Internet Draft Ari Singer, NTRU
Document: draft-ietf-pkix-pkalgs-supp-01.txt William Whyte, NTRU
Expires: September 2002 March 2002
Supplemental Algorithms and Identifiers for the
Internet X.509 Public Key Infrastructure
Certificate and CRL Profile
Status of this Memo
This document is an Internet-Draft and is in full conformance
with all provisions of Section 10 of RFC 2026 [RFC2026].
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF), its areas, and its working groups. Note that
other groups may also distribute working documents as Internet-
Drafts.
Internet-Drafts are draft documents valid for a maximum of six
months and may be updated, replaced, or obsoleted by other documents
at any time. It is inappropriate to use Internet-Drafts as
reference material or to cite them other than as "work in progress."
The list of current Internet-Drafts can be accessed at
http://www.ietf.org/ietf/1id-abstracts.txt
The list of Internet-Draft Shadow Directories can be accessed at
http://www.ietf.org/shadow.html.
Conventions used in this document
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in
this document are to be interpreted as described in RFC 2119
[RFC2119].
Abstract
This document specifies algorithm identifiers and ASN.1 encoding
formats for digital signatures and subject public keys, including
NTRUSign digital signatures and NTRUEncrypt and NTRUSign subject
public keys used in the Internet X.509 Public Key Infrastructure
(PKI). Digital signatures are used to sign certificates and
certificate revocation lists (CRLs). Certificates include the
public key of the named subject. This document is intended to be a
companion to draft-ietf-pkix-ipki-pkalgs-05.txt [PKIX-ALGS] and may
be merged with that document in future revisions if approved by the
PKIX working group.
Table of Contents
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Status of this Memo................................................1
Conventions used in this document..................................1
Abstract...........................................................1
1. Overview........................................................3
2. Algorithm Support...............................................3
2.1 Signature Algorithms...........................................4
2.1.1 NTRUSign Signature Algorithm.................................4
2.2 Subject Public Key Algorithms..................................6
2.2.1 NTRUEncrypt Keys.............................................6
2.2.2 NTRUSign Keys...............................................12
3. ASN.1 Module...................................................15
4. Security Considerations........................................21
5. Intellectual Property Rights...................................21
6. Acknowledgements...............................................21
7. References.....................................................22
Authors' Addresses................................................23
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1. Overview
This document specifies algorithm identifiers and ASN.1 encoding
formats for digital signatures and subject public keys used in the
Internet X.509 Public Key Infrastructure (PKI). This specification
supplements RFC 2459 [RFC2459], "Internet Public Key Infrastructure:
X.509 Certificate and CRL Profile". Implementations of this
specification must also conform to RFC 2459 [RFC2459]. This
document is being written concurrently with the PKIX public key
algorithms Internet Draft [PKIX-ALGS] (the latest version as of this
writing is draft-ietf-pkix-ipki-pkalgs-05.txt). It is intended that
when this document is completed and approved by the PKIX working
group that it be merged with that document. The format of this
document is written to approximately match the format of that
Internet Draft.
This specification defines the contents of the signatureAlgorithm,
signatureValue, signature and subjectPubliKeyInfo fields within
Internet X.509 certificates and CRLs.
This document does not currently introduce any new one-way hash
functions, but it specifies the use of SHA-256, SHA-384 and SHA-512
hash algorithms as defined in the draft of FIPS 180-2 [FIPS180-2] as
well as the SHA-1 hash algorithm as defined in FIPS 180-1 [FIPS180-
1] with the NTRUSign signature algorithm. It is anticipated that
future revisions will include the algorithm identifiers and ASN.1
encoding of the FIPS 180-2 hash algorithms.
This specification describes the encoding of digital signatures
generated with the following cryptographic algorithms;
* NTRUSign Signature Scheme (NTRUSign).
It is anticipated that future revisions of this document will
include the extended version of the Digital Signature Algorithm
(DSA) [FIPS186-2], which has not yet been published. In addition,
it is anticipated that the document will include the algorithm
identifiers and ASN.1 encoding of pre-existing algorithms (e.g. RSA)
when used in conjunction with the FIPS 180-2 hash algorithms.
This document specifies the contents of the subjectPublicKeyInfo
field in Internet X.509 certificates. For each algorithm, the
appropriate alternatives for the keyUsage extension are provided.
This specification describes encoding formats for public keys used
with the following cryptographic algorithms:
* NTRUEncrypt Encryption Scheme (NTRUEncrypt)
* NTRUSign Signature Scheme (NTRUSign)
2. Algorithm Support
This section describes cryptographic algorithms that may be used
with the Internet X.509 Certificate and CRL Profile. In particular,
it describes the NTRUSign digital signature algorithm, which may be
used to sign certificates and CRLs. In addition, this section
identifies OIDs and ASN.1 encoding for NTRUSign and NTRUEncrypt
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public keys contained in a certificate. It is anticipated that
additional algorithms, such as the extended version of DSA, will be
included in future revisions.
Conforming CAs and application are not required to support the
algorithms or algorithm identifiers described in this section.
However, conforming CAs and applications that use the algorithms
identified here MUST support them as specified.
