and a first OTP value OTP1;
2- The server checks OTP1 and if correct, sends back OTP2;
3- The end user checks OTP2 using his HOTP device and if correct,
uses the web site.
Obviously, as indicated previously, all the OTP communications have
to take place over secure https (SSL) connections.
6.4 Throttling at the server 7.3. Throttling at the Server
Truncating the HMAC-SHA1 value to a shorter value makes a brute Truncating the HMAC-SHA-1 value to a shorter value makes a brute
force attack possible. Therefore, the authentication server needs force attack possible. Therefore, the authentication server needs to
to detect and stop brute force attacks. detect and stop brute force attacks.
We RECOMMEND setting a throttling parameter T, which defines the We RECOMMEND setting a throttling parameter T, which defines the
maximum number of possible attempts for One-Time-Password maximum number of possible attempts for One-Time Password validation.
validation. The validation server manages individual counters per The validation server manages individual counters per HOTP device in
HOTP device in order to take note of any failed attempt. We order to take note of any failed attempt. We RECOMMEND T not to be
RECOMMEND T not to be too large, particularly if the too large, particularly if the resynchronization method used on the
resynchronization method used on the server is window-based, and server is window-based, and the window size is large. T SHOULD be
the window size is large. T SHOULD be set as low as possible, while set as low as possible, while still ensuring that usability is not
still ensuring usability is not significantly impacted. significantly impacted.
Another option would be to implement a delay scheme to avoid a Another option would be to implement a delay scheme to avoid a brute
brute force attack. After each failed attempt A, the authentication force attack. After each failed attempt A, the authentication server
server would wait for an increased T*A number of seconds, e.g. say would wait for an increased T*A number of seconds, e.g., say T = 5,
T = 5, then after 1 attempt, the server waits for 5 seconds, at the then after 1 attempt, the server waits for 5 seconds, at the second
second failed attempt, it waits for 5*2 = 10 seconds, etc. failed attempt, it waits for 5*2 = 10 seconds, etc.
The delay or lockout schemes MUST be across login sessions to The delay or lockout schemes MUST be across login sessions to prevent
prevent attacks based on multiple parallel guessing techniques. attacks based on multiple parallel guessing techniques.
6.5 Resynchronization of the counter 7.4. Resynchronization of the Counter
Although the server's counter value is only incremented after a Although the server's counter value is only incremented after a
successful HOTP authentication, the counter on the token is successful HOTP authentication, the counter on the token is
incremented every time a new HOTP is requested by the user. Because incremented every time a new HOTP is requested by the user. Because
of this, the counter values on the server and on the token might be of this, the counter values on the server and on the token might be
out of synchronization. out of synchronization.
We RECOMMEND setting a look-ahead parameter s on the server, which We RECOMMEND setting a look-ahead parameter s on the server, which
defines the size of the look-ahead window. In a nutshell, the defines the size of the look-ahead window. In a nutshell, the server
server can recalculate the next s HOTP-server values, and check can recalculate the next s HOTP-server values, and check them against
them against the received HOTP-client. the received HOTP client.
Synchronization of counters in this scenario simply requires the Synchronization of counters in this scenario simply requires the
server to calculate the next HOTP values and determine if there is server to calculate the next HOTP values and determine if there is a
a match. Optionally, the system MAY require the user to send a match. Optionally, the system MAY require the user to send a
sequence of (say 2, 3) HOTP values for resynchronization purpose, sequence of (say, 2, 3) HOTP values for resynchronization purpose,
since forging a sequence of consecutive HOTP values is even more since forging a sequence of consecutive HOTP values is even more
difficult than guessing a single HOTP value. difficult than guessing a single HOTP value.
The upper bound set by the parameter s ensures the server does not The upper bound set by the parameter s ensures the server does not go
go on checking HOTP values forever (causing a DoS attack) and also on checking HOTP values forever (causing a denial-of-service attack)
restricts the space of possible solutions for an attacker trying to and also restricts the space of possible solutions for an attacker
manufacture HOTP values. s SHOULD be set as low as possible, while trying to manufacture HOTP values. s SHOULD be set as low as
still ensuring usability is not impacted. possible, while still ensuring that usability is not impacted.
6.6 Management of Shared Secrets 7.5. Management of Shared Secrets
The operations dealing with the shared secrets used to generate and The operations dealing with the shared secrets used to generate and
verify OTP values must be performed securely, in order to mitigate verify OTP values must be performed securely, in order to mitigate
risks of any leakage of sensitive information. We describe in this risks of any leakage of sensitive information. We describe in this
section different modes of operations and techniquest to perform section different modes of operations and techniques to perform these
these different operations with respect of the state of the art in different operations with respect to the state of the art in data
terms of data security. security.
We can consider two different avenues for generating and storing We can consider two different avenues for generating and storing
(securely) shared secrets in the Validation system: (securely) shared secrets in the Validation system:
* Deterministic Generation: secrets are derived from a master * Deterministic Generation: secrets are derived from a master
seed, both at provisioning and verification stages and generated seed, both at provisioning and verification stages and generated
on-the-fly whenever it is required; on-the-fly whenever it is required.
* Random Generation: secrets are generated randomly at * Random Generation: secrets are generated randomly at
provisioning stage, and must be stored immediately and kept secure provisioning stage and must be stored immediately and kept
during their life cycle. secure during their life cycle.
Deterministic Generation Deterministic Generation
------------------------ ------------------------
A possible strategy is to derive the shared secrets from a master A possible strategy is to derive the shared secrets from a master
secret. The master secret will be stored at the server only. A secret. The master secret will be stored at the server only. A
tamper resistant device MUST be used to store the master key and tamper-resistant device MUST be used to store the master key and
derive the shared secrets from the master key and some public derive the shared secrets from the master key and some public
information. The main benefit would be to avoid the exposure of the information. The main benefit would be to avoid the exposure of the
shared secrets at any time and also avoid specific requirements on shared secrets at any time and also avoid specific requirements on
storage, since the shared secrets could be generated on-demand when storage, since the shared secrets could be generated on-demand when
needed at provisioning and validation time. needed at provisioning and validation time.
We distinguish two different cases: We distinguish two different cases:
- A single master key MK is used to derive the shared secrets; - A single master key MK is used to derive the shared secrets;
each HOTP device has a different secret, K_i = SHA-1 (MK,i) each HOTP device has a different secret, K_i = SHA-1 (MK,i)
where i stands for a public piece of information that where i stands for a public piece of information that identifies
token ID, etc.; obviously, this is in the context of an uniquely the HOTP device such as a serial number, a token ID,
application or service - different application or service etc. Obviously, this is in the context of an application or
providers will have different secrets and settings; service -- different application or service providers will have
different secrets and settings.
- Several master keys MK_i are used and each HOTP device stores a - Several master keys MK_i are used and each HOTP device stores a
set of different derived secrets, {K_i,j = SHA-1(MK_i,j)} where set of different derived secrets, {K_i,j = SHA-1(MK_i,j)} where
j stands for a public piece of information identifying the j stands for a public piece of information identifying the
device. The idea would be to store ONLY the active master key device. The idea would be to store ONLY the active master key
at the validation server, in the HSM, and keep in a safe place, at the validation server, in the Hardware Security Module (HSM),
using secret sharing methods such as [Shamir] for instance. In and keep in a safe place, using secret sharing methods such as
this case, if a master secret MK_i is compromised, then it is [Shamir] for instance. In this case, if a master secret MK_i is
possible to switch to another secret without replacing all the compromised, then it is possible to switch to another secret
devices. without replacing all the devices.
The drawback in the deterministic case is that the exposure of the The drawback in the deterministic case is that the exposure of the
master secret would obviously enable an attacker to rebuild any master secret would obviously enable an attacker to rebuild any
shared secret based on correct public information. The revocation shared secret based on correct public information. The revocation of
of all secrets would be required, or switching to a new set of all secrets would be required, or switching to a new set of secrets
secrets in the case of multiple master keys. in the case of multiple master keys.
On the other hand, the device used to store the master key(s) and On the other hand, the device used to store the master key(s) and
generate the shared secrets MUST be tamper resistant. Furthermore, generate the shared secrets MUST be tamper resistant. Furthermore,
the HSM will not be exposed outside the security perimeter of the the HSM will not be exposed outside the security perimeter of the
validation system, therefore reducing the risk of leakage. validation system, therefore reducing the risk of leakage.
Random Generation Random Generation
----------------- -----------------
The shared secrets are randomly generated. We RECOMMEND to follow The shared secrets are randomly generated. We RECOMMEND following
the recommendations in [RFC1750] and to select a good and secure the recommendations in [RFC4086] and selecting a good and secure
random source for generating these secrets. A (true) random random source for generating these secrets. A (true) random
generator requires a naturally occurring source of randomness. generator requires a naturally occurring source of randomness.
Practically, there are two possible avenues to consider for the Practically, there are two possible avenues to consider for the
generation of the shared secrets: generation of the shared secrets:
* Hardware-based generators: they exploit the randomness which * Hardware-based generators: they exploit the randomness that
occurs in physical phenomena. A nice implementation can be based on occurs in physical phenomena. A nice implementation can be based on
oscillators, and built in such ways that active attacks are more oscillators and built in such ways that active attacks are more
difficult to perform. difficult to perform.
* Software-based generators: designing a good software random * Software-based generators: designing a good software random
generator is not an easy task. A simple, but efficient, generator is not an easy task. A simple, but efficient,
implementation should be based on various sources, and apply to the implementation should be based on various sources and apply to the
sampled sequence a one-way function such as SHA-1. sampled sequence a one-way function such as SHA-1.
We RECOMMEND to select proven products, being hardware or software We RECOMMEND selecting proven products, being hardware or software
generators for the computation of shared secrets. generators, for the computation of shared secrets.
