


HTTPAUTH Working Group                                           Y. Oiwa
Internet-Draft                                               H. Watanabe
Intended status: Experimental                                  H. Takagi
Expires: May 18, 2017                                         ITRI, AIST
                                                                K. Maeda
                                                              T. Hayashi
                                                                 Lepidum
                                                                 Y. Ioku
                                                              Individual
                                                       November 14, 2016


   Mutual Authentication Protocol for HTTP: KAM3-based Cryptographic
                               Algorithms
                   draft-ietf-httpauth-mutual-algo-07

Abstract

   This document specifies cryptographic algorithms for use with the
   Mutual user authentication method for the Hyper-text Transport
   Protocol (HTTP).

Status of this Memo

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

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at http://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on May 18, 2017.

Copyright Notice

   Copyright (c) 2016 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



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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.


Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
     1.1.  Terminology  . . . . . . . . . . . . . . . . . . . . . . .  3
   2.  Cryptographic Overview (Non-normative) . . . . . . . . . . . .  3
   3.  Authentication Algorithms  . . . . . . . . . . . . . . . . . .  4
     3.1.  Support Functions and Notations  . . . . . . . . . . . . .  5
     3.2.  Functions for Discrete Logarithm Settings  . . . . . . . .  6
     3.3.  Functions for Elliptic-Curve Settings  . . . . . . . . . .  7
   4.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . .  8
   5.  Security Considerations  . . . . . . . . . . . . . . . . . . .  9
     5.1.  General Implementation Considerations  . . . . . . . . . .  9
     5.2.  Cryptographic Assumptions and Considerations . . . . . . .  9
   6.  References . . . . . . . . . . . . . . . . . . . . . . . . . . 10
     6.1.  Normative References . . . . . . . . . . . . . . . . . . . 10
     6.2.  Informative References . . . . . . . . . . . . . . . . . . 10
   Appendix A.  (Informative) Group Parameters for Discrete
                Logarithm Based Algorithms  . . . . . . . . . . . . . 11
   Appendix B.  (Informative) Derived Numerical Values  . . . . . . . 13
   Appendix C.  (Informative) Draft Change Log  . . . . . . . . . . . 14
     C.1.  Changes in Httpauth WG Revision 06 . . . . . . . . . . . . 14
     C.2.  Changes in Httpauth WG Revision 05 . . . . . . . . . . . . 14
     C.3.  Changes in Httpauth WG revision 04 . . . . . . . . . . . . 14
     C.4.  Changes in Httpauth WG revision 03 . . . . . . . . . . . . 14
     C.5.  Changes in Httpauth WG revision 02 . . . . . . . . . . . . 14
     C.6.  Changes in Httpauth WG revision 01 . . . . . . . . . . . . 14
     C.7.  Changes in Httpauth WG revision 00 . . . . . . . . . . . . 14
     C.8.  Changes in HTTPAUTH revision 02  . . . . . . . . . . . . . 14
     C.9.  Changes in HTTPAUTH revision 01  . . . . . . . . . . . . . 15
     C.10. Changes in revision 02 . . . . . . . . . . . . . . . . . . 15
     C.11. Changes in revision 01 . . . . . . . . . . . . . . . . . . 15
     C.12. Changes in revision 00 . . . . . . . . . . . . . . . . . . 15
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 15











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1.  Introduction

   This document specifies algorithms for use with Mutual authentication
   protocol for Hyper-Text Transport Protocol (HTTP)
   [I-D.ietf-httpauth-mutual] (referred as the "core specification"
   hereafter).  The algorithms are based on "Augmented Password-based
   Authenticated Key Exchange" (Augmented PAKE) techniques.  In
   particular, it uses one of three key exchange algorithms defined in
   ISO 11770-4: "Key management - Mechanisms based on weak secrets"
   [ISO.11770-4.2006] as its basis.