2.1 Signature Algorithms
Certificates and CRLs conforming to RFC 2459 [RFC2459] may be signed
with any public key signature algorithm. The certificate or CRL
indicates the algorithm through an algorithm identifier, which
appears in the signatureAlgorithm field within the Certificate or
CertificateList. An algorithm identifier consists of an OID and
(optionally) associated parameters. This section describes OIDs and
parameter encoding for NTRUSign.
Signature algorithms are always used in conjunction with a one-way
hash function.
The data to be signed (e.g. the one-way hash function output value)
is formatted for the signature algorithm to be used. Then, a
private key operation (e.g. NTRUSign signature primitive) is
performed to generate the signature value. This signature value is
then ASN.1 encoded as a BIT STRING and included in the Certificate
or CertificateList in the signature field.
2.1.1 NTRUSign Signature Algorithm
The NTRUSign signature algorithm was invented by Hoffstein,
Howgrave-Graham, Pipher, Silverman and Whyte. It is defined in
Efficient Embedded Security Standard (EESS) #1 [EESS#1]. This
profile defines a single signature algorithm, the NTRUSign signature
algorithm with the SHA-1, SHA-256, SHA-384 or SHA-512 one-way hash
function.
The signature algorithm is implemented using the padding and
encoding conventions described in EESS #1 [EESS#1]. The message
digest is computed using the SHA-1 Hash Algorithm [FIPS180-1] or any
of the SHA-2 algorithms [FIPS180-2] and the message digest is
encoded using the MGF1 mask generation function as specified in Std
IEEE 1363-2000 [IEEE1363].
Unlike previously defined public-key signature algorithms, the
object identifier for the NTRUSign signature algorithm does not
specify the hash function. Rather, the parameter field in the
AlgorithmIdentifier contains an indication of the hash function as
well as the encoding methods that are to be used.
The ASN.1 object identifier used to identify this signature
algorithm is named id-ntru-EESS1v1-NTRUSign and is given by the
following ASN.1:
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ntru OBJECT IDENTIFIER ::=
{iso(1) identified-organization(3) dod(6) internet(1)
private(4) enterprises(1) ntruCryptosystems (8342) }
id-eess1 OBJECT IDENTIFIER ::= {ntru eess(1) 1}
id-eess1-algs OBJECT IDENTIFIER ::= {id-eess1 1}
id-ntru-EESS1v1-NTRUSign OBJECT IDENTIFIER ::=
{id-eess1-algs 3}
When this OID appears in the signatureAlgorithm field or the
signature field of an X.509 certificate, the encoding SHALL omit the
parameters field. That is, the AlgorithmIdentifier shall be a
SEQUENCE of one component: the OBJECT IDENTIFIER id-ntru-EESS1v1-
SVSSA.
The NTRUSign parameters in the subjectPublicKeyInfo field of the
certificate of the issuer shall apply to the verification of the
signature.
When signing, the NTRUSign algorithm generates a signature
polynomial. This polynomial SHALL be encoded as an OCTET STRING as
described in EESS #1 [EESS#1]. The signature SHALL be ASN.1 encoded
using the following ASN.1 structure:
NTRUSignSignedData ::= NTRUPublicVector
NTRUPublicVector ::= CHOICE {
modQVector [0] IMPLICIT ModQVector,
packedModQVector [1] IMPLICIT PackedModQVector,
...}
ModQVector ::= OCTET STRING
PackedModQVector ::= OCTET STRING
The field choices of type NTRUPublicVector have the following
meanings:
modQVector is the representation of the NTRUPublicVector in
unpacked form. For a polynomial of degree N-1 with
coefficients reduced mod q, each of the N bytes of the OCTET
STRING represent integers x in the range 0 <= x < q
corresponding to the coefficient values of the polynomial from
lowest degree to highest.
packedModQVector is the representation of the NTRUPublicVector
in packed form. For a polynomial of degree N-1 with
coefficients reduced mod q, each log_2(q) bits of the OCTET
STRING represent integers x in the range 0 <= x < q
corresponding to the coefficient values of the polynomial from
lowest degree to highest. The values are concatenated bitwise,
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without any intermediate padding, and irrespective of the byte
boundaries. If necessary, zero bits are appended to the packed
data in order to make the length a multiple of 8 bits.
Implementations that sign certificates using NTRUSign SHOULD encode
the signature as a ModQVector.
2.2 Subject Public Key Algorithms
Certificates conforming to RFC 2459 [RFC2459] may convey a public
key for any public key algorithm. The certificate indicates the
algorithm through an algorithm identifier. This algorithm
identifier consists of an OID and optionally associated parameters.
This section identifies preferred OIDs and parameters for the
NTRUEncrypt and NTRUSign algorithms. Conforming CAs MUST use the
identified OIDs when issuing certificates containing public keys for
these algorithms. Conforming applications supporting any of these
algorithms MUST, at a minimum, recognize the OIDs identified in this
section.
2.2.1 NTRUEncrypt Keys
This section identifies the preferred OID and parameter encoding for
the inclusion of an NTRUEncrypt public key in a certificate. The
NTRUEncrypt encryption algorithm is defined in EESS #1 [EESS#1].