We also RECOMMEND storing the shared secrets securely, and more We also RECOMMEND storing the shared secrets securely, and more
specifically encrypting the shared secrets when stored using specifically encrypting the shared secrets when stored using tamper-
tamper-resistant hardware encryption, and exposing them only when resistant hardware encryption and exposing them only when required:
required: e.g. the shared secret is decrypted when needed to verify for example, the shared secret is decrypted when needed to verify an
an HOTP value, and re-encrypted immediately to limit exposure in HOTP value, and re-encrypted immediately to limit exposure in the RAM
shared secrets MUST be in a secure area, to avoid as much as for a short period of time. The data store holding the shared
possible direct attack on the validation system and secrets secrets MUST be in a secure area, to avoid as much as possible direct
database. attack on the validation system and secrets database.
Particularly, access to the shared secrets should be limited to Particularly, access to the shared secrets should be limited to
programs and processes required by the validation system only. We programs and processes required by the validation system only. We
will not elaborate on the different security mechanisms to put in will not elaborate on the different security mechanisms to put in
place, but obviously, the protection of shared secrets is of the place, but obviously, the protection of shared secrets is of the
uttermost importance. uttermost importance.
7. HOTP Algorithm Security: Overview
The conclusion of the security analysis detailed in the Appendix
section is that, for all practical purposes, the outputs of the
dynamic truncation (DT) on distinct counter inputs are uniformly
and independently distributed 31-bit strings.
The security analysis then details the impact of the conversion
from a string to an integer and the final reduction modulo
10^Digit, where Digit is the number of digits in an HOTP value.
The analysis demonstrates that these final steps introduce a
negligible bias, which does not impact the security of the HOTP
algorithm, in the sense that the best possible attack against the
HOTP function is the brute force attack.
Assuming an adversary is able to observe numerous protocol
exchanges and collect sequences of successful authentication
values. This adversary, trying to build a function F to generate
HOTP values based on his observations, will not have a significant
advantage over a random guess.
The logical conclusion is simply that is best strategy will once
again be to perform a brute force attack to enumerate and try all
the possible values.
Considering the security analysis in the Appendix section of this
document, without loss of generality, we can approximate closely
the security of the HOTP algorithm by the following formula:
Sec = sv/10^Digit
Where:
- Sec is the probability of success of the adversary
- s stands for the look-ahead synchronization window size;
- v stands for the number of verification attempts;
- Digit stands for the number of digits in HOTP values.
Obviously, we can play with s, T (the Throttling parameter that
would limit the number of attempts by an attacker) and Digit until
achieving a certain level of security, still preserving the system
usability.
8. Composite Shared Secrets 8. Composite Shared Secrets
It may be desirable to include additional authentication factors in It may be desirable to include additional authentication factors in
the shared secret K. These additional factors can consist of any the shared secret K. These additional factors can consist of any
data known at the token but not easily obtained by others. Examples data known at the token but not easily obtained by others. Examples
of such data include: of such data include:
* PIN or Password obtained as user input at the token * PIN or Password obtained as user input at the token
* Phone number * Phone number
* Any unique identifier programmatically available at the token * Any unique identifier programmatically available at the token
In this scenario the composite shared secret K is constructed In this scenario, the composite shared secret K is constructed during
during the provisioning process from a random seed value combined the provisioning process from a random seed value combined with one
with one or more additional authentication factors. The server or more additional authentication factors. The server could either
could either build on-demand or store composite secrets - in any build on-demand or store composite secrets -- in any case, depending
case, depending on implementation choice, the token only stores the on implementation choice, the token only stores the seed value. When
seed value. When the token performs the HOTP calculation it the token performs the HOTP calculation, it computes K from the seed
computes K from the seed value and the locally derived or input value and the locally derived or input values of the other
values of the other authentication factors. authentication factors.
The use of composite shared secrets can strengthen HOTP based The use of composite shared secrets can strengthen HOTP-based
authentication systems through the inclusion of additional authentication systems through the inclusion of additional
authentication factors at the token. To the extent that the token authentication factors at the token. To the extent that the token is
is a trusted device this approach has the further benefit of not a trusted device, this approach has the further benefit of not
requiring exposure of the authentication factors (such as the user requiring exposure of the authentication factors (such as the user
input PIN) to other devices. input PIN) to other devices.
9. IANA Considerations 9. Bi-Directional Authentication
This document has no actions for IANA. Interestingly enough, the HOTP client could also be used to
authenticate the validation server, claiming that it is a genuine
entity knowing the shared secret.
Since the HOTP client and the server are synchronized and share the
same secret (or a method to recompute it), a simple 3-pass protocol
could be put in place:
1- The end user enter the TokenID and a first OTP value OTP1;
2- The server checks OTP1 and if correct, sends back OTP2;
3- The end user checks OTP2 using his HOTP device and if correct,
uses the web site.
Obviously, as indicated previously, all the OTP communications have
to take place over a secure channel, e.g., SSL/TLS, IPsec
connections.
10. Conclusion 10. Conclusion
This draft describes HOTP, a HMAC-based One-Time Password This document describes HOTP, a HMAC-based One-Time Password
algorithm. It also recommends the preferred implementation and algorithm. It also recommends the preferred implementation and
related modes of operations for deploying the algorithm. related modes of operations for deploying the algorithm.
The draft also exhibits elements of security and demonstrates that The document also exhibits elements of security and demonstrates that
the HOTP algorithm is practical and sound, the best possible attack the HOTP algorithm is practical and sound, the best possible attack
being a brute force attack that can be prevented by careful being a brute force attack that can be prevented by careful
implementation of countermeasures in the validation server. implementation of countermeasures in the validation server.
Eventually, several enhancements have been proposed, in order to Eventually, several enhancements have been proposed, in order to
improve security if needed for specific applications. improve security if needed for specific applications.
11. Acknowledgements 11. Acknowledgements
The authors would like to thank Siddharth Bajaj, Alex Deacon, Loren The authors would like to thank Siddharth Bajaj, Alex Deacon, Loren
Hart and Nico Popp for their help during the conception and Hart, and Nico Popp for their help during the conception and
redaction of this document. redaction of this document.
12. Contributors 12. Contributors
The authors of this draft would like to emphasize the role of three
persons who have made a key contribution to this document: The authors of this document would like to emphasize the role of
three persons who have made a key contribution to this document:
- Laszlo Elteto is system architect with SafeNet, Inc. - Laszlo Elteto is system architect with SafeNet, Inc.
- Ernesto Frutos is director of Engineering with Authenex, Inc. - Ernesto Frutos is director of Engineering with Authenex, Inc.
- Fred McClain is Founder and CTO with Boojum Mobile, Inc. - Fred McClain is Founder and CTO with Boojum Mobile, Inc.
Without their advice and valuable inputs, this draft would not be Without their advice and valuable inputs, this document would not be
the same. the same.
13. References 13. References
12.1 Normative 13.1. Normative References
[BCK1] M. Bellare, R. Canetti and H. Krawczyk, "Keyed Hash [BCK1] M. Bellare, R. Canetti and H. Krawczyk, "Keyed Hash
Functions and Message Authentication", Proceedings of Functions and Message Authentication", Proceedings of
Crypto'96, LNCS Vol. 1109, pp. 1-15. Crypto'96, LNCS Vol. 1109, pp. 1-15.
[BCK2] M. Bellare, R. Canetti and H. Krawczyk, "HMAC: [BCK2] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
Keyed-Hashing for Message Authentication", IETF Network Hashing for Message Authentication", RFC 2104, February
Working Group, RFC 2104, February 1997. 1997.
[RFC1750] D. Eastlake, 3rd., S. Crocker and J. Schiller,
"Randomness Recommendantions for Security", IETF
Network Working Group, RFC 1750, December 2004.
[RFC2119] S. Bradner, "Key words for use in RFCs to Indicate [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997. Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC3668] S. Bradner, "Intellectual Propery Rights in IETF [RFC3979] Bradner, S., "Intellectual Property Rights in IETF
Technology", BCP 79, RFC 3668, February 2004. Technology", BCP 79, RFC 3979, March 2005.
12.2 Informative [RFC4086] Eastlake, D., 3rd, Schiller, J., and S. Crocker,
"Randomness Requirements for Security", BCP 106, RFC 4086,
June 2005.
13.2. Informative References
[OATH] Initiative for Open AuTHentication [OATH] Initiative for Open AuTHentication
http://www.openauthentication.org http://www.openauthentication.org
[PrOo] B. Preneel and P. van Oorschot, "MD-x MAC and building [PrOo] B. Preneel and P. van Oorschot, "MD-x MAC and building
fast MACs from hash functions", Advances in Cryptology fast MACs from hash functions", Advances in Cryptology
CRYPTO '95, Lecture Notes in Computer Science Vol. 963, CRYPTO '95, Lecture Notes in Computer Science Vol. 963, D.
D. Coppersmith ed., Springer-Verlag, 1995. Coppersmith ed., Springer-Verlag, 1995.
[Crack] Crack in SHA-1 code 'stuns' security gurus [Crack] Crack in SHA-1 code 'stuns' security gurus
http://www.eetimes.com/showArticle.jhtml?articleID=60402150 http://www.eetimes.com/showArticle.jhtml?
articleID=60402150
[Sha1] Bruce Schneier. SHA-1 broken. February 15, 2005. [Sha1] Bruce Schneier. SHA-1 broken. February 15, 2005.
http://www.schneier.com/blog/archives/2005/02/sha1_broken.html http://www.schneier.com/blog/archives/2005/02/
sha1_broken.html
[Res] Researchers: Digital encryption standard flawed [Res] Researchers: Digital encryption standard flawed
http://news.com.com/Researchers+Digital+encryption+standard+flawed/ http://news.com.com/
Researchers+Digital+encryption+standard+flawed/
2100-1002-5579881.html?part=dht&tag=ntop&tag=nl.e703 2100-1002-5579881.html?part=dht&tag=ntop&tag=nl.e703
[Shamir] How to Share a Secret, by Adi Shamir. In Communications [Shamir] How to Share a Secret, by Adi Shamir. In Communications
of the ACM, Vol. 22, No. 11, pp. 612-613, November, 1979. of the ACM, Vol. 22, No. 11, pp. 612-613, November, 1979.
