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Versions: 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 RFC 6637

Network Working Group                                         A. Jivsov
Internet Draft                                          PGP Corporation
Intended status: Internet Draft                          April 28, 2008
Expires: October 25, 2008

                               ECC in OpenPGP

Status of this Memo

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Copyright Notice

   Copyright (C) The IETF Trust (2008).

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   This document proposes an Elliptic Curve Cryptography extension to
   the OpenPGP public key format and specifies three Elliptic Curves
   that enjoy broad support by other standards, including NIST
   standards.  The document aims to standardize an optimal but narrow
   set of parameters for best interoperability and it does so within
   the framework it defines that can be expanded in the future to
   allow more choices.

Conventions used in this document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   this document are to be interpreted as described in [RFC2119].
   An application MAY implement this draft; note that any [RFC2119]
   keyword within this draft applies to an OpenPGP application only if
   it chooses to implement this draft.

Table of Contents
   1. Introduction.................................................2
   2. Elliptic Curve Cryptography..................................3
   3. Supported ECC curves.........................................3
   4. Supported public key algorithms..............................3
   5. Conversion primitives........................................4
   6. Key Derivation Function......................................4
   7. EC DH Algorithm (ECDH).......................................5
   8. Encoding of public and private keys..........................7
   9. Data encoding with public keys...............................8
   10. ECC curve ID................................................8
   11. Compatibility profiles......................................9
      11.1. OpenPGP ECC profile....................................9
      11.2. Suite-B profile........................................9
         11.2.1. Secret information................................9
         11.2.2. Top Secret information............................9
      11.3. Interoperability with Suite-B profile..................9
   12. Security Considerations....................................10
   13. IANA Considerations........................................12
   14. Normative references.......................................13

1. Introduction

   The OpenPGP protocol [RFC4880] supports RSA and DSA public key
   formats.  This document defines the extension to incorporate

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   support for public keys that are based on Elliptic Curve
   Cryptography (ECC).

2. Elliptic Curve Cryptography

   This specification establishes the minimum set of Elliptic Curve
   Cryptography public key parameters and cryptographic methods that
   will likely satisfy the widest range of platforms and applications
   and facilitate interoperability.

   The set meets the requirements of Suite-B and includes an
   additional Elliptic Curve (EC) beyond Suite-B requirements,
   allowing users to match the level of security of every type of AES
   algorithm specified in [RFC4880].
   This document defines a path to expand ECC support in the future.

3. Supported ECC curves

   This standard defines three named prime field curves, that are
   defined in [FIPS 186-2] as "Curve P-256", "Curve P-384", "Curve

   To identify the named curves new ECC public key algorithm-specific
   parameter is introduced: the ECC curve ID, defined in section 10.

4. Supported public key algorithms

   Supported public key algorithms are Elliptic Curve Digital
   Signature Algorithm (ECDSA), defined in [FIPS 186-2], and Elliptic
   Curve Diffie-Hellman (ECDH), defined in section 7.

   Other compatible definition of ECDSA can be found in [SEC1].

   The section 9.1. Public-Key Algorithms of [RFC4880] is expanded to
   define the following public key algorithm IDs:

          ID        Description of algorithm

          19        ECDSA public key algorithm

       [to be       ECDH public key algorithm
    presumably 22

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   Applications MUST support ECDSA and ECDH.

5. Conversion primitives

   The method to convert an EC point to the octet string is defined in
   [SEC1].  This specification only defines uncompressed point
   format.  For convenience, the synopsis of the encoding method is
   given below, however, the [SEC1] is the normative source of the

   The point is encoded in MPI format.  The content of the MPI is the

        B = B0 || x || y
   where x and y are coordinates of the point P = (x, y), each encoded
   in big endian format and zero-padded to the underlying field size.

   B0 is a byte with following values:

    value description

      0   Point O.  In this case there is no x or y octets present.

      4   Uncompressed point.  x and y of EC point values follow.

   Note that point O shall not appear in a public or a private
   key.  Therefore, the size of the MPI payload is always curve_size*2
   + 3 bits.  For example, for "Curve P-256" the point is represented
   as a bit string of length 515 bits.