   In very brief summary, Mutual authentication protocol exchanges four
   values, K_c1, K_s1, VK_c and VK_s, to perform authenticated key
   exchanges, using the password-derived secret pi and its "augmented
   version" J(pi).  This document defines the set of functions K_c1,
   K_s1, and J for a specific algorithm family.

   Please note that from the view of cryptographic literature, the
   original functionality of Augmented PAKE is separated into the
   functions K_c1 and K_s1 as defined in this draft, and the functions
   VK_c and VK_s, which are defined in Section 11 of
   [I-D.ietf-httpauth-mutual] as "default functions".  For the purpose
   of security analysis, please also refer to these functions.

1.1.  Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in
   [RFC2119].

   The term "natural numbers" refers to the non-negative integers
   (including zero) throughout this document.

   This document treats both the input (domain) and the output
   (codomain) of hash functions to be octet strings.  When a natural
   number output of hash function H is required, it will be notated like
   INT(H(s)).


2.  Cryptographic Overview (Non-normative)

   The cryptographic primitive used in this algorithm specification is
   based on a variant of augmented PAKE proposed by T. Kwon, called
   APKAS-AMP, originally submitted to IEEE P1363.2.  The general flow of
   the successful exchange is shown below, for informative purposes
   only.  The multiplicative notations are used for group operators, and
   all modulus operations for finite groups (mod q and mod r) are



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   omitted.

      C: S_c1 = random
      C: K_c1 = g^(S_c1)
                       ----- ID, K_c1 ----->
      C: t_1 = H1(K_c1)                S: t_1 = H1(K_c1)
                                       S: fetch J = g^pi by ID
                                       S: S_s1 = random
                                       S: K_s1 = (J * K_c1^(t_1))^(S_s1)
                       <----- K_s1 -----
      C: t_2 = H2(K_c1, K_s1)          S: t_2 = H2(K_c1, K_s1)
      C: z = K_s1^((S_c1 + t_2) / (S_c1 * t_1 + pi))
                                       S: z' = (K_c1 * g^(t_2))^(S_s1)
      (assumption at this point: z = z' if authentication succeeded)

      C: VK_c = H4(K_c1, K_s1, z)      S: VK_c' = H4(K_c1, K_s1, z')
                       ----- VK_c ------->
                                       S: assert(VK_c = VK_c')

      C: VK_s' = H3(K_c1, K_s1, z)     S: VK_s = H3(K_c1, K_s1, z')
                       <----- VK_s ------
      C: assert(VK_s = VK_s')

   Note that the concrete (binary) message formats (mapping to HTTP
   messages), as well as the formal definitions of equations for the
   latter two messages, are defined in core specification
   [I-D.ietf-httpauth-mutual].  The formal definitions for values
   corresponding to the first two messages are defined in the following
   sections.


3.  Authentication Algorithms

   This document specifies one family of APKAS-AMP based algorithm.
   This family consists of four authentication algorithms, which differ
   only in their underlying mathematical groups and security parameters.
   These algorithms do not add any additional parameters.  The tokens
   for these algorithms are

   o  iso-kam3-dl-2048-sha256: for the 2048-bit discrete logarithm
      setting with the SHA-256 hash function.

   o  iso-kam3-dl-4096-sha512: for the 4096-bit discrete logarithm
      setting with the SHA-512 hash function.

   o  iso-kam3-ec-p256-sha256: for the 256-bit prime-field elliptic-
      curve setting with the SHA-256 hash function.




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   o  iso-kam3-ec-p521-sha512: for the 521-bit prime-field elliptic-
      curve setting with the SHA-512 hash function.

   For discrete logarithm settings, the underlying groups are the 2048-
   bit and 4096-bit MODP groups defined in [RFC3526].  See Appendix A
   for the exact specifications of the groups and associated parameters.
   The hash functions H are SHA-256 for the 2048-bit group and SHA-512
   for the 4096-bit group, respectively, defined in FIPS PUB 180-2
   [FIPS.180-2.2002].  The hash iteration count nIterPi is 16384.  The
   representation of the parameters kc1, ks1, vkc, and vks is base64-
   fixed-number.