14. Authors' Addresses
Primary point of contact (for sending comments and question):
David M'Raihi
VeriSign, Inc.
685 E. Middlefield Road Phone: 1-650-426-3832
Mountain View, CA 94043 USA Email: dmraihi@verisign.com
Other Authors' contact information:
Mihir Bellare
Dept of Computer Science and Engineering, Mail Code 0114
University of California at San Diego
9500 Gilman Drive
La Jolla, CA 92093, USA Email: mihir@cs.ucsd.edu
Frank Hoornaert
VASCO Data Security, Inc.
Koningin Astridlaan 164
1780 Wemmel, Belgium Email: frh@vasco.com
David Naccache
Gemplus Innovation
34 rue Guynemer, 92447,
Issy les Moulineaux, France Email: david.naccache@gemplus.com
and
Information Security Group,
Royal Holloway,
University of London, Egham,
Surrey TW20 0EX, UK Email: david.naccache@rhul.ac.uk
Ohad Ranen
Aladdin Knowledge Systems Ltd.
15 Beit Oved Street
Tel Aviv, Israel 61110 Email: Ohad.Ranen@ealaddin.com
15. Full Copyright Statement
Copyright (C) The Internet Society (2005).
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contained in BCP 78, and except as set forth therein, the authors
retain all their rights.
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REPRESENTS OR IS SPONSORED BY (IF ANY), THE INTERNET SOCIETY AND
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PARTICULAR PURPOSE.
16. Intellectual Property
The IETF takes no position regarding the validity or scope of any
Intellectual Property Rights or other rights that might be claimed
to pertain to the implementation or use of the technology described
in this document or the extent to which any license under such
rights might or might not be available; nor does it represent that
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Copies of IPR disclosures made to the IETF Secretariat and any
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Appendix A - HOTP Algorithm Security: Detailed Analysis Appendix A - HOTP Algorithm Security: Detailed Analysis
The security analysis of the HOTP algorithm is summarized in this The security analysis of the HOTP algorithm is summarized in this
section. We first detail the best attack strategies, and then section. We first detail the best attack strategies, and then
elaborate on the security under various assumptions, the impact of elaborate on the security under various assumptions and the impact of
the truncation and some recommendations regarding the number of the truncation and make some recommendations regarding the number of
digits. digits.
We focus this analysis on the case where Digit = 6, i.e. an HOTP We focus this analysis on the case where Digit = 6, i.e., an HOTP
function that produces 6-digit values, which is the bare minimum function that produces 6-digit values, which is the bare minimum
recommended in this draft. recommended in this document.
A.1 Definitions and Notations A.1. Definitions and Notations
We denote by {0,1}^l the set of all strings of length l. We denote by {0,1}^l the set of all strings of length l.
Let Z_{n} = {0,.., n - 1}. Let Z_{n} = {0,.., n - 1}.
Let IntDiv(a,b) denote the integer division algorithm that takes Let IntDiv(a,b) denote the integer division algorithm that takes
the quotient and remainder, respectively, of the division of a by input integers a, b where a >= b >= 1 and returns integers (q,r)
b. (Thus a = bq + r and 0 <= r < b.)
Let H: {0,1}^k x {0,1}^c --> {0,1}^n be the base function that the quotient and remainder, respectively, of the division of a by b.
takes a k-bit key K and c-bit counter C and returns an n-bit output (Thus, a = bq + r and 0 <= r < b.)
H(K,C). (In the case of HOTP, H is HMAC-SHA-1; we use this formal
definition for generalizing our proof of security)
A.2 The idealized algorithm: HOTP-IDEAL Let H: {0,1}^k x {0,1}^c --> {0,1}^n be the base function that takes
a k-bit key K and c-bit counter C and returns an n-bit output H(K,C).
(In the case of HOTP, H is HMAC-SHA-1; we use this formal definition
for generalizing our proof of security.)
A.2. The Idealized Algorithm: HOTP-IDEAL
We now define an idealized counterpart of the HOTP algorithm. In We now define an idealized counterpart of the HOTP algorithm. In
this algorithm, the role of H is played by a random function that this algorithm, the role of H is played by a random function that
forms the key. forms the key.
To be more precise, let Maps(c,n) denote the set of all functions To be more precise, let Maps(c,n) denote the set of all functions
mapping from {0,1}^c to {0,1}^n. The idealized algorithm has key mapping from {0,1}^c to {0,1}^n. The idealized algorithm has key
space Maps(c,n), so that a "key" for such an algorithm is a space Maps(c,n), so that a "key" for such an algorithm is a function
function h from {0,1}^c to {0,1}^n. We imagine this key (function) h from {0,1}^c to {0,1}^n. We imagine this key (function) to be
to be drawn at random. It is not feasible to implement this drawn at random. It is not feasible to implement this idealized
idealized algorithm, since the key, being a function from is way algorithm, since the key, being a function from {0,1}^c to {0,1}^n,
too large to even store. So why consider it? is way too large to even store. So why consider it?
Our security analysis will show that as long as H satisfies a Our security analysis will show that as long as H satisfies a certain
certain well-accepted assumption, the security of the actual and well-accepted assumption, the security of the actual and idealized
idealized algorithms is for all practical purposes the same. The algorithms is for all practical purposes the same. The task that
task that really faces us, then, is to assess the security of the really faces us, then, is to assess the security of the idealized
idealized algorithm. algorithm.
In analyzing the idealized algorithm, we are concentrating on In analyzing the idealized algorithm, we are concentrating on
assessing the quality of the design of the algorithm itself, assessing the quality of the design of the algorithm itself,
independently of HMAC-SHA-1. This is in fact the important issue. independently of HMAC-SHA-1. This is in fact the important issue.
A.3 Model of Security A.3. Model of Security
The model exhibits the type of threats or attacks that are being The model exhibits the type of threats or attacks that are being
considered and enables to asses the security of HOTP and considered and enables one to assess the security of HOTP and HOTP-
HOTP-IDEAL. We denote ALG as either HOTP or HOTP-IDEAL for the IDEAL. We denote ALG as either HOTP or HOTP-IDEAL for the purpose of
purpose of this security analysis. this security analysis.
The scenario we are considering is that a user and server share a The scenario we are considering is that a user and server share a key
key K for ALG. Both maintain a counter C, initially zero, and the K for ALG. Both maintain a counter C, initially zero, and the user
user authenticates itself by sending ALG(K,C) to the server. The authenticates itself by sending ALG(K,C) to the server. The latter
latter accepts if this value is correct. accepts if this value is correct.
In order to protect against accidental increment of the user In order to protect against accidental increment of the user counter,
counter, the server, upon receiving a value z, will accept as long the server, upon receiving a value z, will accept as long as z equals
as z equals ALG(K,i) for some i in the range C,...,C + s-1, where s ALG(K,i) for some i in the range C,...,C + s-1, where s is the
is the resynchronization parameter and C is the server counter. If resynchronization parameter and C is the server counter. If it
it accepts with some value of i, it then increments its counter to accepts with some value of i, it then increments its counter to i+1.
i+ 1. If it does not accept, it does not change its counter value. If it does not accept, it does not change its counter value.
The model we specify captures what an adversary can do and what it The model we specify captures what an adversary can do and what it
to be able to eavesdrop, meaning see the authenticator transmitted needs to achieve in order to "win". First, the adversary is assumed
by the user. Second, the adversary wins if it can get the server to to be able to eavesdrop, meaning, to see the authenticator
accept an authenticator relative to a counter value for which the transmitted by the user. Second, the adversary wins if it can get
user has never transmitted an authenticator. the server to accept an authenticator relative to a counter value for
which the user has never transmitted an authenticator.
The formal adversary, which we denote by B, starts out knowing The formal adversary, which we denote by B, starts out knowing which
which algorithm ALG is being used, knowing the system design and algorithm ALG is being used, knowing the system design, and knowing
knowing all system parameters. The one and only thing it is not all system parameters. The one and only thing it is not given a
given a priori is the key K shared between the user and the server. priori is the key K shared between the user and the server.
The model gives B full control of the scheduling of events. It has The model gives B full control of the scheduling of events. It has
access to an authenticator oracle representing the user. By calling access to an authenticator oracle representing the user. By calling
this oracle, the adversary can ask the user to authenticate itself this oracle, the adversary can ask the user to authenticate itself
and get back the authenticator in return. It can call this oracle and get back the authenticator in return. It can call this oracle as
as often as it wants and when it wants, using the authenticators it often as it wants and when it wants, using the authenticators it
accumulates to perhaps "learn" how to make authenticators itself. accumulates to perhaps "learn" how to make authenticators itself. At
At any time, it may also call a verification oracle, supplying the any time, it may also call a verification oracle, supplying the
latter with a candidate authenticator of its choice. It wins if the latter with a candidate authenticator of its choice. It wins if the
server accepts this accumulator. server accepts this accumulator.
Consider the following game involving an adversary B that is Consider the following game involving an adversary B that is
attempting to compromise the security of an authentication attempting to compromise the security of an authentication algorithm
algorithm ALG: K x {0,1}^c --> R. ALG: K x {0,1}^c --> R.
Initializations - A key K is selected at random from K, a counter C Initializations - A key K is selected at random from K, a counter C
is initialized to 0, and the Boolean value win is set to false. is initialized to 0, and the Boolean value win is set to false.
