RFC 6637

Internet Engineering Task Force (IETF)                         A. Jivsov
Request for Comments: 6637                          Symantec Corporation
Category: Standards Track                                      June 2012
ISSN: 2070-1721

              Elliptic Curve Cryptography (ECC) in OpenPGP


   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 and
   these Elliptic Curves.

Status of This Memo

   This is an Internet Standards Track document.

   This document is a product of the Internet Engineering Task Force
   (IETF).  It represents the consensus of the IETF community.  It has
   received public review and has been approved for publication by the
   Internet Engineering Steering Group (IESG).  Further information on
   Internet Standards is available in Section 2 of RFC 5741.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at

Copyright Notice

   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
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   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this 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.

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RFC 6637                     ECC in OpenPGP                    June 2012

Table of Contents

   1. Introduction ....................................................3
   2. Conventions used in This Document ...............................3
   3. Elliptic Curve Cryptography .....................................3
   4. Supported ECC Curves ............................................3
   5. Supported Public Key Algorithms .................................4
   6. Conversion Primitives ...........................................4
   7. Key Derivation Function .........................................5
   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 .................................................10
   12. Compatibility Profiles ........................................10
      12.1. OpenPGP ECC Profile ......................................10
      12.2. Suite-B Profile ..........................................11
           12.2.1. Security Strength at 192 Bits .....................11
           12.2.2. Security Strength at 128 Bits .....................11
   13. Security Considerations .......................................12
   14. IANA Considerations ...........................................14
   15. References ....................................................14
      15.1. Normative References .....................................14
      15.2. Informative References ...................................15
   16. Contributors ..................................................15
   17. Acknowledgment ................................................15

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1.  Introduction

   The OpenPGP protocol [RFC4880] supports RSA and DSA (Digital
   Signature Algorithm) 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",
   document are to be interpreted as described in [RFC2119].  Any
   implementation that adheres to the format and methods specified in
   this document is called a compliant application.  Compliant
   applications are a subset of the broader set of OpenPGP applications
   described in [RFC4880].  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.

   The National Security Agency (NSA) of the United States specifies ECC
   for use in its [SuiteB] 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, curve OID.  Section 11 describes in
   detail how this sequence of bytes is formed.

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5.  Supported Public Key Algorithms

   The supported public key algorithms are the Elliptic Curve Digital
   Signature Algorithm (ECDSA) [FIPS-186-3] and the 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 of this document.

   The following public key algorithm IDs are added to expand Section
   9.1 of [RFC4880], "Public-Key Algorithms":

          ID        Description of Algorithm
          --        --------------------------
          18        ECDH public key algorithm
          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

   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.

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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
   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 the compact
   representation of X, defined in Section 4.2 of [RFC6090].

8.  EC DH Algorithm (ECDH)

   The method is a combination of an 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.

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   The KDF parameters are encoded as a 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

         -  a one-octet size of the following field

         - the octets representing a 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 field in the ECDH public key, formatted as

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

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

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

         -  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 parameters 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 key-encryption key (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].

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   The input to the key wrapping method is the value "m" derived from
   the session key, as described in Section 5.1 of [RFC4880], "Public-
   Key Encrypted Session Key Packets (Tag 1)", except that the PKCS #1.5
   (Public-Key Cryptography Standards version 1.5) padding step is
   omitted.  The result is padded using the method described in [PKCS5]
   to the 8-byte granularity.  For example, the following AES-256
   session key, in 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, respectively, to provide
   the same number of octets, 40 total, as an input to the key wrapping

   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

   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.

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         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 of [RFC4880], "Sym. Encrypted Integrity
   Protected Data Packet (Tag 18)", a Modification Detection Code (MDC)
   MUST be used anytime the symmetric key is protected by ECDH.

9. Encoding of Public and Private Keys

   The following algorithm-specific packets are added to Section 5.5.2
   of [RFC4880], "Public-Key Packet Formats", 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:

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

         -  octets representing a curve OID, defined in Section 11

      o  MPI of an EC point representing a public key

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     Algorithm-Specific Fields for ECDH keys:

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

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

         -  the octets representing a curve OID, defined in
            Section 11

         -  MPI of an EC point representing a public key

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

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

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

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

         -  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.

   The following algorithm-specific packets are added to Section 5.5.3.
   of [RFC4880], "Secret-Key Packet Formats", 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 of [RFC4880], "Version 3 Signature Packet Format"
   defines signature formats.  No changes in the format are needed for

   Section 5.1 of [RFC4880], "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.

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   Algorithm-Specific Fields for ECDH:

      o an MPI of an 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 below 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]

   1.2.840.10045.3.1.7    8   2A 86 48 CE 3D 03 01 07   NIST curve P-256           5   2B 81 04 00 22            NIST curve P-384           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 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, as
   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.

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

12.2.1.  Security Strength at 192 Bits

   To achieve the security strength of 192 bits, [SuiteB] 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 an [RFC4880] session key used for message encryption
   must be AES-256.  The hash algorithm restriction means 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.

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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

   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 the 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.  A stronger KDF hash algorithm or
   AES KEK algorithm MAY be used for a given ECC curve.

   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

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   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 infeasible.  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

   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
   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 a 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 of [RFC4880], "Iterated and Salted S2K".

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   Side channel attacks are a concern when a compliant application's use
   of the 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 the ECC point
   addition and doubling operations.

14.  IANA Considerations

   Per this document, IANA has assigned an algorithm number from the
   "Public Key Algorithms" range (or the "name space" in the terminology
   of [RFC5226]) of the "Pretty Good Privacy (PGP)" registry, created by
   [RFC4880].  Two ID numbers have been assigned, as defined in Section
   5.  The first one, value 19, is already designated for ECDSA and is
   currently unused, while the other one, value 18, is new.

15.  References

15.1.  Normative References

   [RFC2119]        Bradner, S., "Key words for use in RFCs to Indicate
                    Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC4880]        Callas, J., Donnerhacke, L., Finney, H., Shaw, D.,
                    and R. Thayer, "OpenPGP Message Format", RFC 4880,
                    November 2007.

   [SuiteB]         National Security Agency, "NSA Suite B
                    Cryptography", March 11, 2010,

   [FIPS-186-3]     National Institute of Standards and Technology, U.S.
                    Department of Commerce, "Digital Signature
                    Standard", FIPS 186-3, June 2009.

   [NIST-SP800-56A] Barker, E., Johnson, D., and M. Smid,
                    "Recommendation for Pair-Wise Key Establishment
                    Schemes Using Discrete Logarithm Cryptography", NIST
                    Special Publication 800-56A Revision 1, March 2007.

   [FIPS-180-3]     National Institute of Standards and Technology, U.S.
                    Department of Commerce, "Secure Hash Standard
                    (SHS)", FIPS 180-3, October 2008.

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RFC 6637                     ECC in OpenPGP                    June 2012

   [RFC3394]        Schaad, J. and R. Housley, "Advanced Encryption
                    Standard (AES) Key Wrap Algorithm", RFC 3394,
                    September 2002.

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

   [RFC5226]        Narten, T. and H. Alvestrand, "Guidelines for
                    Writing an IANA Considerations Section in RFCs", BCP
                    26, RFC 5226, May 2008.

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", RFC 6090,
                    February 2011.

   [SEC1]           Standards for Efficient Cryptography Group, "SEC 1:
                    Elliptic Curve Cryptography", September 2000.

16.  Contributors

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

17.  Acknowledgment

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

Author's Address

   Andrey Jivsov
   Symantec Corporation
   EMail: Andrey_Jivsov@symantec.com

Jivsov                       Standards Track                   [Page 15]