   For the elliptic-curve settings, the underlying groups are the
   elliptic curves over the prime fields P-256 and P-521, respectively,
   specified in the appendix D.1.2 of the FIPS PUB 186-4
   [FIPS.186-4.2013] specification.  The hash functions H, which are
   referenced by the core document, are SHA-256 for the P-256 curve and
   SHA-512 for the P-521 curve, respectively.  Cofactors of these curves
   are 1.  The hash iteration count nIterPi is 16384.  The
   representation of the parameters kc1, ks1, vkc, and vks is hex-fixed-
   number.

   Note: This algorithm is based on the Key Agreement Mechanism 3 (KAM3)
   defined in Section 6.3 of ISO/IEC 11770-4 [ISO.11770-4.2006] with a
   few modifications/improvements.  However, implementers should use
   this document as the normative reference, because the algorithm has
   been changed in several minor details as well as with major
   improvements.

3.1.  Support Functions and Notations

   The algorithm definitions use the support functions and notations
   defined below:

   The integers in the specification are in decimal by default, or in
   hexadecimal when prefixed with "0x".

   The functions named octet(), OCTETS(), and INT() are those defined in
   the core specification [I-D.ietf-httpauth-mutual].

   Note: The definition of OCTETS() is different from the function
   GE2OS_x in the original ISO specification, which takes the shortest
   representation without preceding zeros.

   All of the algorithms defined in this specification use the default
   functions defined in the core specification (defined in Section 11 of
   [I-D.ietf-httpauth-mutual]) for computing the values pi, VK_c and
   VK_s.



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3.2.  Functions for Discrete Logarithm Settings

   In this section, an equation (x / y mod z) denotes a natural number w
   less than z that satisfies (w * y) mod z = x mod z.

   For the discrete logarithm, we refer to some of the domain parameters
   by using the following symbols:

   o  q: for "the prime" defining the MODP group.

   o  g: for "the generator" associated with the group.

   o  r: for the order of the subgroup generated by g.

   The function J is defined as

   J(pi) = g^(pi) mod q.

   The value of K_c1 is derived as

   K_c1 = g^(S_c1) mod q,

   where S_c1 is a random integer within range [1, r-1] and r is the
   size of the subgroup generated by g.  In addition, S_c1 MUST be
   larger than log(q)/log(g) (so that g^(S_c1) > q).

   The server MUST check the condition 1 < K_c1 < q-1 upon reception.

   Let an intermediate value t_1 be

   t_1 = INT(H(octet(1) | OCTETS(K_c1))),

   the value of K_s1 is derived from J(pi) and K_c1 as:

   K_s1 = (J(pi) * K_c1^(t_1))^(S_s1) mod q

   where S_s1 is a random number within range [1, r-1].  The value of
   K_s1 MUST satisfy 1 < K_s1 < q-1.  If this condition is not held, the
   server MUST reject the exchange.  The client MUST check this
   condition upon reception.

   Let an intermediate value t_2 be

   t_2 = INT(H(octet(2) | OCTETS(K_c1) | OCTETS(K_s1))),

   the value z on the client side is derived by the following equation:

   z = K_s1^((S_c1 + t_2) / (S_c1 * t_1 + pi) mod r) mod q.



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   The value z on the server side is derived by the following equation:

   z = (K_c1 * g^(t_2))^(S_s1) mod q.

   (Note: the original ISO specification contained a message pair
   containing verification of value z along with the "transcript" of the
   protocol exchange.  This functionality is contained in the functions
   VK_c and VK_s.)

3.3.  Functions for Elliptic-Curve Settings

   For the elliptic-curve setting, we refer to some of the domain
   parameters by the following symbols:

   o  q: for the prime used to define the group.

   o  G: for the point defined with the underlying group called "the
      generator".

   o  h: for the cofactor of the group.

   o  r: for the order of the subgroup generated by G.