Game execution - Adversary B is provided with the two following Game execution - Adversary B is provided with the two following
oracles: oracles:
Oracle AuthO() Oracle AuthO()
-------------- --------------
A = ALG(K,C) A = ALG(K,C)
skipping to change at line 925 skipping to change at page 19, line 28
-------------- --------------
i = C i = C
While (i <= C + s - 1 and Win == FALSE) do While (i <= C + s - 1 and Win == FALSE) do
If A == ALG(K,i) then Win = TRUE; C = i + 1 If A == ALG(K,i) then Win = TRUE; C = i + 1
Else i = i + 1 Else i = i + 1
Return Win to B Return Win to B
AuthO() is the authenticator oracle and VerO(A) is the verification AuthO() is the authenticator oracle and VerO(A) is the verification
oracle. oracle.
Upon execution, B queries the two oracles at will. Let Adv(B) be Upon execution, B queries the two oracles at will. Let Adv(B) be the
the probability that win gets set to true in the above game. This probability that win gets set to true in the above game. This is the
is the probability that the adversary successfully impersonates the probability that the adversary successfully impersonates the user.
user.
Our goal is to assess how large this value can be as a function of Our goal is to assess how large this value can be as a function of
the number v of verification queries made by B, the number a of the number v of verification queries made by B, the number a of
authenticator oracle queries made by B, and the running time t of authenticator oracle queries made by B, and the running time t of B.
B. This will tell us how to set the throttle, which effectively This will tell us how to set the throttle, which effectively upper
upper bounds v. bounds v.
A.4 Security of the ideal authentication algorithm A.4. Security of the Ideal Authentication Algorithm
This section summarizes the security analysis of HOTP-IDEAL, This section summarizes the security analysis of HOTP-IDEAL, starting
starting with the impact of the conversion modulo 10^Digit and with the impact of the conversion modulo 10^Digit and then focusing
then, focusing on the different possible attacks. on the different possible attacks.
A.4.1 From bits to digits A.4.1. From Bits to Digits
The dynamic offset truncation of a random n-bit string yields a The dynamic offset truncation of a random n-bit string yields a
random 31-bit string. What happens to the distribution when it is random 31-bit string. What happens to the distribution when it is
taken modulo m = 10^Digit, as done in HOTP? taken modulo m = 10^Digit, as done in HOTP?
The following lemma estimates the biases in the outputs in this case.
The following lemma estimates the biases in the outputs in this
case.
Lemma 1 Lemma 1
------- -------
Let N >= m >= 1 be integers, and let (q,r) = IntDiv(N,m). For z in Let N >= m >= 1 be integers, and let (q,r) = IntDiv(N,m). For z in
Z_{m} let: Z_{m} let:
P_{N,m}(z) = Pr [x mod m = z : x randomly pick in Z_{n}] P_{N,m}(z) = Pr [x mod m = z : x randomly pick in Z_{n}]
Then for any z in Z_{m} Then for any z in Z_{m}
P_{N,m}(z) = (q + 1) / N if 0 <= z < r P_{N,m}(z) = (q + 1) / N if 0 <= z < r
q / N if r <= z < m q / N if r <= z < m
Proof of Lemma 1 Proof of Lemma 1
---------------- ----------------
Let the random variable X be uniformly distributed over Z_{N}. Let the random variable X be uniformly distributed over Z_{N}. Then:
Then:
P_{N,m}(z) = Pr [X mod m = z] P_{N,m}(z) = Pr [X mod m = z]
= Pr [X < mq] * Pr [X mod m = z| X < mq] = Pr [X < mq] * Pr [X mod m = z| X < mq]
+ Pr [mq <= X < N] * Pr [X mod m = z| mq <= X < N] + Pr [mq <= X < N] * Pr [X mod m = z| mq <= X < N]
= mq/N * 1/m + = mq/N * 1/m +
(N - mq)/N * 1 / (N - mq) if 0 <= z < N - mq (N - mq)/N * 1 / (N - mq) if 0 <= z < N - mq
0 if N - mq <= z <= m 0 if N - mq <= z <= m
= q/N + = q/N +
r/N * 1 / r if 0 <= z < N - mq r/N * 1 / r if 0 <= z < N - mq
0 if r <= z <= m 0 if r <= z <= m
Let N = 2^31, d = 6 and m = 10^d. If x is chosen at random from
Z_{N} (meaning, is a random 31-bit string), then reducing it to a Simplifying yields the claimed equation.
6-digit number by taking x mod m does not yield a random 6-digit
Let N = 2^31, d = 6, and m = 10^d. If x is chosen at random from
Z_{N} (meaning, is a random 31-bit string), then reducing it to a 6-
digit number by taking x mod m does not yield a random 6-digit
number. number.
Rather, x mod m is distributed as shown in the following table: Rather, x mod m is distributed as shown in the following table:
Values Probability that each appears as output Values Probability that each appears as output
---------------------------------------------------------------- ----------------------------------------------------------------
0,1,...,483647 2148/2^31 roughly equals to 1.00024045/10^6 0,1,...,483647 2148/2^31 roughly equals to 1.00024045/10^6
483648,...,999999 2147/2^31 roughly equals to 0.99977478/10^6 483648,...,999999 2147/2^31 roughly equals to 0.99977478/10^6
If X is uniformly distributed over Z_{2^31} (meaning is a random If X is uniformly distributed over Z_{2^31} (meaning, is a random
31-bit string) then the above shows the probabilities for different 31-bit string), then the above shows the probabilities for different
outputs of X mod 10^6. The first set of values appear with outputs of X mod 10^6. The first set of values appears with
probability slightly greater than 10^-6, the rest with probability probability slightly greater than 10^-6, the rest with probability
slightly less, meaning the distribution is slightly non-uniform. slightly less, meaning that the distribution is slightly non-uniform.
However, as the Figure indicates, the bias is small and as we will However, as the table above indicates, the bias is small, and as we
see later, negligible: the probabilities are very close to 10^-6. will see later, negligible: the probabilities are very close to
10^-6.
A.4.2 Brute force attacks A.4.2. Brute Force Attacks
If the authenticator consisted of d random digits, then a brute If the authenticator consisted of d random digits, then a brute force
force attack using v verification attempts would succeed with attack using v verification attempts would succeed with probability
probability sv/10^Digit. sv/10^Digit.
However, an adversary can exploit the bias in the outputs of HOTP- However, an adversary can exploit the bias in the outputs of
IDEAL, predicted by Lemma 1, to mount a slightly better attack. HOTP-IDEAL, predicted by Lemma 1, to mount a slightly better attack.
Namely, it makes authentication attempts with authenticators which Namely, it makes authentication attempts with authenticators that are
are the most likely values, meaning the ones in the range 0,...,r - the most likely values, meaning the ones in the range 0,...,r - 1,
1, where (q,r) = IntDiv(2^31,10^Digit). where (q,r) = IntDiv(2^31,10^Digit).
The following specifies an adversary in our model of security that The following specifies an adversary in our model of security that
mounts the attack. It estimates the success probability as a mounts the attack. It estimates the success probability as a
function of the number of verification queries. function of the number of verification queries.
For simplicity, we assume the number of verification queries is at For simplicity, we assume that the number of verification queries is
most r. With N = 2^31 and m = 10^6 we have r = 483,648, and the at most r. With N = 2^31 and m = 10^6, we have r = 483,648, and the
throttle value is certainly less than this, so this assumption is throttle value is certainly less than this, so this assumption is not
not much of a restriction. much of a restriction.
Proposition 1 Proposition 1
------------- -------------
Suppose m = 10^Digit < 2^31, and let (q,r) = IntDiv(2^31,m). Assume Suppose m = 10^Digit < 2^31, and let (q,r) = IntDiv(2^31,m). Assume
s <= m. The brute-force attack adversary B-bf attacks HOTP using v s <= m. The brute-force-attack adversary B-bf attacks HOTP using v
<= r verification oracle queries. This adversary makes no <= r verification oracle queries. This adversary makes no
authenticator oracle queries, and succeeds with probability authenticator oracle queries, and succeeds with probability
Adv(B-bf) = 1 - (1 - v(q+1)/2^31)^s Adv(B-bf) = 1 - (1 - v(q+1)/2^31)^s
which is roughly equals to
which is roughly equal to
sv * (q+1)/2^31 sv * (q+1)/2^31
With m = 10^6 we get q = 2,147. In that case, the brute force With m = 10^6 we get q = 2,147. In that case, the brute force attack
attack using v verification attempts succeeds with probability using v verification attempts succeeds with probability
Adv(B-bf) roughly = sv * 2148/2^31 = sv * 1.00024045/10^6 Adv(B-bf) roughly = sv * 2148/2^31 = sv * 1.00024045/10^6
As this equation shows, the resynchronization parameter s has a As this equation shows, the resynchronization parameter s has a
significant impact in that the adversary's success probability is significant impact in that the adversary's success probability is
proportional to s. This means that s cannot be made too large proportional to s. This means that s cannot be made too large
without compromising security. without compromising security.
A.4.3 Brute force attacks are the best possible attacks A.4.3. Brute force attacks are the best possible attacks.
A central question is whether there are attacks any better than the A central question is whether there are attacks any better than the
brute force one. In particular, the brute force attack did not brute force one. In particular, the brute force attack did not
attempt to collect authenticators sent by the user and try to attempt to collect authenticators sent by the user and try to
cryptanalyze them in an attempt to learn how to better construct cryptanalyze them in an attempt to learn how to better construct
authenticators. Would doing this help? Is there some way to "learn" authenticators. Would doing this help? Is there some way to "learn"
how to build authenticators that result in a higher success rate how to build authenticators that result in a higher success rate than
than given by the brute-force attack? given by the brute-force attack?
