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Network Working Group                                        A. Jivsov
Internet Draft                                    Symantec Corporation
Intended status: Standards                              April 11, 2012
Expires: October 8, 2012




                               ECC in OpenPGP
                      draft-jivsov-openpgp-ecc-14.txt

Abstract

   This document defines an Elliptic Curve Cryptography extension to
   the OpenPGP public key format and specifies three Elliptic Curves
   that enjoy broad support by other standards, including standards
   published by the US National Institute of Standards and
   Technology.  The document specifies the conventions for
   interoperability between compliant OpenPGP implementations that
   make use of this extension.

Status of this Memo

   This Internet-Draft is submitted to IETF in full conformance with
   the provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF), its areas, and its working groups.  Note that
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   The list of Internet-Draft Shadow Directories can be accessed at
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   This Internet-Draft will expire on October 8, 2012.

Copyright Notice


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   Copyright (c) 2012 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with
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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.


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..........................8
   10. Message encoding with public keys...........................9
   11. ECC curve OID...............................................9
   12. Compatibility profiles.....................................10
      12.1. OpenPGP ECC profile...................................10
      12.2. Suite-B profile.......................................10
         12.2.1. Security strength at 192 bits....................10
         12.2.2. Security strength at 128 bits....................11
   13. Security Considerations....................................11
   14. IANA Considerations........................................13
   15. References.................................................13
      15.1. Normative references..................................13
      15.2. Informative references................................14

1. Introduction

   The OpenPGP protocol [RFC4880] 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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   Any implementation that adheres to the format and methods specified
   in this document is called a compliant application.  Compliant
   applications is a subset of the the broader set of [RFC4880]
   OpenPGP applications.  Any [RFC2119] keyword within this document
   applies to compliant applications only.

3. Elliptic Curve Cryptography

   This document 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 document includes
   algorithms required by Suite B that are not present in [RFC4880].

   [KOBLITZ] provides a thorough introduction to ECC.

4. Supported ECC curves

   This document references three named prime field curves, defined in
   [FIPS 186-3] as "Curve P-256", "Curve P-384", and "Curve P-521".

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

5. Supported public key algorithms

   The supported public key algorithms are Elliptic Curve Digital
   Signature Algorithm (ECDSA) [FIPS 186-3] and Elliptic Curve Diffie-
   Hellman (ECDH).  A compatible specification of ECDSA is given in
   [RFC6090] as "KT-I Signatures" and in [SEC1]; ECDH is defined in
   section 8.

   The following public key algorithm IDs are added to expand the
   section 9.1. Public-Key Algorithms of [RFC4880]:









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          ID        Description of algorithm

       [to be       ECDH public key algorithm
      ASSIGNED]
    presumably 18

          19        ECDSA public key algorithm



   Compliant applications MUST support ECDSA and ECDH.

6. Conversion primitives

   This document only defines the uncompressed point format.  The
   point is encoded in the Multiprecision Integer (MPI) format
   [RFC4880].  The content of the MPI is the following:

      B = 04 || x || y

   where x and y are coordinates of the point P = (x, y), each encoded
   in the big endian format and zero-padded to the adjusted underlying
   field size.  The adjusted underlying field size is the underlying
   field size that is rounded up to the nearest 8-bit boundary.

   Therefore, the exact size of the MPI payload is 515 bits for "Curve
   P-256", 771 for "Curve P-384", and 1059 for "Curve P-521".

   Even though the zero point, also called the point at infinity, may
   occur as a result of arithmetic operations on points of an elliptic
   curve, it SHALL NOT appear in data structures defined in this
   document.

   This encoding is compatible with the definition given in [SEC1].

   If other conversion methods are defined in the future, a compliant
   application MUST NOT use a new format when in doubt that any
   recipient can support it.  Consider, for example, that while both
   the public key and the per-recipient ECDH data structure,
   respectively defined in sections 9 and 10, contain an encoded point
   field, the format changes to the field in section 10 only affect a
   given recipient of a given message.

7. Key Derivation Function

   A key derivation function (KDF) is necessary to implement the EC
   encryption.  The Concatenation Key Derivation Function (Approved
   Alternative 1) [NIST SP800-56A] with the KDF hash function that is



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   SHA2-256 [FIPS 180-3] or stronger is REQUIRED.  See section 12 for
   the details regarding the choice of the hash function.

   For convenience, the synopsis of the encoding method is given below
   with significant simplifications attributable to the restricted
   choice of hash functions in this document.  However, [NIST SP800-
   56A] is the normative source of the definition.