   The function P(p) converts a curve point p into an integer
   representing point p, by computing x * 2 + (y mod 2), where (x, y)
   are the coordinates of point p.  P'(z) is the inverse of function P,
   that is, it converts an integer z to a point p that satisfies P(p) =
   z.  If such p exists, it is uniquely defined.  Otherwise, z does not
   represent a valid curve point.

   The operator + indicates the elliptic-curve group operation, and the
   operation [x] * p denotes an integer-multiplication of point p: it
   calculates p + p + ... (x times) ... + p.  See the literature on
   elliptic-curve cryptography for the exact algorithms used for those
   functions (e.g.  Section 3 of [RFC6090], which uses different
   notations, though). 0_E represents the infinity point.  The equation
   (x / y mod z) denotes a natural number w less than z that satisfies
   (w * y) mod z = x mod z.

   The function J is defined as

   J(pi) = [pi] * G.

   The value of K_c1 is derived as

   K_c1 = P(K_c1'), where K_c1' = [S_c1] * G,

   where S_c1 is a random number within range [1, r-1].  The server MUST



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   check that the value of received K_c1 represents a valid curve point,
   and [h] * K_c1' is not equal to 0_E.

   Let an intermediate integer t_1 be

   t_1 = INT(H(octet(1) | OCTETS(K_c1))),

   the value of K_s1 is derived from J(pi) and K_c1' = P'(K_c1) as:

   K_s1 = P([S_s1] * (J(pi) + [t_1] * K_c1')),

   where S_s1 is a random number within range [1, r-1].  The value of
   K_s1 MUST represent a valid curve point and satisfy [h] * P'(K_s1) <>
   0_E. If this condition is not satisfied, the server MUST reject the
   exchange.  The client MUST check this condition upon reception.

   Let an intermediate integer t_2 be

   t_2 = INT(H(octet(2) | OCTETS(K_c1) | OCTETS(K_s1))),

   the value z on the client side is derived by the following equation:

   z = P([(S_c1 + t_2) / (S_c1 * t_1 + pi) mod r] * P'(K_s1)).

   The value z on the server side is derived by the following equation:

   z = P([S_s1] * (P'(K_c1) + [t_2] * G)).


4.  IANA Considerations

   This document defines four new tokens to be added to the "HTTP Mutual
   authentication algorithms" registry; iso-kam3-dl-2048-sha256,
   iso-kam3-dl-4096-sha512, iso-kam3-ec-p256-sha256 and
   iso-kam3-ec-p521-sha512, as follows:

   +-------------------------+-------------------------+---------------+
   | Token                   | Description             | Specification |
   +-------------------------+-------------------------+---------------+
   | iso-kam3-dl-2048-sha256 | ISO-11770-4 KAM3,       | This document |
   |                         | 2048-bit DL             |               |
   | iso-kam3-dl-4096-sha512 | ISO-11770-4 KAM3,       | This document |
   |                         | 4096-bit DL             |               |
   | iso-kam3-ec-p256-sha256 | ISO-11770-4 KAM3,       | This document |
   |                         | 256-bit EC              |               |
   | iso-kam3-ec-p521-sha512 | ISO-11770-4 KAM3,       | This document |
   |                         | 521-bit EC              |               |
   +-------------------------+-------------------------+---------------+



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5.  Security Considerations

   Please refer to the corresponding section of the core specification
   [I-D.ietf-httpauth-mutual] for algorithm-independent considerations.

5.1.  General Implementation Considerations

   o  During the exchange, the value VK_s, defined in
      [I-D.ietf-httpauth-mutual], MUST only be sent when the server has
      received a correct (expected) value of VK_c.  This is a
      cryptographic requirement, stated in [ISO.11770-4.2006].

   o  All random numbers used in these algorithms MUST be at least
      cryptographically computationally secure against forward and
      backward guessing attacks.

   o  Computation times of all numerical operations on discrete
      logarithm group elements and elliptic-curve points MUST be
      normalized and made independent of the exact values, to prevent
      timing-based side-channel attacks.