The following says the answer to these questions is no. No matter The following says the answer to these questions is no. No matter
what strategy the adversary uses, and even if it sees, and tries to what strategy the adversary uses, and even if it sees, and tries to
exploit, the authenticators from authentication attempts of the exploit, the authenticators from authentication attempts of the user,
user, its success probability will not be above that of the brute its success probability will not be above that of the brute force
force attack - this is true as long as the number of attack -- this is true as long as the number of authentications it
authentications it observes is not incredibly large. This is observes is not incredibly large. This is valuable information
valuable information regarding the security of the scheme. regarding the security of the scheme.
Proposition 2 Proposition 2 ------------- Suppose m = 10^Digit < 2^31, and let
------------- (q,r) = IntDiv(2^31,m). Let B be any adversary attacking HOTP-IDEAL
Suppose m = 10^Digit < 2^31, and let (q,r) = IntDiv(2^31,m). Let B using v verification oracle queries and a <= 2^c - s authenticator
be any adversary attacking HOTP-IDEAL using v verification oracle oracle queries. Then
queries and a <= 2^c - s authenticator oracle queries. Then
Adv(B) < = sv * (q+1)/ 2^31 Adv(B) < = sv * (q+1)/ 2^31
Note: This result is conditional on the adversary not seeing more Note: This result is conditional on the adversary not seeing more
than 2^c - s authentications performed by the user, which is hardly than 2^c - s authentications performed by the user, which is hardly
restrictive as long as c is large enough. restrictive as long as c is large enough.
With m = 10^6 we get q = 2,147. In that case, Proposition 2 says With m = 10^6, we get q = 2,147. In that case, Proposition 2 says
that any adversary B attacking HOTP-IDEAL and making v verification that any adversary B attacking HOTP-IDEAL and making v verification
attempts succeeds with probability at most attempts succeeds with probability at most
Equation 1 Equation 1
---------- ----------
sv * 2148/2^31 roughly = sv * 1.00024045/10^6 sv * 2148/2^31 roughly = sv * 1.00024045/10^6
Meaning, B's success rate is not more than that achieved by the
brute force attack.
A.5 Security Analysis of HOTP Meaning, B's success rate is not more than that achieved by the brute
force attack.
We have analyzed in the previous sections, the security of the A.5. Security Analysis of HOTP
We have analyzed, in the previous sections, the security of the
idealized counterparts HOTP-IDEAL of the actual authentication idealized counterparts HOTP-IDEAL of the actual authentication
algorithm HOTP. We now show that, under appropriate and algorithm HOTP. We now show that, under appropriate and well-
well-believed assumption on H, the security of the actual believed assumption on H, the security of the actual algorithms is
algorithms is essentially the same as that of its idealized essentially the same as that of its idealized counterpart.
counterpart.
The assumption in question is that H is a secure pseudorandom The assumption in question is that H is a secure pseudorandom
function, or PRF, meaning that its input-output values are function, or PRF, meaning that its input-output values are
indistinguishable from those of a random function in practice. indistinguishable from those of a random function in practice.
Consider an adversary A that is given an oracle for a function f: Consider an adversary A that is given an oracle for a function f:
{0,1}^c --> {0, 1}^n and eventually outputs a bit. We denote Adv(A) {0,1}^c --> {0, 1}^n and eventually outputs a bit. We denote Adv(A)
as the prf-advantage of A, which represents how well the adversary as the prf-advantage of A, which represents how well the adversary
does at distinguishing the case where its oracle is H(K,.) from the does at distinguishing the case where its oracle is H(K,.) from the
case where its oracle is a random function of {0,1}^c to {0,1}^n. case where its oracle is a random function of {0,1}^c to {0,1}^n.
One possible attack is based on exhaustive search for the key K. If One possible attack is based on exhaustive search for the key K. If
A runs for t steps and T denotes the time to perform one A runs for t steps and T denotes the time to perform one computation
computation of H, its prf-advantage from this attack turns out to of H, its prf-advantage from this attack turns out to be (t/T)2^-k.
be (t/T)2^-k . Another possible attack is a birthday one [PrOo], Another possible attack is a birthday one [PrOo], whereby A can
whereby A can attain advantage p^2/2^n in p oracle queries and attain advantage p^2/2^n in p oracle queries and running time about
running time about pT. pT.
Our assumption is that these are the best possible attacks. This Our assumption is that these are the best possible attacks. This
translates into the following. translates into the following.
Assumption 1 Assumption 1
------------ ------------
Let T denotes the time to perform one computation of H. Then if A Let T denotes the time to perform one computation of H. Then if A is
is any adversary with running time at most t and making at most p any adversary with running time at most t and making at most p oracle
oracle queries, queries,
Adv(A) <= (t/T)/2^k + p^2/2^n Adv(A) <= (t/T)/2^k + p^2/2^n
In practice this assumption means that H is very secure as PRF. For In practice, this assumption means that H is very secure as PRF. For
example, given that k = n = 160, an attacker with running time 2^60 example, given that k = n = 160, an attacker with running time 2^60
and making 2^40 oracle queries has advantage at most (about) 2^-80. and making 2^40 oracle queries has advantage at most (about) 2^-80.
Theorem 1 Theorem 1
--------- ---------
Suppose m = 10^Digit < 2^31, and let (q,r) = IntDiv(2^31,m). Let B Suppose m = 10^Digit < 2^31, and let (q,r) = IntDiv(2^31,m). Let B
be any adversary attacking HOTP using v verification oracle be any adversary attacking HOTP using v verification oracle queries,
queries, a <= 2^c - s authenticator oracle queries, and running a <= 2^c - s authenticator oracle queries, and running time t. Let T
time t. Let T denote the time to perform one computation of H. If denote the time to perform one computation of H. If Assumption 1 is
Assumption 1 is true then true, then
Adv(B) <= sv * (q + 1)/2^31 + (t/T)/2^k + ((sv + a)^2)/2^n Adv(B) <= sv * (q + 1)/2^31 + (t/T)/2^k + ((sv + a)^2)/2^n
In practice, the (t/T)2^-k + ((sv + a)^2)2^-n term is much smaller In practice, the (t/T)2^-k + ((sv + a)^2)2^-n term is much smaller
than the sv(q + 1)/2^n term, so that the above says that for all than the sv(q + 1)/2^n term, so that the above says that for all
practical purposes the success rate of an adversary attacking HOTP practical purposes the success rate of an adversary attacking HOTP is
is sv(q + 1)/2^n, just as for HOTP-IDEAL, meaning the HOTP sv(q + 1)/2^n, just as for HOTP-IDEAL, meaning the HOTP algorithm is
algorithm is in practice essentially as good as its idealized in practice essentially as good as its idealized counterpart.
counterpart.
In the case m = 10^6 of a 6-digit output this means that an In the case m = 10^6 of a 6-digit output, this means that an
adversary making v authentication attempts will have a success rate adversary making v authentication attempts will have a success rate
that is at most that of Equation 1. that is at most that of Equation 1.
For example, consider an adversary with running time at most 2^60 For example, consider an adversary with running time at most 2^60
that sees at most 2^40 authentication attempts of the user. Both that sees at most 2^40 authentication attempts of the user. Both
these choices are very generous to the adversary, who will these choices are very generous to the adversary, who will typically
typically not have these resources, but we are saying that even not have these resources, but we are saying that even such a powerful
such a powerful adversary will not have more success than indicated adversary will not have more success than indicated by Equation 1.
by Equation 1.
We can safely assume sv <= 2^40 due to the throttling and bounds on We can safely assume sv <= 2^40 due to the throttling and bounds on
s. So: s. So:
(t/T)/2^k + ((sv + a)^2)/2^n <= 2^60/2^160 + (2^41)^2/2^160 (t/T)/2^k + ((sv + a)^2)/2^n <= 2^60/2^160 + (2^41)^2/2^160
roughly <= 2^-78 roughly <= 2^-78
which is much smaller than the success probability of Equation 1 which is much smaller than the success probability of Equation 1 and
and negligible compared to it. negligible compared to it.
Appendix B - SHA-1 Attacks Appendix B - SHA-1 Attacks
This sections addresses the impact of the recent attacks on SHA-1 This sections addresses the impact of the recent attacks on SHA-1 on
on the security of the HMAC-SHA-1 based HOTP. We begin with some the security of the HMAC-SHA-1-based HOTP. We begin with some
discussion of the situation of SHA-1 and then discuss the relevance discussion of the situation of SHA-1 and then discuss the relevance
to HMAC-SHA-1 and HOTP. Cited references are at the bottom of the to HMAC-SHA-1 and HOTP. Cited references are in Section 13.
document.
B.1 SHA-1 status B.1. SHA-1 Status
A collision for a hash function h means a pair x,y of different A collision for a hash function h means a pair x,y of different
inputs such that h(x)=h(y). Since SHA-1 outputs 160 bits, a inputs such that h(x)=h(y). Since SHA-1 outputs 160 bits, a birthday
birthday attack finds a collision in 2^{80} trials. (A trial means attack finds a collision in 2^{80} trials. (A trial means one
one computation of the function.) This was thought to be the best computation of the function.) This was thought to be the best
possible until Wang, Yin and Yu announced on February 15, 2005 that possible until Wang, Yin, and Yu announced on February 15, 2005, that
they had an attack finding collisions in 2^{69} trials. they had an attack finding collisions in 2^{69} trials.
Is SHA-1 broken? For most practical purposes we would say probably Is SHA-1 broken? For most practical purposes, we would say probably
not, since the resources needed to mount the attack are huge. Here not, since the resources needed to mount the attack are huge. Here
is one way to get a sense of it: we can estimate it is about the is one way to get a sense of it: we can estimate it is about the same
same as the time we would need to factor a 760-bit RSA modulus, and as the time we would need to factor a 760-bit RSA modulus, and this
this is currently considered out of reach. is currently considered out of reach.