The OID id-ntru-EESS1v1-SVES identifies NTRUEncrypt public keys.
id-ntru-EESS1v1-SVES OBJECT IDENTIFIER ::= {id-eess1-algs 1}
The id-ntru-EESS1v1-SVES OID is intended to be used in the algorithm
field of a value of type AlgorithmIdentifier. NTRUEncrypt requires
use of certain parameters with the public key. The parameters may
be implied by context, implicitly included through reference of a
degree, implicitly included through reference of a standard
parameter set or explicitly included in the certificate. The
parameters associated with id-ntru-EESS1v1-SVES are EESS1v1-SVES-
Parameters.
EESS1v1-SVES-Parameters ::= CHOICE {
degree Degree,
standardNTRUParameters StandardNTRUParameters,
explicitNTRUParameters ExplicitNTRUParameters,
externalParameters NULL
}
When the parameters are implied by context, the parameters field
SHALL contain externalParameters, which is a value of the ASN.1 type
NULL.
When the parameters are specified by degree, the values are
restricted to 251, 347 and 503. For the three permitted choices,
the parameters are defined to be ees251ep1, ees347ep1 and ees503ep1
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respectively as defined in EESS #1 [EESS#1]. Specifying the degree
is the preferred way for transmitting parameter information for the
scheme when the parameters are not implied by context.
Degree ::= INTEGER (251 | 347 | 503, ...)
When the parameters are specified by reference of a standard, the
parameters shall consist of an OID chosen from the list
NTRUParameters. The current list of NTRUParameters OIDs is:
StandardNTRUParameters ::= OIDS.&id({NTRUParameters})
NTRUParameters OIDS ::= {
{ OID id-ees251ep1 }|
{ OID id-ees347ep1 }|
{ OID id-ees503ep1 },
...}
The above object identifiers are specified by:
id-eess1-params OBJECT IDENTIFIER ::= {id-eess1 2}
id-ees251ep1 OBJECT IDENTIFIER ::= {id-eess1-params 1}
id-ees347ep1 OBJECT IDENTIFIER ::= {id-eess1-params 2}
id-ees503ep1 OBJECT IDENTIFIER ::= {id-eess1-params 3}
When the parameters are explicitly included, they SHALL be encoded
in the ASN.1 structure ExplicitNTRUParameters:
ExplicitNTRUParameters ::= SEQUENCE {
version Version,
degree INTEGER,
bigModulus INTEGER,
smallModulus SmallModulus,
mrgm NTRUMRGMAlgorithmIdentifier,
db INTEGER,
bvgm NTRUBVGMAlgorithmIdentifier,
...}
Version ::= INTEGER { v0(0) } (v0, ...)
SmallModulus ::= CHOICE {
integerValue INTEGER,
polynomialValue NTRUGeneralPolynomial
}
NTRUGeneralPolynomial ::= SEQUENCE {
numberOfEntries INTEGER,
modulus INTEGER,
coefficients GeneralVector
}
GeneralVector ::= OCTET STRING
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The fields of type NTRUGeneralPolynomial have the following
meanings:
numberOfEntries is the number of coefficients used to represent
the polynomial - this number is equal to the degree of the
polynomial plus 1.
modulus is an upper bound on the value of the coefficients.
coefficients is the list of numberOfEntries coefficients,
represented in order from lowest degree to highest degree. If
modulus < 257, each coefficient is stored in a single byte. If
modulus > 256 and modulus < 2^16, each coefficient is stored in
two bytes.
The fields of type SmallModulus have the following meanings:
integerValue is the value of p if p is an integer.
polynomialValue is the value of p if p is a polynomial.
The fields of type ExplicitNTRUParameters have the following
meanings:
version is the version number, for compatibility with future
revisions of this document. It SHALL be 0 for this version of
the document.
degree is the value N.
bigModulus is the value q. q will be 256 or less.
smallModulus is the value p. It SHALL be represented with the
SmallModulus type.
mrgm identifies the message representative generation method
using an allowed AlgorithmIdentifier.
db is the size of the random component.
bvgm identifies the blinding value generation method using an
allowed AlgorithmIdentifier.
The ASN.1 for the mrgm used in ExplicitNTRUParameters is specified
below.
NTRUMRGMAlgorithmIdentifier ::=
AlgorithmIdentifier {{NTRUEESS1v1MRGMs}}
NTRUEESS1v1MRGMs ALGORITHM ::= {
{OID id-mrgm-ntru-1 PARMS NTRUMRGM1-params},
...}
id-eess1-encodingMethods OBJECT IDENTIFIER ::= {id-eess1 3}
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id-mrgm-ntru-1 OBJECT IDENTIFIER ::=
{id-eess1-encodingMethods 1}
NTRUMRGM1-params ::= NTRUHashAlgorithmIdentifier
NTRUHashAlgorithmIdentifier ::=
AlgorithmIdentifier {{NTRUEESS1v1Hashes}}
The identifier id-mrgm-ntru-1 identifies the message representative
generation method MRGM-NTRU1, defined in EESS #1 [EESS#1]. The
parameters identify the hashing mechanism using an allowed
AlgorithmIdentifier.
NTRUEESS1v1Hashes ALGORITHM ::= {
{OID id-sha1 PARMS NULL}|
{OID id-sha256 PARMS NULL }|
{OID id-sha384 PARMS NULL }|
{OID id-sha512 PARMS NULL },
...}
These identifiers identify the one-way hash algorithms SHA-1
[FIPS180-1] and SHA-2 [TBD].