5.2.  Cryptographic Assumptions and Considerations

   The notices in this subsection are for those who analyze the security
   of this algorithm, and those who might want to make a derived work
   from this algorithm specification.

   o  handling of an invalid K_s1 value in the exchange has been changed
      from the original ISO specification.  The original specifies that
      the sender should retry with another random S_s1 value, while we
      specify that the exchange must be rejected.  This is due to an
      observation that this condition is less likely to result from the
      random error caused by an unlucky choice of S_s1, but more likely
      the result of a systematic failure from an invalid J(pi) value
      (even implying possible denial-of-service attacks).

   o  The usual construction of authenticated key exchange algorithms
      consists of a key exchange phase and a key verification phase.
      The latter usually involves some kinds of exchange transaction to
      be verified, to avoid security risks or vulnerabilities caused by
      mixing values from from two or more key exchanges.  In the design
      of the algorithms in this document, such a functionality is
      defined in a generalized manner in the core specification
      [I-D.ietf-httpauth-mutual] (see definitions of VK_c and VK_s).  If
      the algorithm defined above is used in other protocols, this
      aspect MUST be given careful consideration.





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   o  The domain parameters chosen and specified in this draft are based
      on a few assumptions.  In the discrete-logarithm setting, q has to
      be a safe prime ([(q - 1) / 2] must also be prime), and r should
      be the largest possible value [(q - 1) / 2].  In the elliptic-
      curve setting, r has to be prime.  Defining a variation of this
      algorithm using a different domain parameter SHOULD be attentive
      to these conditions.


6.  References

6.1.  Normative References

   [FIPS.180-2.2002]
              National Institute of Standards and Technology, "Secure
              Hash Standard", FIPS PUB 180-2, August 2002, <http://
              csrc.nist.gov/publications/fips/fips180-2/fips180-2.pdf>.

   [FIPS.186-4.2013]
              National Institute of Standards and Technology, "Digital
              Signature Standard (DSS)", FIPS PUB 186-4, July 2013, <htt
              p://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf>.

   [I-D.ietf-httpauth-mutual]
              Oiwa, Y., Watanabe, H., Takagi, H., Maeda, K., Hayashi,
              T., and Y. Ioku, "Mutual Authentication Protocol for
              HTTP", draft-ietf-httpauth-mutual-11 (work in progress),
              November 2016.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/
              RFC2119, March 1997,
              <http://www.rfc-editor.org/info/rfc2119>.

   [RFC3526]  Kivinen, T. and M. Kojo, "More Modular Exponential (MODP)
              Diffie-Hellman groups for Internet Key Exchange (IKE)",
              RFC 3526, DOI 10.17487/RFC3526, May 2003,
              <http://www.rfc-editor.org/info/rfc3526>.

6.2.  Informative References

   [ISO.11770-4.2006]
              International Organization for Standardization,
              "Information technology - Security techniques - Key
              management - Part 4: Mechanisms based on weak secrets",
              ISO Standard 11770-4, May 2006.

   [RFC6090]  McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic



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              Curve Cryptography Algorithms", RFC 6090, DOI 10.17487/
              RFC6090, February 2011,
              <http://www.rfc-editor.org/info/rfc6090>.


Appendix A.  (Informative) Group Parameters for Discrete Logarithm Based
             Algorithms

   The MODP group used for the iso-kam3-dl-2048-sha256 algorithm is
   defined by the following parameters.

   The prime is:

    q = 0xFFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
          29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
          EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
          E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
          EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
          C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
          83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
          670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
          E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
          DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
          15728E5A 8AACAA68 FFFFFFFF FFFFFFFF.

   The generator is:

    g = 2.