Burr of NIST is quoted [Crack] as saying ``Large national Burr of NIST is quoted in [Crack] as saying "Large national
intelligence agencies could do this in a reasonable amount of time intelligence agencies could do this in a reasonable amount of time
with a few million dollars in computer time.'' However, the with a few million dollars in computer time". However, the
computation may be out of reach of all but such well-funded computation may be out of reach of all but such well-funded agencies.
agencies.
One should also ask what impact finding SHA-1 collisions actually One should also ask what impact finding SHA-1 collisions actually has
has on security of real applications such as signatures. To exploit on security of real applications such as signatures. To exploit a
a collision x,y to forge signatures, you need to somehow obtain a collision x,y to forge signatures, you need to somehow obtain a
signature of x and then you can forge a signature of y. How signature of x and then you can forge a signature of y. How damaging
damaging this is depends on the content of y: the y created by the this is depends on the content of y: the y created by the attack may
attack may not be meaningful in the application context. Also, one not be meaningful in the application context. Also, one needs a
needs a chosen-message attack to get the signature of x. This seems chosen-message attack to get the signature of x. This seems possible
possible in some contexts, but not others. Overall, it is not clear in some contexts, but not others. Overall, it is not clear that the
the impact on the security of signatures is significant. impact on the security of signatures is significant.
Indeed, one can read that SHA-1 is ``broken,'' [Sha1], that Indeed, one can read in the press that SHA-1 is "broken" [Sha1] and
encryption and SSL are ``broken'' [Res], in the press. The media that encryption and SSL are "broken" [Res]. The media have a
have a tendency to magnify events: it would hardly be interesting tendency to magnify events: it would hardly be interesting to
to announce in the news that a team of cryptanalysts did very announce in the news that a team of cryptanalysts did very
interesting theoretical work in attacking SHA-1. interesting theoretical work in attacking SHA-1.
Cryptographers are excited too. But mainly because this is an Cryptographers are excited too. But mainly because this is an
important theoretical breakthrough. Attacks can only get beter with important theoretical breakthrough. Attacks can only get better with
time: it is therefore important to monitor any progress in hash time: it is therefore important to monitor any progress in hash
functions cryptanalysis and be prepared for any really practical functions cryptanalysis and be prepared for any really practical
break with a sound migration plan for the future. break with a sound migration plan for the future.
B.2 HMAC-SHA-1 status B.2. HMAC-SHA-1 Status
The new attacks on SHA-1 have no impact on the security of HMAC- The new attacks on SHA-1 have no impact on the security of
SHA-1. The best attack on the latter remains one needing a sender HMAC-SHA-1. The best attack on the latter remains one needing a
to authenticate 2^{80} messages before an adversary can create a sender to authenticate 2^{80} messages before an adversary can create
forgery. Why? a forgery. Why?
HMAC is not a hash function. It is a message authentication code HMAC is not a hash function. It is a message authentication code
(MAC) that uses a hash function internally. A MAC depends on a (MAC) that uses a hash function internally. A MAC depends on a
secret key, while hash functions don't. What one needs to worry secret key, while hash functions don't. What one needs to worry
about with a MAC is forgery, not collisions. HMAC was designed so about with a MAC is forgery, not collisions. HMAC was designed so
that collisions in the hash function (here SHA-1) do not yield that collisions in the hash function (here SHA-1) do not yield
forgeries for HMAC. forgeries for HMAC.
Recall that HMAC-SHA-1(K,x) = SHA-1(K_o,SHA-1(K_i,x)) where the Recall that HMAC-SHA-1(K,x) = SHA-1(K_o,SHA-1(K_i,x)) where the keys
keys K_o,K_i are derived from K. Suppose the attacker finds a pair K_o,K_i are derived from K. Suppose the attacker finds a pair x,y
x,y such that SHA-1(K_i,x)=SHA-1(K_i,y). (Call this a hidden-key such that SHA-1(K_i,x) = SHA-1(K_i,y). (Call this a hidden-key
collision.) Then if it can obtain the MAC of x (itself a tall collision.) Then if it can obtain the MAC of x (itself a tall
order), it can forge the MAC of y. (These values are the same.) But order), it can forge the MAC of y. (These values are the same.) But
finding hidden-key collisions is harder than finding collisions, finding hidden-key collisions is harder than finding collisions,
because the attacker does not know the hidden key K_i. All it may because the attacker does not know the hidden key K_i. All it may
have is some outputs of HMAC-SHA-1 with key K. To date there are no have is some outputs of HMAC-SHA-1 with key K. To date, there are no
claims or evidence that the recent attacks on SHA-1 extend to find claims or evidence that the recent attacks on SHA-1 extend to find
hidden-key collisions. hidden-key collisions.
Historically, the HMAC design has already proven itself in this Historically, the HMAC design has already proven itself in this
regard. MD5 is considered broken in that collisions in this hash regard. MD5 is considered broken in that collisions in this hash
function can be found relatively easily. But there is still no function can be found relatively easily. But there is still no
attack on HMAC-MD5 better than the trivial 2^{64} time birthday attack on HMAC-MD5 better than the trivial 2^{64} time birthday one.
one. (MD5 outputs 128 bits, not 160.) We are seeing this strength (MD5 outputs 128 bits, not 160.) We are seeing this strength of HMAC
of HMAC coming into play again in the SHA-1 context. coming into play again in the SHA-1 context.
B.3 HOTP status B.3. HOTP Status
Since no new weakness has surfaced in HMAC-SHA-1, there is no Since no new weakness has surfaced in HMAC-SHA-1, there is no impact
impact on HOTP. The best attacks on HOTP remain those described in on HOTP. The best attacks on HOTP remain those described in the
the document, namely to try to guess output values. document, namely, to try to guess output values.
The security proof of HOTP requires that HMAC-SHA-1 behave like a The security proof of HOTP requires that HMAC-SHA-1 behave like a
pseudorandom function. The quality of HMAC-SHA-1 as a pseudorandom pseudorandom function. The quality of HMAC-SHA-1 as a pseudorandom
function is not impacted by the new attacks on SHA-1, and so function is not impacted by the new attacks on SHA-1, and so neither
neither is this proven guarantee. is this proven guarantee.
Appendix C - HOTP Algorithm: Reference Implementation Appendix C - HOTP Algorithm: Reference Implementation
/* /*
* OneTimePasswordAlgorithm.java * OneTimePasswordAlgorithm.java
* OATH Initiative, * OATH Initiative,
* HOTP one-time password algorithm * HOTP one-time password algorithm
* *
*/ */
skipping to change at line 1282 skipping to change at page 27, line 31
* that such works are identified as * that such works are identified as
* "derived from OATH HOTP algorithm" * "derived from OATH HOTP algorithm"
* in all material mentioning or referencing the derived work. * in all material mentioning or referencing the derived work.
* *
* OATH (Open AuTHentication) and its members make no * OATH (Open AuTHentication) and its members make no
* representations concerning either the merchantability of this * representations concerning either the merchantability of this
* software or the suitability of this software for any particular * software or the suitability of this software for any particular
* purpose. * purpose.
* *
* It is provided "as is" without express or implied warranty * It is provided "as is" without express or implied warranty
* of any kind and OATH AND ITS MEMBERS EXPRESSELY DISCLAIMS * of any kind and OATH AND ITS MEMBERS EXPRESSaLY DISCLAIMS
* ANY WARRANTY OR LIABILITY OF ANY KIND relating to this software. * ANY WARRANTY OR LIABILITY OF ANY KIND relating to this software.
* *
* These notices must be retained in any copies of any part of this * These notices must be retained in any copies of any part of this
* documentation and/or software. * documentation and/or software.
*/ */
package org.openauthentication.otp;
import java.io.IOException; import java.io.IOException;
import java.io.File; import java.io.File;
import java.io.DataInputStream; import java.io.DataInputStream;
import java.io.FileInputStream ; import java.io.FileInputStream ;
import java.lang.reflect.UndeclaredThrowableException; import java.lang.reflect.UndeclaredThrowableException;
import java.security.GeneralSecurityException; import java.security.GeneralSecurityException;
import java.security.NoSuchAlgorithmException; import java.security.NoSuchAlgorithmException;
import java.security.InvalidKeyException; import java.security.InvalidKeyException;
skipping to change at line 1300 skipping to change at page 28, line 4
import java.io.DataInputStream; import java.io.DataInputStream;
import java.io.FileInputStream ; import java.io.FileInputStream ;
import java.lang.reflect.UndeclaredThrowableException; import java.lang.reflect.UndeclaredThrowableException;
import java.security.GeneralSecurityException; import java.security.GeneralSecurityException;
import java.security.NoSuchAlgorithmException; import java.security.NoSuchAlgorithmException;
import java.security.InvalidKeyException; import java.security.InvalidKeyException;
import javax.crypto.Mac; import javax.crypto.Mac;
import javax.crypto.spec.SecretKeySpec; import javax.crypto.spec.SecretKeySpec;
/** /**
* This class contains static methods that are used to calculate the * This class contains static methods that are used to calculate the
* One-Time Password (OTP) using * One-Time Password (OTP) using
* JCE to provide the HMAC-SHA1. * JCE to provide the HMAC-SHA-1.
* *
* @author Loren Hart * @author Loren Hart
* @version 1.0 * @version 1.0
*/ */
public class OneTimePasswordAlgorithm { public class OneTimePasswordAlgorithm {
private OneTimePasswordAlgorithm() {} private OneTimePasswordAlgorithm() {}
// These are used to calculate the check-sum digits. // These are used to calculate the check-sum digits.