The ASN.1 for the bvgm used in ExplicitNTRUParameters is specified
below.
NTRUBVGMAlgorithmIdentifier ::=
AlgorithmIdentifier {{NTRUEESS1v1BVGMs}}
NTRUEESS1v1BVGMs ALGORITHM ::= {
{OID id-bvgm-ntru-1 PARMS NTRUBVGM1-params}|
{OID id-bvgm-ntru-2 PARMS NTRUBVGM2-params},
...}
id-bvgm-ntru-1 OBJECT IDENTIFIER ::=
{id-eess1-encodingMethods 2}
NTRUBVGM1-params ::= SEQUENCE {
c INTEGER,
prng NTRUPRNGAlgorithmIdentifier,
dr INTEGER
}
id-bvgm-ntru-2 OBJECT IDENTIFIER ::=
{id-eess1-encodingMethods 3}
NTRUBVGM2-params ::= SEQUENCE {
c INTEGER,
prng NTRUPRNGAlgorithmIdentifier,
dr1 INTEGER,
dr2 INTEGER,
dr3 INTEGER
}
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The identifier id-bvgm-ntru-1 identifies blinding value generation
method BVGM-NTRU1, defined in EESS #1 [EESS#1]. The identifier id-
bvgm-ntru-2 identifies blinding value generation method BVGM-NTRU2,
defined in EESS #1 [EESS#1].
The fields of type NTRUBVGM1-params have the following meanings:
c is the random polynomial generation constant used to select
the polynomial r.
prng identifies the pseudo-random number generation algorithm
using an allowed AlgorithmIdentifier.
dr is the number of 1s in the blinding value r.
The fields of type NTRUBVGM2-params have the following meanings:
c is the random polynomial generation constant used to select
the polynomial r.
prng identifies the pseudo-random number generation algorithm
using an allowed AlgorithmIdentifier.
dr1 is the number of 1s in the blinding value component r1.
dr2 is the number of 1s in the blinding value component r2.
dr3 is the number of 1s in the blinding value component r3.
The allowed pseudo-random number generation algorithms are defined
by:
NTRUPRNGAlgorithmIdentifier ::=
AlgorithmIdentifier {{NTRUEESS1v1PRNGs}}
NTRUEESS1v1PRNGs ALGORITHM ::= {
NTRUMGFAlgorithms,
...}
This identifies the pseudo-random number generation algorithm to be
used when generating blinding values. The only allowed algorithms
are MGF1 (see [IEEE 1363]) using SHA-1 [FIPS180-1] or SHA-2
[FIPS180-2].
NTRUMGFAlgorithms ALGORITHM ::= {
{OID id-mgf1 PARMS MGF1Parameters},
...}
pkcs-1 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1)
1}
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id-mgf1 OBJECT IDENTIFIER ::= {pkcs-1 8}
MGF1Parameters ::= AlgorithmIdentifier {{NTRUEESS1v1Hashes}}
The NTRUEncrypt public key MUST be encoded using the ASN.1 type
NTRUPublicKey.
NTRUPublicKey ::= SEQUENCE {
publicKeyVector NTRUPublicVector, -- h
ntruKeyExtensions NTRUKeyExtensions OPTIONAL
}
NTRUKeyExtensions ::=
SEQUENCE SIZE(1..MAX) OF NTRUKeyExtension
NTRUKeyExtension ::= CHOICE {
keyID [0] IMPLICIT INTEGER,
...}
The fields of the type NTRUPublicKey have the following meanings:
publicKeyVector is the polynomial h. If the NTRUPublicVector
is a ModQVector, each coefficient will be represented by one
byte starting with the lowest degree and going to the highest.
If the NTRUPublicVector is a PackedModQVector, this is the
OCTET STRING representing h obtained using RE2BSP and then
BS2OSP as defined in EESS #1 [EESS#1]. All coefficients up to
X^(N-1) SHALL be explicitly included in publicKeyVector.
Representing the NTRUEncrypt public key as a ModQVector is the
preferred method.
ntruKeyExtensions is provided for future extensibility. Only
one extension is currently defined.
The fields of the type NTRUKeyExtension have the following meanings:
keyID can be used to associate a unique key identifier with the
key.
If the keyUsage extension is present in an end entity certificate
that conveys an NTRUEncrypt public key, any combination of the
following values MAY be present:
keyEncipherment;
dataEncipherment;
If the keyUsage extension is present in a CA certificate that
conveys an NTRUEncrypt public key, any combination of the following
values MAY be present:
keyEncipherment; and
dataEncipherment.
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2.2.2 NTRUSign Keys
This section identifies the preferred OID and parameter encoding for
the inclusion of an NTRUSign public key in a certificate. The
NTRUSign signature algorithm is defined in EESS #1 [EESS#1].
The OID id-ntru-EESS1v1-SVSSA identifies NTRUSign public keys.
id-ntru-EESS1v1-NTRUSign OBJECT IDENTIFIER ::=
{id-eess1-algs 3}
The id-ntru-EESS1v1-NTRUSign OID is intended to be used in the
algorithm field of a value of type AlgorithmIdentifier. NTRUSign
requires use of certain parameters with the public key. The
parameters may be implied by context (e.g. they may be inherited
from the issuer), implicitly included through reference of a degree,
implicitly included through reference of a standard parameter set or
explicitly included in the certificate. The parameters associated
with id-ntru-EESS1v1-NTRUSign are EESS1v1-NTRUSign-Parameters.