   If other conversion methods are defined in the future, the
   application MAY use them only when it is certain that every
   recipient of the data supports the other format.

6. Key Derivation Function

   A key derivation function (KDF) is necessary to implement EC
   encryption.  The Concatenation Key Derivation Function (Approved
   Alternative 1) defined in [NIST SP800-56A] is REQUIRED with the
   following restriction: the KDF hash function MAY be any of the
   following hash functions specified by [FIPS 180-2]: SHA2-256,
   SHA2-384, SHA2-512.  See section 12 for the details regarding the
   choice of the hash function.

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   For convenience, the synopsis of the encoding method is given
   below, however, [NIST SP800-56A] is the normative source of the

       //   Implements KDF( X, oBits, P );
       //   Input: point X = (x,y)
       //   oBits - the desired size of output
       //   hBits - the size of output of hash function Hash
       //   P - octets representing the parameters

       threshold = (oBits + hBits - 1) / hBits;
       // Convert the point P to octet string as defined in section 6:
       //   ZB' = 04 || x || y
       // and extract the x portion from ZB':
       ZB = x;
       do {
        C32 = (uint32)big_endian(counter);
        HB = Hash ( ZB || C32 || P );
        MB = MB || HB;
       } while( counter <= threshold );
       return oBits leftmost bits of MB

7. EC DH Algorithm (ECDH)

   The method is a combination of ECC Diffie-Hellman method to
   establish a shared secret and a key wrapping method that uses the
   shared secret to protect symmetric encryption key.

   One-Pass Diffie-Hellman method C(1, 1, ECC CDH), defined in [NIST
   SP800-56A], SHOULD be implemented with the following restrictions:
   ECC CDH primitive employed by this method is modified to always
   assume the cofactor as 1, KDF specified in section 6 is used, and
   KDF parameters specified below are used.

   Key derivation parameters MUST be encoded as 40 octets.  These 40
   octets are the result of concatenation of the following 7 fields,
   each of them is considered a fixed-length field of corresponding

   o    a one-octet curve ID defined in section 10

   o    a one-octet public key algorithm ID defined in section 4

   o    a one-octet value 01, reserved for future extensions

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  o    a one-octet hash function ID used in KDF; according to section
       6, this octet is 08 for SHA2-256, 09 for SHA2-384, or 10 for

  o    a one-octet algorithm ID for the symmetric algorithm used to
       wrap the symmetric key for message encryption; the method is
       defined later in this section

  o    15 octets representing the UTF-8 encoding of the string

  o    20 octets representing recipient encryption subkey or master key
       fingerprint, identifying the key material that is needed for
  The key wrapping method is based on [RFC3394].  KDF produces the
  AES key that is used as KEK according to [RFC3394].  Refer to
  section 12 for the details regarding the choice of the KEK
  algorithm, which MUST be one of three AES algorithms.

  The input to key wrapping method is the value "m" derived from the
  session key as described in section 5.1. Public-Key Encrypted
  Session Key Packets (Tag 1) of [RFC4880], except, the PKCS#1.5
  padding step is omitted.

  The output of the method consists of two fields.  The first field
  is the MPI with the ephemeral key used to establish shared
  secret.  The second field is composed of the following two fields:

  o    a one octet, encoding the size in octets of the result of the
       key wrapping method; the value 255 is reserved for future

  o    up to 254 octets representing the result of the key wrapping
       method applied to session key encoded as described above

  Note that for session key sizes 128, 192, and 256 bits the size of
  the result of the key wrapping method is, respectfully, 32, 40, and
  48 octets.

  For convenience, the synopsis of the encoding method is given
  below, however, this section, [NIST SP800-56A], and [RFC3394] are
  the normative sources of the definition.

      Obtain authenticated recipient public key R
      Generate ephemeral key pair {v, V=vG}
      Compute shared point S = vR;
      m = symm_alg_ID || session key.