   The size of the subgroup generated by g is:

    r = (q - 1) / 2 =
        0x7FFFFFFF FFFFFFFF E487ED51 10B4611A 62633145 C06E0E68
          94812704 4533E63A 0105DF53 1D89CD91 28A5043C C71A026E
          F7CA8CD9 E69D218D 98158536 F92F8A1B A7F09AB6 B6A8E122
          F242DABB 312F3F63 7A262174 D31BF6B5 85FFAE5B 7A035BF6
          F71C35FD AD44CFD2 D74F9208 BE258FF3 24943328 F6722D9E
          E1003E5C 50B1DF82 CC6D241B 0E2AE9CD 348B1FD4 7E9267AF
          C1B2AE91 EE51D6CB 0E3179AB 1042A95D CF6A9483 B84B4B36
          B3861AA7 255E4C02 78BA3604 650C10BE 19482F23 171B671D
          F1CF3B96 0C074301 CD93C1D1 7603D147 DAE2AEF8 37A62964
          EF15E5FB 4AAC0B8C 1CCAA4BE 754AB572 8AE9130C 4C7D0288
          0AB9472D 45565534 7FFFFFFF FFFFFFFF.

   The MODP group used for the iso-kam3-dl-4096-sha512 algorithm is
   defined by the following parameters.

   The prime is:



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    q = 0xFFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
          29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
          EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
          E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
          EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
          C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
          83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
          670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
          E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
          DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
          15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64
          ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7
          ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B
          F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
          BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31
          43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7
          88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA
          2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
          287C5947 4E6BC05D 99B2964F A090C3A2 233BA186 515BE7ED
          1F612970 CEE2D7AF B81BDD76 2170481C D0069127 D5B05AA9
          93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34063199
          FFFFFFFF FFFFFFFF.

   The generator is:

    g = 2.

   The size of the subgroup generated by g is:























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    r = (q - 1) / 2 =
        0x7FFFFFFF FFFFFFFF E487ED51 10B4611A 62633145 C06E0E68
          94812704 4533E63A 0105DF53 1D89CD91 28A5043C C71A026E
          F7CA8CD9 E69D218D 98158536 F92F8A1B A7F09AB6 B6A8E122
          F242DABB 312F3F63 7A262174 D31BF6B5 85FFAE5B 7A035BF6
          F71C35FD AD44CFD2 D74F9208 BE258FF3 24943328 F6722D9E
          E1003E5C 50B1DF82 CC6D241B 0E2AE9CD 348B1FD4 7E9267AF
          C1B2AE91 EE51D6CB 0E3179AB 1042A95D CF6A9483 B84B4B36
          B3861AA7 255E4C02 78BA3604 650C10BE 19482F23 171B671D
          F1CF3B96 0C074301 CD93C1D1 7603D147 DAE2AEF8 37A62964
          EF15E5FB 4AAC0B8C 1CCAA4BE 754AB572 8AE9130C 4C7D0288
          0AB9472D 45556216 D6998B86 82283D19 D42A90D5 EF8E5D32
          767DC282 2C6DF785 457538AB AE83063E D9CB87C2 D370F263
          D5FAD746 6D8499EB 8F464A70 2512B0CE E771E913 0D697735
          F897FD03 6CC50432 6C3B0139 9F643532 290F958C 0BBD9006
          5DF08BAB BD30AEB6 3B84C460 5D6CA371 047127D0 3A72D598
          A1EDADFE 707E8847 25C16890 54908400 8D391E09 53C3F36B
          C438CD08 5EDD2D93 4CE1938C 357A711E 0D4A341A 5B0A85ED
          12C1F4E5 156A2674 6DDDE16D 826F477C 97477E0A 0FDF6553
          143E2CA3 A735E02E CCD94B27 D04861D1 119DD0C3 28ADF3F6
          8FB094B8 67716BD7 DC0DEEBB 10B8240E 68034893 EAD82D54
          C9DA754C 46C7EEE0 C37FDBEE 48536047 A6FA1AE4 9A0318CC
          FFFFFFFF FFFFFFFF.


Appendix B.  (Informative) Derived Numerical Values

   This section provides several numerical values for implementing this
   protocol, derived from the above specifications.  The values shown in
   this section are for informative purposes only.