EESS1v1-NTRUSign-Parameters ::= CHOICE {
degree Degree,
standardNTRUSignParameters
StandardNTRUSignParameters,
explicitNTRUSignParameters
ExplicitNTRUSignParameters,
externalParameters NULL
}
When the parameters are implied by context, the parameters field
SHALL contain externalParameters, which is the ASN.1 value NULL.
When the parameters are specified by degree, the value is restricted
to 251. For the permitted choice, the parameters are defined to be
ees251sp2 as defined in EESS #1 [EESS#1]. Specifying the degree is
the preferred way for transmitting parameter information for the
scheme when the parameters are not implied by context.
When the parameters are specified by reference of a standard, the
parameters shall consist of an OID chosen from the list
NTRUSignParameters. The current list of NTRUSignParameters OIDs is:
StandardNTRUSignParameters ::= OIDS.&id({NTRUSignParameters})
NTRUSignParameters OIDS ::= {
{ OID id-ees251sp2 },
...}
The above object identifier is specified by:
id-ees251sp2 OBJECT IDENTIFIER ::= {id-eess1-params 7}
When the parameters are explicitly included, they SHALL be encoded
in the ASN.1 structure ExplicitNTRUSignParameters:
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ExplicitNTRUSignParameters ::= SEQUENCE {
version Version,
degree INTEGER,
bigModulus INTEGER,
normBound INTEGER,
messageRandLength INTEGER,
hash NTRUSignHashAlgIdentifier,
mrgm NTRUSignMRGMAlgIdentifier,
...}
The fields of type ExplicitNTRUSignParameters have the following
meanings:
version is the version number, for compatibility with future
revisions of this document. It SHALL be 0 for this version of
the document.
degree is the value N.
bigModulus is the value q. q will be 256 or less.
normBound is the maximum norm of the signature
messageRandLength is the length of the randomization padding
appended to the message digest before generating the message
representative
hash identifies the hash algorithm used using an allowed
AlgorithmIdentifier.
mrgm identifies the message representative generation method
using an allowed AlgorithmIdentifier.
The AlgorithmIdentifiers for the field hash of
ExplicitNTRUSignParameters are chosen from the set
NTRUEESS1v1Hashes, which is defined in section 2.2.1.
NTRUSignHashAlgIdentifier ::=
AlgorithmIdentifier {{NTRUEESS1v1Hashes}}
The AlgorithmIdentifiers for the field mrgm of
ExplicitNTRUSignParameters are specified below.
NTRUSignMRGMAlgIdentifier ::=
AlgorithmIdentifier {{NTRUSignEESS1v1MRGMs}}
NTRUSignEESS1v1MRGMs ALGORITHM ::= {
{OID id-mrgm-ntrusign-1 PARMS NTRUSignMRGM1-params}|
{OID id-mrgm-ntrusign-2 PARMS NTRUSignMRGM2-params},
...}
id-mrgm-ntrusign-1 OBJECT IDENTIFIER ::=
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{id-eess1-encodingMethods 6}
NTRUSignMRGM1-params ::= NTRUSignPRNGAlgIdentifier
id-mrgm-ntrusign-2 OBJECT IDENTIFIER ::=
{id-eess1-encodingMethods 7}
NTRUSignMRGM2-params ::= SEQUENCE {
c INTEGER,
numGroups INTEGER,
numElements INTEGER,
prng NTRUSignPRNGAlgIdentifier
}
NTRUSignPRNGAlgIdentifier ::=
AlgorithmIdentifier {{NTRUEESS1v1PRNGs}}
The identifier id-mrgm-ntrusign-2 identifies the message
representative generation method MRGM-NTRUSign1, defined in EESS #1
[EESS#1]. The identifier id-mrgm-ntrusign-2 identifies the message
representative generation method MRGM-NTRUSign2, defined in EESS #1
[EESS#1].
The fields of type NTRUSignMRGM1-params have the following meanings:
NTRUSignPRNGAlgIdentifier is the pseudo-random number
generation method using an allowed AlgorithmIdentifier
The fields of type NTRUSignMRGM2-params have the following meanings:
c is the random polynomial generation constant used to select
the message representative.
numGroups is the number of factors combined to form the message
representative.
numElements is the number of non-zero coefficients in each
factor of the message representative
prng identifies the pseudo-random number generation method
using an allowed AlgorithmIdentifier.
The allowed pseudo-random number generation algorithms are chosen
from the set NTRUEESS1v1PRNGs, which is defined in section 2.2.1.
The NTRUSign public key MUST be encoded using the ASN.1 type
NTRUSignPublicKey.
NTRUSignPublicKey ::= SEQUENCE {
publicKeyVector NTRUPublicVector, -- h
ntruSignKeyExtensions NTRUSignKeyExtensions OPTIONAL
}
NTRUSignKeyExtensions ::=
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SEQUENCE SIZE(1..MAX) OF NTRUSignKeyExtension
NTRUSignKeyExtension ::= CHOICE {
keyID [0] IMPLICIT INTEGER,
...}
The fields of the type NTRUSignPublicKey have the following
meanings:
publicKeyVector is the polynomial h. If the NTRUPublicVector
is a ModQVector, each coefficient will be represented by one
byte starting with the lowest degree and going to the highest.