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    Param = curve_ID || public_key_alg_ID || 01 || KDF_hash_ID ||
       AES_alg_ID for AESKeyWrap ||
       "AnonymousSender" || recipient_fingerprint;
    Z_len = key size for AES_alg_ID to be used with AESKeyWrap
    Compute Z = KDF( S, Z_len, Param );
    Compute C = AESKeyWrap( Z, m ) as per [RFC3394]
    VB = convert point V to octet string
    Output (MPI(VB) || len(C) || C).

   The decryption is the inverse of the method given.  Note that the
   recipient obtains the shared secret by calculating

    S = rV = rvG, where (r,R) is the recipient's key pair.

   Consistent with section 5.13 Sym. Encrypted Integrity Protected
   Data Packet (Tag 18) of [RFC4880], the MDC SHOULD be used anytime
   symmetric key is protected by ECDH.

8. Encoding of public and private keys

   The following algorithm-specific packets are added to Section 5.5.2
   Public-Key Packet Formats of [RFC4880] to support ECDH and ECDSA.

   This algorithm-specific portion is:

     Algorithm-Specific Fields for ECDH keys:

        o   a one-octet curve ID number, defined in section 10

        o   a one-octet value 01, reserved for future extension

        o   a one-octet hash function ID used with KDF

        o   a one-octet algorithm ID for the symmetric algorithm used
            to wrap the symmetric key for message encryption, see
            section 7 for details

        o   MPI of EC point representing public key

     Algorithm-Specific Fields for ECDSA keys:
       o a one-octet curve ID number, defined in section 10

        o   MPI of EC point representing public key

   The following algorithm-specific packets are added to section
   5.5.3. Secret-Key Packet Formats of [RFC4880] to support ECDH and

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     Algorithm-Specific Fields for ECDH or ECDSA secret keys:

        o    MPI of an integer representing the secret key, which is a
             scalar of the EC point

9. Data encoding with public keys

   Section 5.2.2. Version 3 Signature Packet Format defines signature
   formats.  No changes in format are needed for ECDSA.

   Section 5.1. Public-Key Encrypted Session Key Packets (Tag 1) is
   extended to support ECDH.  The following two fields are result of
   applying KDF, as described in section 7.

    Algorithm Specific Fields for ECDH:
       o an MPI of EC point representing ephemeral public key

        o    a one octet size, followed by symmetric key encoded using
             the method described in section [RFC3394].

10. ECC curve ID

   The parameter ECC curve ID is an integer that defines the named

       ID       Curve description                   Curve name

        0       Reserved

        1       NIST Curve P-256 [FIPS 186-2]       "NIST P256"

        2       NIST Curve P-384 [FIPS 186-2]       "NIST P384"

        3       NIST Curve P-521 [FIPS 186-2]       "NIST P521"

     100-110    Private/Experimental curves

       255      Reserved for future expansion

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11. Compatibility profiles

11.1. OpenPGP ECC profile

   Application MUST implement curve with ID 1, MAY implement curve
   with ID 2, and SHOULD implement curve with ID 3, defined in section
   10.  Application MUST implement SHA2-256 and SHOULD implement
   SHA2-512.  Application MUST implement AES-128 and SHOULD implement

   Application SHOULD follow section 12 regarding the choice of the
   following algorithms for each curve

   o   the KDF hash algorithm
   o   KEK algorithm

   o   message digest algorithm and hash algorithm used in key

   o   message encryption symmetric algorithm.

   It is recommended that the chosen symmetric algorithm for message
   encryption be no less secure than the KEK algorithm.

11.2. Suite-B profile

   A subset of algorithms allowed by this specification can be used to
   achieve NSA Suite-B compatibility.

11.2.1. Secret information

   Applications MUST use curve ID 1.  KEK SHOULD be used with AES-128,
   but MAY be used with AES-256.  SHA2-256 SHOULD be used for KDF, but
   SHA2-384 MAY be used for KDF.