       //   Implements KDF( X, oBits, Param );
       //   Input: point X = (x,y)
       //   oBits - the desired size of output
       //   hBits - the size of output of hash function Hash
       //   Param - octets representing the parameters
       //   Assumes that oBits <= hBits
      // Convert the point X to the octet string, see section 6:
      //   ZB' = 04 || x || y
      // and extract the x portion from ZB'
      ZB = x;
      MB = Hash ( 00 || 00 || 00 || 01 || ZB || Param );
      return oBits leftmost bits of MB.
   Note that ZB in the KDF description above is is the compact
   representation of X, defined in section 4.2 of [RFC6090]

8. EC DH Algorithm (ECDH)

   The method is a combination of a ECC Diffie-Hellman method to
   establish a shared secret, a 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.

   The One-Pass Diffie-Hellman method C(1, 1, ECC CDH) [NIST SP800-56A]
   MUST be implemented with the following restrictions: the ECC CDH
   primitive employed by this method is modified to always assume the
   cofactor as 1, the KDF specified in section 7 is used, and the KDF
   parameters specified below are used.

   The KDF parameters are encoded as concatenation of the following 5
   variable-length and fixed-length fields, compatible with the
   definition of the OtherInfo bitstring [NIST SP800-56A]:

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

        o    a one-octet size of the following field

        o    the octets representing a curve OID, defined in section 11




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

   o    a variable-length field containing KDF parameters, identical to
        the corresponding field 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 extensions

          o   a one-octet hash function ID used with the 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    ", which is the octet sequence
         41 6E 6F 6E 79 6D 6F 75 73 20 53 65 6E 64 65 72 20 20 20 20

   o    20 octets representing a recipient encryption subkey or a master
        key fingerprint, identifying the key material that is needed for
        the decryption

   The size of the KDF pameters sequence, defined above, is either 54
   or 51 for the three curves defined in this document.

   The key wrapping method is described in [RFC3394].  KDF produces a
   symmetric key that is used as a KEK as specified in
   [RFC3394].  Refer to section 13 for the details regarding the
   choice of the KEK algorithm, which SHOULD be one of three AES
   algorithms.  Key wrapping and unwrapping is performed with the
   Default Initial Value of [RFC3394].

   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

   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.  For example, assuming that an AES
   algorithm is used for the session key, the sender MAY use 21, 13,
   and 5 bytes of padding for AES-128, AES-192, and AES-256,

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   respectively, 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 containing the ephemeral key used to establish the
   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, respectively, 32, 40, and
   48 octets, unless the 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 the authenticated recipient public key R
         Generate an ephemeral key pair {v, V=vG}
         Compute the 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 || KEK_alg_ID for AESKeyWrap || "Anonymous
         Sender    " || recipient_fingerprint;
         Z_len = the key size for the KEK_alg_ID used with AESKeyWrap
         Compute Z = KDF( S, Z_len, Param );
         Compute C = AESKeyWrap( Z, m ) as per [RFC3394]
         VB = convert point V to the 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], MDC MUST 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 ECDSA keys:
        o a variable-length field containing a 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 a curve OID, defined in section 11

        o   MPI of an EC point representing a public key

     Algorithm-Specific Fields for ECDH keys:

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

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

              o   the octets representing a 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 extensions

              o   a one-octet hash function ID used with a KDF

              o   a one-octet algorithm ID for the symmetric algorithm
                  used to wrap the symmetric key used for the message
                  encryption; see section 8 for details

   Observe that an ECDH public key is composed of the same sequence of
   fields that define an ECDSA key, plus the KDF parameters field.




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

10. Message encoding with public keys

   Section 5.2.2. Version 3 Signature Packet Format defines signature
   formats.  No changes in the 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 the result
   of applying the KDF, as described in section 8.

   Algorithm Specific Fields for ECDH:
       o an MPI of EC point representing an 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 a named
   curve.  The table bellow specifies the exact sequence of bytes for
   each named curve referenced in this document:

   ASN.1 Object          OID Curve OID bytes in         Curve name in
   Identifier            len hexadecimal                [FIPS 186-3]
                             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 the Distinguished Encoding Rules (DER) to the ASN.1 Object
   Identifier with subsequent truncation.  The truncation removes the
   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



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   example, the complete ASN.1 DER encoding for the NIST P-256 curve
   OID 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.  Only the truncated sequence of octets is the valid
   representation of a curve OID.

12. Compatibility profiles

12.1. OpenPGP ECC profile

   A compliant application MUST implement NIST curve P-256, MAY
   implement NIST curve P-384, and SHOULD implement NIST curve P-521,
   defined in section 11.  A compliant application MUST implement
   SHA2-256, and SHOULD implement SHA2-384 and SHA2-512.  A compliant
   application MUST implement AES-128 and SHOULD implement AES-256.