If the NTRUPublicVector is a PackedModQVector, this is the
OCTET STRING representing h obtained using RE2BSP and then
BS2OSP as defined in EESS #1 [EESS#1]. All coefficients up to
X^(N-1) SHALL be explicitly included in publicKeyVector.
Representing the NTRUSign public key as a ModQVector is the
preferred method.
ntruSignKeyExternsions is provided for future extensibility.
Only one extension is currently defined.
The fields of the type NTRUSignKeyExtension have the following
meanings:
keyID can be used to associate a unique key identifier with the
key.
If the keyUsage extension is present in an end entity certificate
that conveys an NTRUSign public key, any combination of the
following values MAY be present:
digitalSignature;
nonRepudiation;
If the keyUsage extension is present in a CA certificate that
conveys an NTRUSign public key, any combination of the following
values MAY be present:
digitalSignature;
nonRepudiation;
keyCertSign; and
cRLSign.
3. ASN.1 Module
PKIXAlgorithmOIDTBD -- {TBD} --
DEFINITIONS EXPLICIT TAGS ::= BEGIN
-- EXPORTS ALL; --
-- IMPORTS None; --
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-- Supporting definitions
AlgorithmIdentifier { ALGORITHM: IOSet } ::= SEQUENCE {
algorithm ALGORITHM.&id({IOSet}),
parameters ALGORITHM.&Type({IOSet}{@algorithm})
OPTIONAL
}
ALGORITHM ::= CLASS {
&id OBJECT IDENTIFIER UNIQUE,
&Type OPTIONAL
}
WITH SYNTAX { OID &id [PARMS &Type] }
OIDS ::= ALGORITHM
-- Informational object identifiers
pkcs-1 OBJECT IDENTIFIER ::=
{iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1)
1}
id-mgf1 OBJECT IDENTIFIER ::= {pkcs-1 8}
id-sha1 OBJECT IDENTIFIER ::=
{iso(1) identified-organization(3) oiw(14) secsig(3)
algorithms(2) 26}
id-sha256 OBJECT IDENTIFIER ::=
{joint-iso-itu-t(2) country(16) us(840) organization(1)
gov(101) csor(3) nistalgorithm(4) hashalgs(2) 1}
id-sha384 OBJECT IDENTIFIER ::=
{joint-iso-itu-t(2) country(16) us(840) organization(1)
gov(101) csor(3) nistalgorithm(4) hashalgs(2) 2}
id-sha512 OBJECT IDENTIFIER ::=
{joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101)
csor(3) nistalgorithm(4) hashalgs(2) 3}
-- NTRU Object Identifiers
ntru OBJECT IDENTIFIER ::=
{iso(1) identified-organization(3) dod(6) internet(1)
private(4) enterprises(1) ntruCryptosystems (8342) }
id-eess1 OBJECT IDENTIFIER ::= {ntru eess(1) 1}
id-eess1-algs OBJECT IDENTIFIER ::= {id-eess1 1}
id-eess1-params OBJECT IDENTIFIER ::= {id-eess1 2}
id-eess1-encodingMethods OBJECT IDENTIFIER ::= {id-eess1 3}
-- OID for NTRUSign Algorithm and Public Key
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id-ntru-EESS1v1-NTRUSign OBJECT IDENTIFIER ::=
{id-eess1-algs 3}
-- OID for NTRUSign Parameter Set
id-ees251sp2 OBJECT IDENTIFIER ::= {id-eess1-params 7}
-- OIDs for NTRUSign Encoding Methods
id-mrgm-ntrusign-1 OBJECT IDENTIFIER ::=
{id-eess1-encodingMethods 6}
id-mrgm-ntrusign-2 OBJECT IDENTIFIER ::=
{id-eess1-encodingMethods 7}
-- OID for NTRUEncrypt Algorithm and Public Key
id-ntru-EESS1v1-SVES OBJECT IDENTIFIER ::=
{id-eess1-algs 1}
-- OIDs for NTRUEncrypt Parameter Sets
id-ees251ep1 OBJECT IDENTIFIER ::= {id-eess1-params 1}
id-ees347ep1 OBJECT IDENTIFIER ::= {id-eess1-params 2}
id-ees503ep1 OBJECT IDENTIFIER ::= {id-eess1-params 3}
-- OIDs for NTRUEncrypt Encoding Methods
id-mrgm-ntru-1 OBJECT IDENTIFIER ::=
{id-eess1-encodingMethods 1}
id-bvgm-ntru-1 OBJECT IDENTIFIER ::=
{id-eess1-encodingMethods 2}
id-bvgm-ntru-2 OBJECT IDENTIFIER ::=
{id-eess1-encodingMethods 3}
-- General Types
NTRUPublicVector ::= CHOICE {
modQVector [0] IMPLICIT ModQVector,
packedModQVector [1] IMPLICIT PackedModQVector,
...}
ModQVector ::= OCTET STRING
PackedModQVector ::= OCTET STRING
NTRUGeneralPolynomial ::= SEQUENCE {
numberOfEntries INTEGER,
modulus INTEGER,
coefficients GeneralVector
}
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GeneralVector ::= OCTET STRING
SmallModulus ::= CHOICE {
integerValue INTEGER,
polynomialValue NTRUGeneralPolynomial
}
Degree ::= INTEGER (251 | 347 | 503, ...)