11.2.2. Top Secret information

   Application MUST use curve ID 2.  KEK MUST be used with
   AES-256.  SHA2-384 MUST be used for KDF.

11.3. Interoperability with Suite-B profile

   For brevity, in this section applications complying with [RFC4880]
   and OpenPGP profile defined in section 11.1 are called compliant
   with OpenPGP and ECC specifications.

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   The set of symmetric key encryption, hash, and public key
   algorithms allowed by Suite-B is a subset of algorithms allowed by
   OpenPGP and ECC specifications.  Care must be taken to ensure
   interoperability between applications implementing OpenPGP and ECC
   and applications following Suite-B.  Encryption to multiple
   recipients is one example in which incompatibilities are possible.
   According to [RFC4880], even though there is no shared symmetric
   encryption algorithm in the OpenPGP recipients' preferences, the
   specification requires TripleDES to be effectively in the
   intersection of the encryption preferences.  TripleDES as implicit
   default is inherited from [RFC4880] by this specification to
   improve interoperability.

   While TripleDES ensures interoperability between applications
   complaint with OpenPGP and ECC specifications, it doesn't help
   interoperability with Suite-B profile.  Suppose TripleDES is the
   only shared algorithm within a set of recipients.  If Suite-B
   compliant recipient is added to the mentioned recipient set, the
   sender SHALL NOT send out a message.  This is because TripleDES is
   excluded from Suite-B and sending out two copies of the same
   message, one encrypted with TripleDES and another with AES-128 or
   AES-256, would mean that the same information that must have been
   protected with Suite-B compliant algorithm was protected instead
   with non-compliant TripleDES.  This restriction covers other cases
   in which none of recipients' shared algorithms are allowed by
   Suite-B.  One of available methods to a recipient to help ensure
   interoperability with Suite-B is to include one of two Suite-B
   symmetric algorithms, AES-128 or AES-256, or both, in the set of
   preferred algorithms.

   Only hash algorithms defined in section 11.2 must be used in key
   certifications, including key self-signatures, and in message
   digests for Suite-B interoperability.

12. Security Considerations

   The curves proposed in this document correspond to the symmetric
   key sizes 128 bits, 192 bits, and 256 bits as described in the
   table below.  This allows OpenPGP application to offer security
   comparable with the strength of each AES algorithms allowed by

   The following table defines the hash and symmetric encryption
   algorithm that SHOULD be used with specific curve for ECDSA or
   ECDH.  Stronger hash algorithm or symmetric key algorithm MAY be
   used for a given ECC curve.  However, note that the increase in the

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  strength of the hash algorithm or symmetric key algorithm may not
  increase the overall security offered by the given ECC key.

   Curve Curve name      ECC        RSA         Hash size   Symmetric
   ID                    strength   strength,               key size

     1     "NIST P256"   256        3072        256         128

     2     "NIST P384"   384        7680        384         192

     3     "NIST P521"   521        15360       512         256

  Requirement levels indicated elsewhere in this document result in
  the effective support for the following combinations of algorithms
  in OpenPGP profile: MUST implement curve ID 1 / SHA2-256 / AES-128,
  SHOULD implement curve ID 3 / SHA2-512 / AES-256, MAY implement
  curve ID 2 / SHA2-384 / AES-256, among other allowed combinations.

  Consistent with the table above, the following table defines the
  KDF hash algorithm and AES KEK encryption algorithm that SHOULD be
  used with specific curve for ECDH.  Stronger KDF hash algorithm or
  KEK algorithm MAY be used for a given ECC curve.

   Curve   Curve name    Recommended KDF hash   Recommended KEK
   ID                    algorithm              encryption algorithm

      1    "NIST P256"   SHA2-256               AES-128

      2    "NIST P384"   SHA2-384               AES-192

      3    "NIST P521"   SHA2-512               AES-256

  Applications SHOULD implement, advertise through key preferences,
  and use in compliance with [RFC4880] strongest algorithms specified
  in this document.