// 0 1 2 3 4 5 6 7 8 9 // 0 1 2 3 4 5 6 7 8 9
private static final int[] doubleDigits = private static final int[] doubleDigits =
skipping to change at line 1339 skipping to change at page 28, line 42
boolean doubleDigit = true; boolean doubleDigit = true;
int total = 0; int total = 0;
while (0 < digits--) { while (0 < digits--) {
int digit = (int) (num % 10); int digit = (int) (num % 10);
num /= 10; num /= 10;
if (doubleDigit) { if (doubleDigit) {
digit = doubleDigits[digit]; digit = doubleDigits[digit];
} }
total += digit; total += digit;
doubleDigit = !doubleDigit; doubleDigit = !doubleDigit;
}
int result = total % 10; int result = total % 10;
if (result > 0) { if (result > 0) {
result = 10 - result; result = 10 - result;
} }
return result; return result;
} }
/** /**
* This method uses the JCE to provide the HMAC-SHA1 * This method uses the JCE to provide the HMAC-SHA-1
* algorithm. * algorithm.
* HMAC computes a Hashed Message Authentication Code and * HMAC computes a Hashed Message Authentication Code and
* in this case SHA1 is the hash algorithm used. * in this case SHA1 is the hash algorithm used.
* *
* @param keyBytes the bytes to use for the HMAC-SHA1 key * @param keyBytes the bytes to use for the HMAC-SHA-1 key
* @param text the message or text to be authenticated. * @param text the message or text to be authenticated.
* *
* @throws NoSuchAlgorithmException if no provider makes * @throws NoSuchAlgorithmException if no provider makes
* either HmacSHA1 or HMAC-SHA1 * either HmacSHA1 or HMAC-SHA-1
* digest algorithms available. * digest algorithms available.
* @throws InvalidKeyException * @throws InvalidKeyException
* The secret provided was not a valid HMAC-SHA1 key. * The secret provided was not a valid HMAC-SHA-1 key.
* *
*/ */
public static byte[] hmac_sha1(byte[] keyBytes, byte[] text) public static byte[] hmac_sha1(byte[] keyBytes, byte[] text)
throws NoSuchAlgorithmException, InvalidKeyException throws NoSuchAlgorithmException, InvalidKeyException
{ {
// try { // try {
Mac hmacSha1; Mac hmacSha1;
try { try {
hmacSha1 = Mac.getInstance("HmacSHA1"); hmacSha1 = Mac.getInstance("HmacSHA1");
} catch (NoSuchAlgorithmException nsae) { } catch (NoSuchAlgorithmException nsae) {
hmacSha1 = Mac.getInstance("HMAC-SHA1"); hmacSha1 = Mac.getInstance("HMAC-SHA-1");
} }
SecretKeySpec macKey = SecretKeySpec macKey =
new SecretKeySpec(keyBytes, "RAW"); new SecretKeySpec(keyBytes, "RAW");
hmacSha1.init(macKey); hmacSha1.init(macKey);
return hmacSha1.doFinal(text); return hmacSha1.doFinal(text);
// } catch (GeneralSecurityException gse) { // } catch (GeneralSecurityException gse) {
// throw new UndeclaredThrowableException(gse); // throw new UndeclaredThrowableException(gse);
// } // }
} }
private static final int[] DIGITS_POWER private static final int[] DIGITS_POWER
// 0 1 2 3 4 5 6 7 8 // 0 1 2 3 4 5 6 7 8
= {1,10,100,1000,10000,100000,1000000,10000000,100000000}; = {1,10,100,1000,10000,100000,1000000,10000000,100000000};
/** /**
* This method generates an OTP value for the given * This method generates an OTP value for the given
* set of parameters. * set of parameters.
* *
* @param secret the shared secret * @param secret the shared secret
* @param movingFactor the counter, time, or other value that
* changes on a per use basis. * changes on a per use basis.
* @param codeDigits the number of digits in the OTP, not * @param codeDigits the number of digits in the OTP, not
* including the checksum, if any. * including the checksum, if any.
* @param addChecksum a flag that indicates if a checksum digit * @param addChecksum a flag that indicates if a checksum digit
* should be appended to the OTP. * should be appended to the OTP.
* @param truncationOffset the offset into the MAC result to * @param truncationOffset the offset into the MAC result to
* begin truncation. If this value is out of * begin truncation. If this value is out of
* the range of 0 ... 15, then dynamic * the range of 0 ... 15, then dynamic
* truncation will be used. * truncation will be used.
* Dynamic truncation is when the last 4 * Dynamic truncation is when the last 4
* bits of the last byte of the MAC are * bits of the last byte of the MAC are
* used to determine the start offset. * used to determine the start offset.
* @throws NoSuchAlgorithmException if no provider makes * @throws NoSuchAlgorithmException if no provider makes
* either HmacSHA1 or HMAC-SHA1 * either HmacSHA1 or HMAC-SHA-1
* digest algorithms available. * digest algorithms available.
* @throws InvalidKeyException * @throws InvalidKeyException
* The secret provided was not * The secret provided was not
* a valid HMAC-SHA1 key. * a valid HMAC-SHA-1 key.
* *
* @return A numeric String in base 10 that includes * @return A numeric String in base 10 that includes
* {@link codeDigits} digits plus the optional checksum * {@link codeDigits} digits plus the optional checksum
* digit if requested. * digit if requested.
*/ */
static public String generateOTP(byte[] secret, static public String generateOTP(byte[] secret,
long movingFactor, long movingFactor,
int codeDigits, int codeDigits,
boolean addChecksum, boolean addChecksum,
int truncationOffset) int truncationOffset)
skipping to change at line 1443 skipping to change at page 31, line 4
// put selected bytes into result int // put selected bytes into result int
int offset = hash[hash.length - 1] & 0xf; int offset = hash[hash.length - 1] & 0xf;
if ( (0<=truncationOffset) && if ( (0<=truncationOffset) &&
(truncationOffset<(hash.length-4)) ) { (truncationOffset<(hash.length-4)) ) {
offset = truncationOffset; offset = truncationOffset;
} }
int binary = int binary =
((hash[offset] & 0x7f) << 24) ((hash[offset] & 0x7f) << 24)
| ((hash[offset + 1] & 0xff) << 16) | ((hash[offset + 1] & 0xff) << 16)
| ((hash[offset + 2] & 0xff) << 8) | ((hash[offset + 2] & 0xff) << 8)
| (hash[offset + 3] & 0xff);
int otp = binary % DIGITS_POWER[codeDigits]; int otp = binary % DIGITS_POWER[codeDigits];
if (addChecksum) { if (addChecksum) {
otp = (otp * 10) + calcChecksum(otp, codeDigits); otp = (otp * 10) + calcChecksum(otp, codeDigits);
} }
result = Integer.toString(otp); result = Integer.toString(otp);
while (result.length() < digits) { while (result.length() < digits) {
result = "0" + result; result = "0" + result;
} }
return result; return result;
} }
} }
Appendix D - HOTP Algorithm: Test Values Appendix D - HOTP Algorithm: Test Values
The following test data uses the ASCII string The following test data uses the ASCII string
"123456787901234567890" for the secret: "12345678901234567890" for the secret:
Secret = 0x3132333435363738393031323334353637383930 Secret = 0x3132333435363738393031323334353637383930
Table 1 details for each count, the intermediate hmac value. Table 1 details for each count, the intermediate HMAC value.
Count Hexadecimal HMAC-SHA1(secret, count) Count Hexadecimal HMAC-SHA-1(secret, count)
0 cc93cf18508d94934c64b65d8ba7667fb7cde4b0 0 cc93cf18508d94934c64b65d8ba7667fb7cde4b0
1 75a48a19d4cbe100644e8ac1397eea747a2d33ab 1 75a48a19d4cbe100644e8ac1397eea747a2d33ab
2 0bacb7fa082fef30782211938bc1c5e70416ff44 2 0bacb7fa082fef30782211938bc1c5e70416ff44
3 66c28227d03a2d5529262ff016a1e6ef76557ece 3 66c28227d03a2d5529262ff016a1e6ef76557ece
4 a904c900a64b35909874b33e61c5938a8e15ed1c 4 a904c900a64b35909874b33e61c5938a8e15ed1c
5 a37e783d7b7233c083d4f62926c7a25f238d0316 5 a37e783d7b7233c083d4f62926c7a25f238d0316
6 bc9cd28561042c83f219324d3c607256c03272ae 6 bc9cd28561042c83f219324d3c607256c03272ae
7 a4fb960c0bc06e1eabb804e5b397cdc4b45596fa 7 a4fb960c0bc06e1eabb804e5b397cdc4b45596fa
8 1b3c89f65e6c9e883012052823443f048b4332db 8 1b3c89f65e6c9e883012052823443f048b4332db
9 1637409809a679dc698207310c8c7fc07290d9e5 9 1637409809a679dc698207310c8c7fc07290d9e5
Table details for each count the truncated values (both in Table 2 details for each count the truncated values (both in
hexadecimal and decimal) and then the HOTP value. hexadecimal and decimal) and then the HOTP value.
