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Network Working Group                                          A. Jivsov
Internet Draft                                           PGP Corporation
Intended status: Internet Draft                             July 6, 2008
Expires: January 2, 2009




                               ECC in OpenPGP
                      draft-jivsov-openpgp-ecc-01.txt

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   This Internet-Draft will expire on January 2, 2009.

Copyright Notice

   Copyright (C) The IETF Trust (2008).








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Abstract

   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",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in
   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 OID...............................................8
   11. Compatibility profiles......................................9
      11.1. OpenPGP ECC profile....................................9
      11.2. Suite-B profile.......................................10
         11.2.1. Secret information...............................10
         11.2.2. Top Secret information...........................10
   12. Security Considerations....................................10
   13. IANA Considerations........................................12
   14. Normative references.......................................13

1. Introduction

   The OpenPGP protocol supports RSA and DSA public key formats.  This
   document defines the extension to incorporate support for public
   keys that are based on Elliptic Curve Cryptography (ECC).






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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.  This specification offers
   efficient cryptographic method for applications 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.

   National Security Agency (NSA) of the United States specifies ECC
   for use in its Suite B set of algorithms [Suite B].  This
   specification includes algorithms permitted by Suite B, so it would
   be possible to build a Suite B compatible implementation based on a
   subset of [RFC4880] and this specification.

3. Supported ECC curves

   This standard references three named prime field curves, which are
   defined in [FIPS 186-2] as "Curve P-256", "Curve P-384", and "Curve
   P-521".

   In data structures that this specification defines the named curves
   are referenced as a sequence of bytes, called throughout this
   specification as Curve OID. Section 10 describes in details how
   this sequence of bytes is formed.

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
      ASSIGNED]
    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
   definition.

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

        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.

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




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       //   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

       counter=1;
       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 ( C32 || ZB || P );
          MB = MB || HB;
          counter = counter + 1;
       } 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 concatenation of the
   following 7 fields, each of them, except the first one, is
   considered a fixed-length field of corresponding size:

   o    a variable-length field containing curve OID, formatted as
        follows

            o   a one-octet size of the following field

            o   octets representing curve OID, 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
      SHA2-512

  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
      "AnonymousSender"

  o   20 octets representing recipient encryption subkey or master key
      fingerprint, identifying the key material that is needed for
      decryption
  For three curves defined in this specification the size of the key
  derivation parameters sequence, defined above, is either 48 or 45.

  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
      extensions

  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.






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    Obtain authenticated recipient public key R
    Generate ephemeral key pair {v, V=vG}
    Compute shared point S = vR;
    m = symm_alg_ID || session key.
    curve_OID_len = (byte)len(curve_OID);
    Param = curve_OID_len || curve_OID || 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 variable-length field containing curve OID, formatted as
            follows
              o   a one-octet size of the following field; values 0 and
                  0xFF are reserved for future extensions

              o   octets representing curve OID, 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



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     Algorithm-Specific Fields for ECDSA keys:
       o a variable-length field containing curve OID, formatted as
          follows

              o   a one-octet size of the following field; values 0 and
                  0xFF are reserved for future extensions

              o   octets representing curve OID, 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
   ECDSA.
     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 7.

10. ECC curve OID

   The parameter curve OID is an array of octets that define the named
   curve.  The table bellow specifies the exact sequence of bytes for
   each named curve referenced in this specification:












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   ASN.1 Object          OID Curve OID bytes in         Curve name in
   Identifier            len hexadecimal representation [FIPS 186-2]

   1.2.840.10045.3.1.7   8   2A 86 48 CE 3D 03 01 07    NIST curve
                                                        P-256

   1.3.132.0.34          5   2B 81 04 00 22             NIST curve
                                                        P-384

   1.3.132.0.35          5   2B 81 04 00 23             NIST curve
                                                        P-521



   The sequence of octets in the third column is the result of
   applying Distinguished Encoding Rules (DER) to the ASN.1 Object
   Identifier with subsequent truncation.  The truncation removes two
   fields of encoded Object Identifier.  The first omitted field is
   one octet representing the Object Identifier tag and the second
   omitted field is the length of the Object Identifier body.  For
   example, the complete ASN.1 DER encoding for the NIST P-256 curve
   is "06 08 2A 86 48 CE 3D 03 01 07", from which the entry in the
   table above is constructed by omitting two first octets.

11. Compatibility profiles

11.1. OpenPGP ECC profile

   Application MUST implement NIST curve P-256, MAY implement NIST
   curve P-384, and SHOULD implement NIST curve P-521, defined in
   section 10.  Application MUST implement SHA2-256 and SHOULD
   implement SHA2-512.  Application MUST implement AES-128 and SHOULD
   implement AES-256.

   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
       certifications

   o   message encryption symmetric algorithm.






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   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 [Suite B] compatibility.  The references to [Suite B] in
   this document are informative.  This document is primarily
   concerned with format specification, leaving unspecified additional
   security restrictions, such as matching security level of
   information with authorized recipients or interoperability concerns
   arising from fewer allowed algorithms in [Suite B] than in
   [RFC4880].

11.2.1. Secret information
   Applications MUST use NIST curves P-256 or P-384.  KEK MUST be used
   with AES-128 or AES-256.  KDF MUST be used with SHA2-256 or
   SHA2-384.

   Note that the most secure algorithm in of each of 3 categories
   above is also listed in the section 11.2.2.

11.2.2. Top Secret information

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

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
   [RFC4880].

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










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

   NIST curve P-256   256           3072             256         128

   NIST curve P-384   384           7680             384         192

   NIST curve P-521   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 NIST curve P-256 / SHA2-256 /
  AES-128, SHOULD implement NIST curve P-521 / SHA2-512 / AES-256,
  MAY implement NIST curve P-384 / 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 name            Recommended KDF hash       Recommended KEK
                         algorithm                  encryption algorithm

   NIST curve P-256      SHA2-256                   AES-128

   NIST curve P-384      SHA2-384                   AES-192

   NIST curve P-521      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
  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





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   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
   available.

   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 3.7.1.3 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).

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



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   [Suite B] NSA, US Government, Fact Sheet NSA Suite B Cryptography,
   2005, http://www.nsa.gov/ia/Industry/crypto_suite_b.cfm

   [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",

Contributors

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

Acknowledgment

   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, Werner Koch. [to be continued]

Author's Address

   Andrey Jivsov
   PGP Corporation
   Email: ajivsov@pgp.com

Intellectual Property Statement

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   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
   it has made any independent effort to identify any such
   rights.  Information on the procedures with respect to rights in
   RFC documents can be found in BCP 78 and BCP 79.



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Copyright Statement

   Copyright (C) The IETF Trust (2008).

   This document is subject to the rights, licenses and restrictions
   contained in BCP 78, and except as set forth therein, the authors
   retain all their rights.




















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