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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                                    Symantec Corporation
Intended status: Internet Draft                     September 18, 2010
Expires: March 17, 2011




                               ECC in OpenPGP
                      draft-jivsov-openpgp-ecc-06.txt

Status of this Memo

   This Internet-Draft is submitted to IETF in full conformance with
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   This Internet-Draft will expire on March 17, 2011.

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   Copyright (c) 2009 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

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   document must include Simplified BSD License text as described in
   Section 4.e of the Trust Legal Provisions and are provided without
   warranty as described in the Simplified BSD License.

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.

Table of Contents
   1. Introduction.................................................2
   2. Conventions used in this document............................2
   3. Elliptic Curve Cryptography..................................3
   4. Supported ECC curves.........................................3
   5. Supported public key algorithms..............................3
   6. Conversion primitives........................................4
   7. Key Derivation Function......................................4
   8. EC DH Algorithm (ECDH).......................................5
   9. Encoding of public and private keys..........................7
   10. Data encoding with public keys..............................8
   11. ECC curve OID...............................................9
   12. Compatibility profiles......................................9
      12.1. OpenPGP ECC profile....................................9
      12.2. Suite-B profile.......................................10
         12.2.1. Secret information...............................10
         12.2.2. Top Secret information...........................10
   13. Security Considerations....................................10
   14. IANA Considerations........................................12
   15. Normative references.......................................12

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).

2. 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].





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   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.

3. Elliptic Curve Cryptography

   This specification establishes the minimum set of Elliptic Curve
   Cryptography (ECC) public key parameters and cryptographic methods
   that will likely satisfy the widest range of platforms and
   applications and facilitate interoperability.  It adds a more
   efficient method for applications to balance the overall level of
   security with any AES algorithm specified in [RFC4880] than by
   simply increasing the size of RSA keys.

   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.  This specification
   includes algorithms required by Suite B, so it would be possible to
   build a Suite B compatible implementation based on a subset of
   [RFC4880] and this specification.

4. 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".

   The named curves are referenced as a sequence of bytes in this
   specification, called throughout this document as Curve OID.
   Section 11 describes in details how this sequence of bytes is
   formed.

5. 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 8.

   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:









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          ID        Description of algorithm

       [to be       ECDH public key algorithm
      ASSIGNED]
    presumably 18

          19        ECDSA public key algorithm



   Applications MUST support ECDSA and ECDH.

6. 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 another format.








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7. 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 based on any of
   the following hash functions specified by [FIPS 180-2]: SHA2-256,
   SHA2-384, SHA2-512.  See section 13 for the details regarding the
   choice of the hash function.

   For convenience, the synopsis of the encoding method is given below
   with significant simplifications applicable to the choice of hash
   function. However, [NIST SP800-56A] is the normative source of the
   definition.
     //   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
     //   Assumes that oBits <= 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;
     MB   = Hash ( 00 || 00 || 00 || 01 || ZB || P );

     return oBits leftmost bits of MB.


8. EC DH Algorithm (ECDH)

   The method is a combination of ECC Diffie-Hellman method to
   establish a shared secret, key derivation method to process the
   shared secret into a derived key, and a key wrapping method that
   uses the derived key to protect a session key used to encrypt a
   message.

   One-Pass Diffie-Hellman method C(1, 1, ECC CDH), defined in [NIST
   SP800-56A], MUST 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 7 is used, and
   KDF parameters specified below are used.

   Key derivation function parameters MUST be encoded as concatenation
   of the following 5 variable-length and fixed-length fields:





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   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 11

   o    a one-octet public key algorithm ID defined in section 5

   o    a variable-length field containing KDF parameters, identical to
        the corresponding filed in the ECDH public key, formatted as
        follows

          o   a one-octet size of the following fields; values 0 and 0xff
              are reserved for future extensions
          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 8 for details

   o    20 octets representing the UTF-8 encoding of the string
        "Anonymous Sender    "

   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 54 or 51.