  Note that [RFC4880] symmetric algorithm preference list may
  restrict the use of balanced strength of symmetric key algorithms
  for corresponding public key.  For example, the presence of

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   symmetric key algorithms and their order in key preference list
   affects the choices available to encoding side for compliance with
   the table above.  Therefore, applications need to be concerned with
   this compliance throughout the life of the key, starting
   immediately after key generation when the key preferences are first
   added to a key.  It is generally advisable to have at the head of
   the key preference list a symmetric algorithm of strength
   corresponding to the public key.

   Often encryption to multiple recipients results in an unordered
   intersection subset.  For example, given two recipients, if first
   recipient's set is {A, B} and second's is {B, A}, the intersection
   is unordered set of two algorithms A and B.  In this case
   application SHOULD choose stronger encryption algorithm.
   Resource constraint, such as limited computational power, is the
   likely reason why an application might prefer to use weakest
   algorithms.  On the other side of the spectrum are applications
   that can implement every algorithm defined in this document.  Most
   of applications are expected to fall into either of two
   categories.  An application in the second or strongest category
   SHOULD prefer AES-256 to AES-192.

   While some statements in this specification refer to TripleDES
   algorithm, this is only done to help interoperability with existing
   application and already generated keys; AES-256 is the recommended
   alternative to TripleDES in all circumstances when AES-256 is

   SHA-1 MUST NOT be used for ECDSA or as part of ECDH method.

   MDC MUST be used when symmetric encryption key is protected by
   ECDH.  None of the ECC methods described in this document are
   allowed with deprecated V3 keys.  The application MUST only use
   Iterated and Salted S2K to protect private keys, as defined in
   section Iterated and Salted S2K of [RFC4880].

13. IANA Considerations

   This document asks IANA to assign an algorithm number from OpenPGP
   Public-Key Algorithms range, or "name space" in the terminology of
   [RFC2434], that was created by [RFC4880].  Two ID numbers are
   requested, as defined in section 4.  The first one with value 19 is
   already designated for ECDSA and currently unused, while another
   one is new (and expected to be 22).

   Finally, this document creates the name space for curve IDs defined
   in section 10.  Its initial content is defined in the section 10

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   and includes IDs for newly introduced curves, private space for
   experimental work, and the ID reserved for future name space
   expansion.  Future allocations in the registry will be done by IETF
   Expert Review process after general consensus between implementors
   of the standard is reached.  Most important motivation to add new
   curve to the registry is expected to be the need for stronger

14. Normative references

   [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
   Requirement Levels", March 1997

   [RFC4880] Callas, J., Donnerhacke, L., Finney, H., Shaw, D., and R.
   Thayer, "OpenPGP Message Format", November 2007
   [FIPS 186-2] US Dept. of Commerce / NIST, "DIGITAL SIGNATURE
   STANDARD (DSS)", 2001 October 5

   [SEC1] Certicom Research, "SEC 1: Elliptic Curve Cryptography",
   September 20, 2000

   [NIST SP800-56A] Elaine Barker, Don Johnson, and Miles Smid,
   "Recommendation for Pair-WiseKey Establishment Schemes Using
   Discrete Logarithm Cryptography (Revised)", March, 2007

   [FIPS 180-2] NIST, SECURE HASH STANDARD, 2002 August 1

   [RFC3394] J. Schaad, R. Housley, "Advanced Encryption Standard
   (AES) Key Wrap Algorithm", September 2002

   [RFC2434] Narten, T., Alvestrand, H., "Guidelines for Writing an
   IANA Considerations Section in RFCs",


   Hal Finney provided important criticism on compliance with [NIST
   SP800-56A] and NSA Suite-B, and pointed out a few other mistakes.


   The author would like to acknowledge the help of many individuals
   who kindly voiced their opinions on IETF OpenPGP Working Group
   mailing list and, in particular the help of Jon Callas, David
   Crick, Ian G. [to be continued]

Author's Address

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   Andrey Jivsov
   PGP Corporation
   Email: ajivsov@pgp.com

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