Version ::= INTEGER { v0(0) } (v0, ...)
NTRUEESS1v1Hashes ALGORITHM ::= {
{OID id-sha1 PARMS NULL}|
{OID id-sha256 PARMS NULL }|
{OID id-sha384 PARMS NULL }|
{OID id-sha512 PARMS NULL },
...}
NTRUEESS1v1PRNGs ALGORITHM ::= {
NTRUMGFAlgorithms,
...}
NTRUMGFAlgorithms ALGORITHM ::= {
{OID id-mgf1 PARMS MGF1Parameters},
...}
MGF1Parameters ::= AlgorithmIdentifier
{{NTRUEESS1v1Hashes}}
-- Encoding for NTRUSign Signatures
NTRUSignSignedData ::= NTRUPublicVector
-- Encoding for NTRUSign Public Keys
NTRUSignPublicKey ::= SEQUENCE {
publicKeyVector NTRUPublicVector, -- h
ntruSignKeyExtensions NTRUSignKeyExtensions OPTIONAL
}
NTRUSignKeyExtensions ::=
SEQUENCE SIZE(1..MAX) OF NTRUSignKeyExtension
NTRUSignKeyExtension ::= CHOICE {
keyID [0] IMPLICIT INTEGER,
...}
EESS1v1-NTRUSign-Parameters ::= CHOICE {
degree Degree,
standardNTRUSignParameters
StandardNTRUSignParameters,
explicitNTRUSignParameters
ExplicitNTRUSignParameters,
externalParameters NULL
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}
StandardNTRUSignParameters ::= OIDS.&id({NTRUSignParameters})
NTRUSignParameters OIDS ::= {
{ OID id-ees251sp2 },
...}
ExplicitNTRUSignParameters ::= SEQUENCE {
version Version,
degree INTEGER,
bigModulus INTEGER,
normBound INTEGER,
messageRandLength INTEGER,
hash NTRUSignHashAlgIdentifier,
mrgm NTRUSignMRGMAlgIdentifier,
...}
NTRUSignHashAlgIdentifier ::=
AlgorithmIdentifier {{NTRUEESS1v1Hashes}}
NTRUSignMRGMAlgIdentifier ::=
AlgorithmIdentifier {{NTRUSignEESS1v1MRGMs}}
NTRUSignEESS1v1MRGMs ALGORITHM ::= {
{OID id-mrgm-ntrusign-1 PARMS NTRUSignMRGM1-params}|
{OID id-mrgm-ntrusign-2 PARMS NTRUSignMRGM2-params},
...}
NTRUSignMRGM1-params ::= NTRUSignPRNGAlgIdentifier
NTRUSignMRGM2-params ::= SEQUENCE {
c INTEGER,
numGroups INTEGER,
numElements INTEGER,
prng NTRUSignPRNGAlgIdentifier
}
NTRUSignPRNGAlgIdentifier ::=
AlgorithmIdentifier {{NTRUEESS1v1PRNGs}}
-- Encoding for NTRUEncrypt Public Keys
NTRUPublicKey ::= SEQUENCE {
publicKeyVector NTRUPublicVector, -- h
ntruKeyExtensions NTRUKeyExtensions OPTIONAL
}
NTRUKeyExtensions ::=
SEQUENCE SIZE(1..MAX) OF NTRUKeyExtension
NTRUKeyExtension ::= CHOICE {
keyID [0] IMPLICIT INTEGER,
...}
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EESS1v1-SVES-Parameters ::= CHOICE {
degree Degree,
standardNTRUParameters StandardNTRUParameters,
explicitNTRUParameters ExplicitNTRUParameters,
externalParameters NULL
}
StandardNTRUParameters ::= OIDS.&id({NTRUParameters})
NTRUParameters OIDS ::= {
{ OID id-ees251ep1 }|
{ OID id-ees347ep1 }|
{ OID id-ees503ep1 },
...}
ExplicitNTRUParameters ::= SEQUENCE {
version Version,
degree INTEGER,
bigModulus INTEGER,
smallModulus SmallModulus,
mrgm NTRUMRGMAlgorithmIdentifier,
db INTEGER,
bvgm NTRUBVGMAlgorithmIdentifier,
...}
NTRUMRGMAlgorithmIdentifier ::=
AlgorithmIdentifier {{NTRUEESS1v1MRGMs}}
NTRUBVGMAlgorithmIdentifier ::=
AlgorithmIdentifier {{NTRUEESS1v1BVGMs}}
NTRUEESS1v1MRGMs ALGORITHM ::= {
{OID id-mrgm-ntru-1 PARMS NTRUMRGM1-params},
...}
NTRUMRGM1-params ::= NTRUHashAlgorithmIdentifier
NTRUHashAlgorithmIdentifier ::=
AlgorithmIdentifier {{NTRUEESS1v1Hashes}}
NTRUEESS1v1BVGMs ALGORITHM ::= {
{OID id-bvgm-ntru-1 PARMS NTRUBVGM1-params}|
{OID id-bvgm-ntru-2 PARMS NTRUBVGM2-params},
...}
NTRUBVGM1-params ::= SEQUENCE {
c INTEGER,
prng NTRUPRNGAlgorithmIdentifier,
dr INTEGER
}
NTRUBVGM2-params ::= SEQUENCE {
c INTEGER,
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Supplemental Algorithms and Identifiers March 2002
prng NTRUPRNGAlgorithmIdentifier,
dr1 INTEGER,
dr2 INTEGER,
dr3 INTEGER
}
NTRUPRNGAlgorithmIdentifier ::= AlgorithmIdentifier
{{NTRUEESS1v1PRNGs}}
END -- PKIXAlgorithmOIDTBD --
4. Security Considerations
This document is entirely concerned with security mechanisms. It is
based on the Internet X.509 Public Key Infrastructure Certificate
and CRL Profile [RFC 2459], IEEE P1363.1 [P1363.1] and EESS #1
[EESS#1] and the appropriate security considerations from those
documents apply.