   The key wrapping method is based on [RFC3394].  KDF produces the
   AES key that is used as KEK as specified in [RFC3394].  Refer to
   section 13 for the details regarding the choice of the KEK
   algorithm, which MUST be one of three AES algorithms.

   The input to the 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 result is padded using the method
   described in [PKCS5] to the 8-byte granularity.  For example, a
   following AES-256 session key, which 32 octets are denoted from k0
   to k31, is composed to form the following 40 octet sequence:

       09 k0 k1 ... k31 c0 c1 05 05 05 05 05




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   The octets c0 and c1 above denote the checksum.  This encoding
   allows the sender to obfuscate the size of the symmetric encryption
   key used to encrypt the data.  To do this the sender MAY use 21,
   13, and 5 bytes of padding for AES-128, AES-192, and AES-256,
   respectfully, to provide the same number of octets, 40 total, as an
   input to the key wrapping method.

   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 the 8-byte padded session key, 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, unless size obfuscation is used.

   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 || checksum || pkcs5_padding;
       curve_OID_len = (byte)len(curve_OID);
       Param = curve_OID_len || curve_OID || public_key_alg_ID || 03 ||
           01 || KDF_hash_ID || AES_alg_ID for AESKeyWrap ||
          "Anonymous Sender    " || 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.



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9. 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 11

        o   MPI of EC point representing public key

        o   a variable-length field containing KDF parameters,
            formatted as follows

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

              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 used for message
                  encryption; see section 8 for details

     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 11

        o   MPI of EC point representing public key

   As an implementation note, observe that the ECDH public key fields
   are the super-set of the ECDH key fields.






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   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

10. 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 8.

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

        o   a one octet size, followed by a symmetric key encoded
            using the method described in section 8.

11. 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:

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

   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




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   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 first entry in
   the table above is constructed by omitting the first two octets.

12. Compatibility profiles

12.1. 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 11.  Application MUST implement SHA2-256 and SHOULD
   implement SHA2-512.  Application MUST implement AES-128 and SHOULD
   implement AES-256.
   Application SHOULD follow section 13 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   symmetric algorithm used for message encryption.

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

12.2. 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 additional security
   restrictions unspecified, such as matching assigned security level
   of information to authorized recipients or interoperability
   concerns arising from fewer allowed algorithms in [Suite B] than
   allowed by [RFC4880].

12.2.1. 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 based on SHA2-256 or
   SHA2-384.

   Note that the most secure algorithm applicable to each of 3
   categories above is listed in the section 12.2.2.



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12.2.2. Top Secret information

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

13. 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 balanced
   public key security which is compatible with symmetric key strength
   for 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.

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

   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 lead to 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.









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   Curve name          Recommended KDF      Recommended KEK
                       hash 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
   added to a key.  It is generally advisable to have a symmetric
   algorithm of strength matching the public key at the head of the
   key preference list.

   Often encryption to multiple recipients results in an unordered
   intersection subset.  For example, given two recipients, if the
   first recipient's set is {A, B} and the 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
   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.





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   SHA-1 MUST NOT be used for ECDSA or with KDF in 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].

14. 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 5.  The first one with value 19 is
   already designated for ECDSA and currently unused, while another
   one is new (and suggested to be 18; there is an implementation
   advantage in having consecutive ID values for two complementary
   algorithms).

15. Normative references

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

   [Suite B] NSA, US Government, NSA Suite B Cryptography, March 11,
   2010,
   http://www.nsa.gov/ia/programs/suiteb_cryptography/index.shtml

   [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)", October 5, 2001

   [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", August 1, 2002

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

   [PKCS5] RSA Laboratories, "PKCS #5 v2.0: Password-Based
   Cryptography Standard", March 25, 1999



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   [RFC2434] Narten, T., Alvestrand, H., "Guidelines for Writing IANA
   Considerations Section in RFCs", October 1998

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.
Author's Address

   Andrey Jivsov
   Symantec Corporation
   Email: Andrey_Jivsov@symantec.com
































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