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                                                            E. Rescorla
INTERNET-DRAFT                                     Terisa Systems, Inc.
<draft-ietf-smime-x942-00.txt>         June 1998 (Expires December 1998)

                  Diffie-Hellman Key Agreement Method

Status of this Memo

   This document is an Internet-Draft.  Internet-Drafts are working
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Abstract

   This document standardizes one particular Diffie-Hellman variant,
   based on the ANSI X9.42 standard, developed by the ANSI X9F1 working
   group. An algorithm for converting the shared secret into an arbi-
   trary amount of keying material is provided. In addition, a standard
   group that meets the X9.42 requirements is provided.

TODO

   Redo the examples to match the new algorithm for computing K.  Actu-
   ally generate the group.

1.  Introduction

   In [DH76] Diffie and Hellman describe a means for two parties to
   agree upon a shared secret in such a way that the secret will be una-
   vailable to eavesdroppers. This secret may then be converted into
   cryptographic keying material for other (symmetric) algorithms.  A
   large number of minor variants of this process exist. This document
   describes one such variant, based on the ANSI X9.42 specification.






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1.1.  Discussion of this Draft

   This draft is being discussed on the "ietf-smime" mailing list.  To
   join the list, send a message to <ietf-smime-request@imc.org> with
   the single word "subscribe" in the body of the message.  Also, there
   is a Web site for the mailing list at <http://www.imc.org/ietf-
   smime/>.

1.2.  Requirements Terminology

   Keywords "MUST", "MUST NOT", "REQUIRED", "SHOULD", "SHOULD NOT" and
   "MAY" that appear in this document are to be interpreted as described
   in [RFC2119].

2.  Overview Of Method

   Diffie-Hellman key agreement requires that both the sender and reci-
   pient of a message have key pairs. By combining one's private key and
   the other party's public key, both parties can compute the same
   shared secret number. This number can then be converted into crypto-
   graphic keying material. That keying material is typically used as a
   key encryption key (KEK) to encrypt (wrap) a key (a message encryp-
   tion key -- MEK) which is in turn used to encrypt the message data.

2.1.  Key Agreement

   The first stage of the key agreement process is to compute a shared
   secret number ZZ (which will be constant for any pair of Diffie-
   Hellman keys). ZZ is then converted into a shared symmetric key. Note
   that the symmetric key will be different for each key agreement, due
   to the introduction of public random components.

2.1.1.  Generation of ZZ

   X9.42 defines that the shared secret ZZ is generated as follows:

           ZZ = g ^ (xb * xa) (mod p)

   Note that the individual parties actually perform the computations:

           ZZ = yb ^ xa    (mod p) = ya ^ xb  (mod p)

   where ^ denotes exponentiation
         ya is party a's public key; ya = g ^ xa (mod p)
         yb is party b's public key; yb = g ^ xb (mod p)
         xa is party a's private key
         xb is party b's private key
         p is a large prime



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         g is a generator for the integer group specified by p.
         (See Section 2.2 for criteria for keys and parameters)

   In CMS, the recipient's key is identified by the CMS RecipientIden-
   tifier, which points to the recipient's certificate.  The sender's
   key is identified using the OriginatorIdentifier field, either by
   reference to the sender's certificate or by inline inclusion of a
   key.

   Senders SHOULD verify the receiver's public key using the procedure
   of Section 2.1.5 before generating shared secrets. This check MAY be
   omitted if the CA which certified the key performs this check. Simi-
   larly, recipient's SHOULD verify the sender's public key before
   decrypting messages.

2.1.2.  Generation of Keying Material

   X9.42 provides an algorithm for generating an essentially arbitrary
   amount of keying material from ZZ. Our algorithm is derived from that
   algorithm by mandating some optional fields and omitting others.

           KM = H ( ZZ || OtherInfo)


   H is the message digest function SHA-1 [FIPS-180] ZZ is the shared
   key computed in Section 2.1.1 OtherInfo is the DER encoding of the
   following structure:

           OtherInfo ::= SEQUENCE {
             keyInfo KeySpecificInfo,
             pubInfo [2] OCTET STRING OPTIONAL,
           }

           KeySpecificInfo ::= SEQUENCE {
             algorithm OBJECT IDENTIFIER,
             counter OCTET STRING SIZE (4..4) }

   algorithm is the ASN.1 algorithm OID of the symmetric algorithm with which
     this KEK will be used.
   counter is a 32 bit number, represented in network byte order.
   Its initial value is 1, i.e. the byte sequence 00 00 00 01 (hex)
   pubInfo is a random string provided by the sender. In CMS, it is provided
   as a parameter in the UserKeyingMaterial field (a 512 bit byte string).