Truncated Truncated
Count Hexadecimal Decimal HOTP Count Hexadecimal Decimal HOTP
0 4c93cf18 1284755224 755224 0 4c93cf18 1284755224 755224
1 41397eea 1094287082 287082 1 41397eea 1094287082 287082
2 82fef30 137359152 359152 2 82fef30 137359152 359152
3 66ef7655 1726969429 969429 3 66ef7655 1726969429 969429
4 61c5938a 1640338314 338314 4 61c5938a 1640338314 338314
5 33c083d4 868254676 254676 5 33c083d4 868254676 254676
skipping to change at line 1493 skipping to change at page 33, line 6
2 82fef30 137359152 359152 2 82fef30 137359152 359152
3 66ef7655 1726969429 969429 3 66ef7655 1726969429 969429
4 61c5938a 1640338314 338314 4 61c5938a 1640338314 338314
5 33c083d4 868254676 254676 5 33c083d4 868254676 254676
6 7256c032 1918287922 287922 6 7256c032 1918287922 287922
7 4e5b397 82162583 162583 7 4e5b397 82162583 162583
8 2823443f 673399871 399871 8 2823443f 673399871 399871
9 2679dc69 645520489 520489 9 2679dc69 645520489 520489
Appendix E - Extensions Appendix E - Extensions
We introduce in this section several enhancements to the HOTP We introduce in this section several enhancements to the HOTP
algorithm. These are not recommended extensions or part of the algorithm. These are not recommended extensions or part of the
standard algorithm, but merely variations that could be used for standard algorithm, but merely variations that could be used for
customized implementations. customized implementations.
E.1 Number of Digits E.1. Number of Digits
A simple enhancement in terms of security would be to extract more A simple enhancement in terms of security would be to extract more
digits from the HMAC-SHA1 value. digits from the HMAC-SHA-1 value.
For instance, calculating the HOTP value modulo 10^8 to build an For instance, calculating the HOTP value modulo 10^8 to build an 8-
8-digit HOTP value would reduce the probability of success of the digit HOTP value would reduce the probability of success of the
adversary from sv/10^6 to sv/10^8. adversary from sv/10^6 to sv/10^8.
This could give the opportunity to improve usability, e.g. by This could give the opportunity to improve usability, e.g., by
increasing T and/or s, while still achieving a better security increasing T and/or s, while still achieving a better security
overall. For instance, s = 10 and 10v/10^8 = v/10^7 < v/10^6 which overall. For instance, s = 10 and 10v/10^8 = v/10^7 < v/10^6 which
is the theoretical optimum for 6-digit code when s = 1. is the theoretical optimum for 6-digit code when s = 1.
E.2 Alpha-numeric Values E.2. Alphanumeric Values
Another option is to use A-Z and 0-9 values; or rather a subset of Another option is to use A-Z and 0-9 values; or rather a subset of 32
32 symbols taken from the alphanumerical alphabet in order to avoid symbols taken from the alphanumerical alphabet in order to avoid any
any confusion between characters: 0, O and Q as well as l, 1 and I confusion between characters: 0, O, and Q as well as l, 1, and I are
are very similar, and can look the same on a small display. very similar, and can look the same on a small display.
The immediate consequence is that the security is now in the order The immediate consequence is that the security is now in the order of
of sv/32^6 for a 6-digit HOTP value and sv/32^8 for an 8-digit HOTP sv/32^6 for a 6-digit HOTP value and sv/32^8 for an 8-digit HOTP
value. value.
32^6 > 10^9 so the security of a 6-alphanumeric HOTP code is 32^6 > 10^9 so the security of a 6-alphanumeric HOTP code is slightly
slightly better than a 9-digit HOTP value, which is the maximum better than a 9-digit HOTP value, which is the maximum length of an
length of an HOTP code supported by the proposed algorithm. HOTP code supported by the proposed algorithm.
32^8 > 10^12 so the security of an 8-alphanumeric HOTP code is 32^8 > 10^12 so the security of an 8-alphanumeric HOTP code is
significantly better than a 9-digit HOTP value. significantly better than a 9-digit HOTP value.
Depending on the application and token/interface used for Depending on the application and token/interface used for displaying
displaying and entering the HOTP value, the choice of alphanumeric and entering the HOTP value, the choice of alphanumeric values could
values could be a simple and efficient way to improve security at a be a simple and efficient way to improve security at a reduced cost
reduced cost and impact on users. and impact on users.
E.3 Sequence of HOTP values E.3. Sequence of HOTP Values
As we suggested for the resynchronization to enter a short sequence As we suggested for the resynchronization to enter a short sequence
(say 2 or 3) of HOTP values, we could generalize the concept to the (say, 2 or 3) of HOTP values, we could generalize the concept to the
protocol, and add a parameter L that would define the length of the protocol, and add a parameter L that would define the length of the
HOTP sequence to enter. HOTP sequence to enter.
Per default, the value L SHOULD be set to 1, but if security needs Per default, the value L SHOULD be set to 1, but if security needs to
to be increased, users might be asked (possibly for a short period be increased, users might be asked (possibly for a short period of
of time, or a specific operation) to enter L HOTP values. time, or a specific operation) to enter L HOTP values.
This is another way, without increasing the HOTP length or using This is another way, without increasing the HOTP length or using
alphanumeric values to tighten security. alphanumeric values to tighten security.
Note: The system MAY also be programmed to request synchronization Note: The system MAY also be programmed to request synchronization on
on a regular basis (e.g. every night, or twice a week, etc.) and to a regular basis (e.g., every night, twice a week, etc.) and to
achieve this purpose, ask for a sequence of L HOTP values. achieve this purpose, ask for a sequence of L HOTP values.
E.4 A Counter-based Re-Synchronization Method E.4. A Counter-Based Resynchronization Method
In this case, we assume that the client can access and send not In this case, we assume that the client can access and send not only
only the HOTP value but also other information, more specifically the HOTP value but also other information, more specifically, the
the counter value. counter value.
A more efficient and secure method for resynchronization is A more efficient and secure method for resynchronization is possible
possible in this case. The client application will not send the in this case. The client application will not send the HOTP-client
HOTP-client value only, but the HOTP-client and the related value only, but the HOTP-client and the related C-client counter
C-client counter value, the HOTP value acting as a message value, the HOTP value acting as a message authentication code of the
authentication code of the counter. counter.
Resynchronization Counter-based Protocol (RCP) Resynchronization Counter-based Protocol (RCP)
---------------------------------------------- ----------------------------------------------
The server accepts if the following are all true, where C-server is The server accepts if the following are all true, where C-server is
its own current counter value: its own current counter value:
1) C-client >= C-server 1) C-client >= C-server
2) C-client - C-server <= s 2) C-client - C-server <= s
3) Check that HOTP-client is valid HOTP(K,C-Client) 3) Check that HOTP client is valid HOTP(K,C-Client)
4) If true, the server sets C to C-client + 1 and client is 4) If true, the server sets C to C-client + 1 and client is
authenticated authenticated
In this case, there is no need for managing a look-ahead window In this case, there is no need for managing a look-ahead window
anymore. The probability of success of the adversary is only v/10^6 anymore. The probability of success of the adversary is only v/10^6
or roughly v in one million. A side benefit is obviously to be able or roughly v in one million. A side benefit is obviously to be able
to increase s "infinitely" and therefore improve the system to increase s "infinitely" and therefore improve the system usability
usability without impacting the security. without impacting the security.
This resynchronization protocol SHOULD be use whenever the related This resynchronization protocol SHOULD be used whenever the related
impact on the client and server applications is deemed acceptable. impact on the client and server applications is deemed acceptable.
E.5 Data Field E.5. Data Field
Another interesting option is the introduction of a Data field, Another interesting option is the introduction of a Data field, which
that would be used for generating the One-Time password values: would be used for generating the One-Time Password values: HOTP (K,
HOTP (K, C, [Data]) where Data is an optional field that can be the C, [Data]) where Data is an optional field that can be the
concatenation of various pieces of identity-related information - concatenation of various pieces of identity-related information,
e.g. Data = Address | PIN. e.g., Data = Address | PIN.
We could also use a Timer, either as the only moving factor or in We could also use a Timer, either as the only moving factor or in
combination with the Counter - in this case, e.g. Data = Timer, combination with the Counter -- in this case, e.g., Data = Timer,
where Timer could be the UNIX-time (GMT seconds since 1/1/1970) where Timer could be the UNIX-time (GMT seconds since 1/1/1970)
divided by some factor (8, 16, 32, etc.) in order to give a divided by some factor (8, 16, 32, etc.) in order to give a specific
then equal to the time step multiplied by the resynchronization time step. The time window for the One-Time Password is then equal
parameter as defined before - e.g. if we take 64 seconds as the to the time step multiplied by the resynchronization parameter as
time step and 7 for the resynchronization parameter, we obtain an defined before. For example, if we take 64 seconds as the time step
acceptance window of +/- 3 minutes. and 7 for the resynchronization parameter, we obtain an acceptance
window of +/- 3 minutes.
Using a Data field opens for more flexibility in the algorithm Using a Data field opens for more flexibility in the algorithm
implementation, provided that the Data field is clearly specified. implementation, provided that the Data field is clearly specified.
Authors' Addresses
David M'Raihi (primary contact for sending comments and questions)
VeriSign, Inc.
685 E. Middlefield Road
Mountain View, CA 94043 USA
Phone: 1-650-426-3832
EMail: dmraihi@verisign.com
Mihir Bellare
Dept of Computer Science and Engineering, Mail Code 0114
University of California at San Diego
9500 Gilman Drive
La Jolla, CA 92093, USA
EMail: mihir@cs.ucsd.edu
Frank Hoornaert
VASCO Data Security, Inc.
Koningin Astridlaan 164
1780 Wemmel, Belgium
EMail: frh@vasco.com
David Naccache
Gemplus Innovation
34 rue Guynemer, 92447,
Issy les Moulineaux, France
and
Information Security Group,
Royal Holloway,
University of London, Egham,
Surrey TW20 0EX, UK
EMail: david.naccache@gemplus.com, david.naccache@rhul.ac.uk
Ohad Ranen
Aladdin Knowledge Systems Ltd.
15 Beit Oved Street
Tel Aviv, Israel 61110
EMail: Ohad.Ranen@ealaddin.com
Full Copyright Statement
Copyright (C) The Internet Society (2005).
This document is subject to the rights, licenses and restrictions
contained in BCP 78, and except as set forth therein, the authors
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