   +----------------+---------+---------+---------+---------+----------+
   |                | dl-2048 | dl-4096 | ec-p256 | ec-p521 |          |
   +----------------+---------+---------+---------+---------+----------+
   | Size of K_c1   | 2048    | 4096    | 257     | 522     | (bits)   |
   | etc.           |         |         |         |         |          |
   | hSize, Size of | 256     | 512     | 256     | 512     | (bits)   |
   | H(...)         |         |         |         |         |          |
   | length of      | 256     | 512     | 33      | 66      | (octets) |
   | OCTETS(K_c1)   |         |         |         |         |          |
   | etc.           |         |         |         |         |          |
   | length of kc1, | 344 *   | 684 *   | 66      | 132     | (octets) |
   | ks1 param.     |         |         |         |         |          |
   | values.        |         |         |         |         |          |
   | length of vkc, | 44 *    | 88 *    | 64      | 128     | (octets) |
   | vks param.     |         |         |         |         |          |
   | values.        |         |         |         |         |          |




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   | minimum        | 2048    | 4096    | 1       | 1       |          |
   | allowed S_c1   |         |         |         |         |          |
   +----------------+---------+---------+---------+---------+----------+

   (The numbers marked with an * do not include any enclosing quotation
   marks.)


Appendix C.  (Informative) Draft Change Log

C.1.  Changes in Httpauth WG Revision 06

   o  Authors' addresses updated.

C.2.  Changes in Httpauth WG Revision 05

   o  Several comments from reviewers are reflected to the text.

C.3.  Changes in Httpauth WG revision 04

   o  Authors address updated.

C.4.  Changes in Httpauth WG revision 03

   o  IANA registration information added.

C.5.  Changes in Httpauth WG revision 02

   o  No technical changes: references updated.

C.6.  Changes in Httpauth WG revision 01

   o  Changed behavior on failed generation of K_s1.

   o  Security considerations updated.

C.7.  Changes in Httpauth WG revision 00

   o  Added a note on the choice of elliptic curves.

C.8.  Changes in HTTPAUTH revision 02

   o  Added nIterPi parameter to adjust to the changes to the core
      draft.

   o  Added a note on the verification of exchange transaction.





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C.9.  Changes in HTTPAUTH revision 01

   o  Notation change: integer output of hash function will be notated
      as INT(H(*)), changed from H(*).

C.10.  Changes in revision 02

   o  Implementation hints in appendix changed (number of characters for
      base64-fixed-number does not contain double-quotes).

C.11.  Changes in revision 01

   o  Parameter names renamed.

   o  Some expressions clarified without changing the value.

C.12.  Changes in revision 00

   The document is separated from the revision 08 of the core
   documentation.


Authors' Addresses

   Yutaka Oiwa
   National Institute of Advanced Industrial Science and Technology
   Information Technology Research Institute
   Tsukuba Central 1
   1-1-1 Umezono
   Tsukuba-shi, Ibaraki
   JP

   Email: y.oiwa@aist.go.jp


   Hajime Watanabe
   National Institute of Advanced Industrial Science and Technology
   Information Technology Research Institute
   Tsukuba Central 1
   1-1-1 Umezono
   Tsukuba-shi, Ibaraki
   JP

   Email: h-watanabe@aist.go.jp







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   Hiromitsu Takagi
   National Institute of Advanced Industrial Science and Technology
   Information Technology Research Institute
   Tsukuba Central 1
   1-1-1 Umezono
   Tsukuba-shi, Ibaraki
   JP

   Email: takagi.hiromitsu@aist.go.jp


   Kaoru Maeda
   Lepidum Co. Ltd.
   Village Sasazuka 3, Suite #602
   1-30-3 Sasazuka
   Shibuya-ku, Tokyo
   JP

   Email: maeda@lepidum.co.jp


   Tatsuya Hayashi
   Lepidum Co. Ltd.
   Village Sasazuka 3, Suite #602
   1-30-3 Sasazuka
   Shibuya-ku, Tokyo
   JP

   Email: hayashi@lepidum.co.jp


   Yuichi Ioku
   Individual

   Email: mutual-work@ioku.org
















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