   Note that the only source of secret entropy in this computation is
   ZZ, so the security of this data is limited to the size of ZZ, even
   if more data than ZZ is generated. However, since pubInfo is dif-
   ferent for each message, a different KEK will be generated for each



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   message.

2.1.3.  KEK Computation

   Each key encryption algorithm requires a specific size key (n). The
   KEK is generated by mapping the left n-most bytes of KM onto the key.
   Consequently, for a DES [FIPS-46-1] key, which requires 64 bits of
   keying material, the algorithm is only run once, with a counter value
   of 1.  The first 64 bits of the output are parity adjusted and con-
   verted into a DES key.  For 3DES, which requires 192 bits of keying
   material, the algorithm must be run twice, once with a counter value
   of 1 (to generate K1', K2', and the first 32 bits of K3') and once
   with a counter value of 2 (to generate the last 32 bits of K3).
   K1',K2' and K3' are then parity adjusted to generate the 3 DES keys
   K1,K2 and K3.

2.1.4.  Keylengths for common algorithms

   Some common key encryption algorithms have KEKs of the following
   lengths.

           DES-ECB         64 bits
           3DES-EDE-ECB    192 bits
           RC2 (all)       256 bits


2.1.5.  Public Key Validation

   The following algorithm may be used to validate received public keys.

           1. Verify that y lies within the interval [2,p-1]. If it does not,
           the key is invalid.
           2. Compute y^q (mod p). If the result == 1, the key is valid.
           Otherwise the key is invalid.


2.1.6.  Example

   TBD

2.2.  Key and Parameter Requirements

   X9.42 requires that the group parameters be of the form p=jq + 1
   where q is a large prime of length m and j>=2. An algorithm for gen-
   erating primes of this form can be found in FIPS PUB 186-1[DSS] and
   ANSI, X9.30-1 1996 [X930], as well as in [X942].

   X9.42 requires that the private key x be in the interval [2^(m-1) +



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   1, (q - 2)]. x should be randomly generated in this interval. y is
   then computed by calculating g^x (mod p).  To comply with this draft,
   m MUST be >=128, (consequently, q and x MUST each be at least 128
   bits long). When symmetric ciphers stronger than DES are to be used,
   a larger m may be advisable.


2.2.1.  Common Group

   This standard specifies a common IETF DH group that satisfies the
   above parameters. Standards incorporating this key exchange method
   may choose to require support of this group.  TBD

Acknowledgements

   The Key Agreement method described in this document is based on work
   done by the ANSI X9F1 working group. The author wishes to extend his
   thanks for their assistance.

   The author also wishes to thank Russ Housley, Brian Korver, Mark
   Schertler, and Peter Yee for their expert advice and review.

References
   [CMS] Housley, R., "Cryptographic Message Syntax", draft-ietf-smime-cms-05.txt.

   [FIPS-46-1] Federal Information Processing Standards Publication (FIPS PUB)
        46-1, Data Encryption Standard, Reaffirmed 1988 January 22
        (supersedes FIPS PUB 46, 1977 January 15).

   [FIPS-81] Federal Information Processing Standards Publication (FIPS PUB)
        81, DES Modes of Operation, 1980 December 2.

   [FIPS-180] Federal Information Processing Standards Publication (FIPS PUB)
       180-1, "Secure Hash Standard", 1995 April 17.

   [X942] "Agreement Of Symmetric Keys Using Diffie-Hellman and MQV Algorithms",
       ANSI draft, 1998.

Security Considerations

   All the security in this system is provided by the secrecy of the
   private keying material. If either sender or recipient private keys
   are disclosed, all messages sent or received using that key are
   compromised. Similarly, loss of the private key results in an inabil-
   ity to read messages sent using that key.

Author's Address




Rescorla                                                         [Page 5]Internet-Draft    Diffie-Hellman Key Agreement Method


Eric Rescorla <ekr@terisa.com>
Terisa Systems, Inc.
4984 El Camino Real
Los Altos, CA 94022
Phone: (650) 919-1753














































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                           Table of Contents




1. Introduction ...................................................    1

1.1. Discussion of this Draft .....................................    2

1.2. Requirements Terminology .....................................    2

2. Overview Of Method .............................................    2

2.1. Key Agreement ................................................    2

2.1.1. Generation of ZZ ...........................................    2

2.1.2. Generation of Keying Material ..............................    3

2.1.3. KEK Computation ............................................    4

2.1.4. Keylengths for common algorithms ...........................    4

2.1.5. Public Key Validation ......................................    4

2.1.6. Example ....................................................    4

2.2. Key and Parameter Requirements ...............................    4

2.2.1. Common Group ...............................................    5

2.2.1. Acknowledgements ...........................................    5

2.2.1. References .................................................    5

Security Considerations ...........................................    5

Author's Address ..................................................    5


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