   A compliant application SHOULD follow section 13 regarding the
   choice of the following algorithms for each curve:

   o   the KDF hash algorithm

   o   the KEK algorithm

   o   the message digest algorithm and the hash algorithm used in the
       key certifications

   o   the 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 document 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. Security strength at 192 bits

   To achieve the security strength of 192 bits [Suite B] requires
   NIST curve P-384, AES-256, and SHA2-384.  The symmetric algorithm
   restriction means that the algorithm of KEK used for key wrapping
   in section 8 and a [RFC4880] session key used for message
   encryption must be AES-256.  The hash algorithm restriction means


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   that the hash algorithms of KDF and the [RFC4880] message digest
   calculation must be SHA-384.

12.2.2. Security strength at 128 bits

   The set of algorithms in section 12.2.1 is extended to allow NIST
   curve P-256, AES-128, and SHA2-256.

13. Security Considerations

   Refer to [FIPS 186-3] B.4.1 for the method to generate a uniformly
   distributed ECC private key.

   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 a compliant application to offer balanced
   public key security which is compatible with the symmetric key
   strength for each AES algorithm allowed by [RFC4880].

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



   This document explicitly discourages the use of algorithms other
   than AES as a KEK algorithm because backward compatibility of the
   ECDH format is not a concern.  The KEK algorithm is only used
   within the scope of a Public-Key Encrypted Session Key Packet,
   which represents an ECDH key recipient of a message.  Compare this
   with the algorithm used for the session key of the message, which
   MAY be different from a KEK algorithm.

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

   Note that the [RFC4880] symmetric algorithm preference list may
   make it impossible to use the balanced strength of symmetric key
   algorithms for a corresponding public key.  For example, the
   presence of the symmetric key algorithm IDs and their order in the
   key preference list affects the algorithm choices available to the
   encoding side, which in turn may make the adherence to the table
   above unfeasible.  Therefore, compliance with this specification is
   a concern throughout the life of the key, starting immediately
   after the key generation when the key preferences are first added
   to a key.  It is generally advisable to position a symmetric
   algorithm ID of strength matching the public key at the head of the
   key preference list.

   Encryption to multiple recipients often results in an unordered
   intersection subset.  For example, if the first recipient's set is
   {A, B} and the second's is {B, A}, the intersection is an unordered
   set of two algorithms A and B.  In this case a compliant
   application SHOULD choose the stronger encryption algorithm.

   Resource constraints, such as limited computational power, is a
   likely reason why an application might prefer to use the weakest
   algorithm.  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.  A




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   compliant application in the second, or strongest, category SHOULD
   prefer AES-256 to AES-192.

   SHA-1 MUST NOT be used with the ECDSA or the KDF in the 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.  A compliant 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].

   Side channel attacks are a concern when a compliant application's
   use of OpenPGP format can be modeled by a decryption or signing
   oracle model, for example, when an application is a network service
   performing decryption to unauthenticated remote users.  ECC scalar
   multiplication operations used in ECDSA and ECDH are vulnerable to
   side channel attacks.  Countermeasures can often be taken at the
   higher protocol level, such as limiting the number of allowed
   failures or time-blinding of the operations associated with each
   network interface.  Mitigations at the scalar multiplication level
   seek to eliminate any measurable distinction between ECC point
   addition and doubling operations.

14. IANA Considerations

   This document asks IANA to assign an algorithm number from the
   OpenPGP Public-Key Algorithms range, or the "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 is currently unused,
   while another one is new (and suggested to be 18; there is an
   implementation advantage in having consecutive ID values for the
   two complementary algorithms).

15. References

15.1. 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

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

   [FIPS 186-3] US Dept. of Commerce / NIST, "Digital Signature
   Standard (DSS)", June 2009

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

   [FIPS 180-3] NIST, "Secure Hash Standard (SHS)", October 2008

   [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

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

15.2. Informative references

   [KOBLITZ] N. Koblitz, "A course in number theory and cryptography",
   Chapter VI. Elliptic Curves, ISBN: 0-387-96576-9, Springer-Verlag,
   1987

   [RFC6090] McGrew, D., Igoe, K., and M. Salter, "Fundamental
   Elliptic Curve Cryptography Algorithms", February 2011,

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

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, Marko Kreen.

Author's Address

   Andrey Jivsov
   Symantec Corporation
   Email: Andrey_Jivsov@symantec.com







A. Jivsov              Expires October 8, 2012               [Page 14]


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