5. Intellectual Property Rights
NTRU Cryptosystems, Inc. has been granted U.S. Patent No. 6,081,597,
which covers aspects of the NTRUEncrypt public-key encryption
scheme, and has applied for a patent (or patents) that covers the
NTRUSign public-key signature scheme. In addition, NTRU
Cryptosystems may have applied for additional patent coverage on
implementation techniques related to the use of NTRUEncrypt or
NTRUSign. This and any additional patent information will be sent
to the IETF.
The IETF takes no position regarding the validity or scope of any
intellectual property 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; neither does it represent that it
has made any effort to identify any such rights. Information on the
IETF's procedures with respect to rights in standards-track and
standards-related documentation can be found in BCP-11. Copies of
claims of rights made available for publication and any assurances
of licenses to be made available, or the result of an attempt made
to obtain a general license or permission for the use of such
proprietary rights by implementers or users of this specification
can be obtained from the IETF Secretariat.
The IETF invites any interested party to bring to its attention any
copyrights, patents or patent applications, or other proprietary
rights, which may cover technology that may be required to implement
the techniques in this document. Please address the information to
the IETF Executive Director.
6. Acknowledgements
The authors would like to thank Phil Griffin for his considerable
aid in the formulation of the ASN.1 structures for this document.
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Supplemental Algorithms and Identifiers March 2002
7. References
[EESS#1] Efficient Embedded Security Standards (EESS) #1:
Implementation Aspects of NTRU and NTRUSign, Draft Version 4, March
2002, Consortium for Efficient Embedded Security Standards,
Available at http://www.ceesstandards.org.
[FIPS180-1] FIPS PUB 180-1, Secure Hash Standard, Federal
Information Processing Standards Publication 180-1, U.S. Department
of Commerce/National Institute of Standards and Technology, National
Technical Information Service, Springfield, Virginia, April 17, 1995
(supersedes FIPS PUB 180). Available at
http://www.itl.nist.gov/div897/pubs/fip180-1.htm.
[FIPS180-2] Draft FIPS PUB 180-2, Secure Hash Standard, Federal
Information Processing Standards Publication 180-2, U.S. Department
of Commerce/National Institute of Standards and Technology, National
Technical Information Service, Springfield, Virginia, May 30, 2001
(draft available at http://csrc.nist.gov/encryption/shs/dfips-180-
2.pdf)
[FIPS186-2] FIPS PUB 186-2, Digital Signature Standard, Federal
Information Processing Standards Publication 186-2, U.S. Department
of Commerce/National Institute of Standards and Technology, National
Technical Information Service, Springfield, Virginia, 2000.
Available at http://csrc.nist.gov/publications/fips/fips186-
2/fips186-2.pdf
[IEEE1363] IEEE Std 1363-2000: IEEE Standard Specifications for
Public-Key Cryptography, IEEE Computer Society, New York, NY, August
2000, Institute of Electrical and Electronics Engineers
[P1363.1] IEEE Draft Standard P1363.1 D2: IEEE Standard
Specifications for Public-Key Cryptographic Techniques Based on Hard
Problems over Lattices, Draft 2, May 2001, Available at
http://grouper.ieee.org/groups/1363.
[PKIX-ALGS] L. Bassham, R. Housley, W. Polk, "Algorithms and
Identifiers for the Internet X.509 Public Key Infrastructure
Certificate and CRL Profile", draft-ietf-pkix-pkalgs-05.txt, October
2001
[RFC2026] S. Bradner, "The Internet Standards Process", IETF RFC
2026, October 1996
[RFC2119] S. Bradner, "Key Words for Use in RFCs to Indicate
Requirement Levels", IETF RFC 2119, March 1997
[RFC2459] R. Housley, W. Ford, W. Polk and D. Solo, "Internet X.509
Public Key Infrastructure Certificate and CRL Profile", IETF RFC
2459, January 1999
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NTRU Algorithms and Identifiers February 2002
Authors' Addresses
Ari Singer
NTRU
5 Burlington Woods Phone: 1-781-418-2500
Burlington, MA 01803, USA Email: asinger@ntru.com
William Whyte
NTRU
5 Burlington Woods Phone: 1-781-418-2500
Burlington, MA 01803, USA Email: wwhyte@ntru.com
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