Internet Research Task Force                                  D. Harkins
Internet-Draft                                             HP Enterprise
Intended status: Informational                           January 2, 2017
Expires: July 6, 2017

                          Public Key Exchange


   This memo describes a password-authenticated protocol to allow two
   devices to exchange "raw" (uncertified) public keys and establish
   trust that the keys belong to their respective identities.

Status of This Memo

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

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   This Internet-Draft will expire on July 6, 2017.

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Requirements Language . . . . . . . . . . . . . . . . . .   3
     1.2.  Notation  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Properties  . . . . . . . . . . . . . . . . . . . . . . . . .   4
   3.  Assumptions . . . . . . . . . . . . . . . . . . . . . . . . .   5
   4.  Cryptographic Primitives  . . . . . . . . . . . . . . . . . .   5
   5.  Protocol Definition . . . . . . . . . . . . . . . . . . . . .   6
     5.1.  Exchange Phase  . . . . . . . . . . . . . . . . . . . . .   6
     5.2.  Commit/Reveal Phase . . . . . . . . . . . . . . . . . . .   7
   6.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   8
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .   8
   8.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   9
     8.1.  Normative References  . . . . . . . . . . . . . . . . . .   9
     8.2.  Informative References  . . . . . . . . . . . . . . . . .  10
   Appendix A.  Role-specific Elements . . . . . . . . . . . . . . .  10
     A.1.  ECC Role-specific Elements  . . . . . . . . . . . . . . .  11
       A.1.1.  Role-specific Elements for NIST p256  . . . . . . . .  11
       A.1.2.  Role-specific Elements for NIST p384  . . . . . . . .  12
       A.1.3.  Role-specific Elements for NIST p521  . . . . . . . .  13
       A.1.4.  Role-specific Elements for brainpool p256r1 . . . . .  15
       A.1.5.  Role-specific Elements for brainpool p384r1 . . . . .  15
       A.1.6.  Role-specific Elements for brainpool p512r1 . . . . .  16
     A.2.  FFC Role-specific Elements  . . . . . . . . . . . . . . .  17
       A.2.1.  Role-specific Elements for 2048-bit FFC group . . . .  18
       A.2.2.  Role-specific Elements for 3072-bit FFC group . . . .  19
       A.2.3.  Role-specific Elements for 4096-bit FFC group . . . .  21
       A.2.4.  Role-specific Elements for 8192-bit FFC group . . . .  24
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  30

1.  Introduction

   Many authenticated key exchange protocols allow for authentication
   using uncertified, or "raw", public keys.  Usually these
   specifications-- e.g.  [RFC7250] for TLS and [RFC7670] for IKEv2--
   assume keys are exchanged in some out-of-band mechanism.

   [RFC7250] further states that "the main security challenge [to using
   'raw' public keys] is how to associate the public key with a specific
   entity.  Without a secure binding between identifier and key, the
   protocol will be vulnerable to man-in-the- middle attacks."

   The Public Key Exchange (PKEX) is designed to fill that gap: it
   establishs a secure binding between exchanged public keys and
   identifiers, it provides proof-of-possession of the exchanged public
   keys to each peer, and it enables the establishment of trust in

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   public keys that can subsequently be used to faccilitate
   authentication in other authentication and key exchange protocols.

1.1.  Requirements Language

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   document are to be interpreted as described in RFC 2119 [RFC2119].

1.2.  Notation

   This memo describes a cryptographic exchange using sets of elements
   called groups.  Groups can be either traditional finite field or can
   be based on elliptic curves.  The public keys exchanged by PKEX are
   elements in a group.  Elements in groups are denoted in upper-case
   and scalar values are denoted with lower-case.  The generator of the
   group is G.

   When both the initator and responder use a similar, but unique, datum
   it is denoted by appending an "i" for initiator or "r" for responder,
   e.g. if each side needs an element C then the initiator's is Ci and
   the responder's is Cr.

   During the exchange, one side will generate data and the other side
   will attempt to reconstruct it.  The reconstructed data is "primed".
   That is, if the initiator generates C then when responder tries to
   reconstruct it, the responder will refer to it as C'.  Data that is
   directly sent and received is not primed.

   The following notation is used in this memo:

   C = A + B
       The "group operation" on two elements, A and B, that produces a
       third element, C.  For finite field cryptography this is the
       modular multiplication, for elliptic curve cryptography this is
       point addition.

   C = A - B
       The "group operation" on element A and the inverse of element B
       to produce a third element, C.  Inversion is defined such that
       the group operation on an element and its inverse results in the
       identity element, the value one (1) for finite field cryptography
       and the "point at infinity" for elliptic curve cryptography.

   C = a * B
       This denotes repeated application of the group operation to B--
       i.e.  B + B-- (a - 1) times.

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   a = H(b)
       A cryptographic hash function that takes data b of indeterminate
       length and returns a fixed sized digest a.

   a = F(B)
       A mapping function that takes an element and returns a scalar.
       For elliptic curve cryptography, F() returns the x-coordinate of
       the point B.  For finite field cryptography, F() is the identity

   a = KDF-b(c, d)
       A key derivation function that derives an output key a of length
       b from an input key c and context d.

   a = HMAC(b, c)
       A keyed MAC function that produces a digest a using key b and
       text c.

   a | b
       Concatentation of data a with data b.

       Authenticated-encryption of data a with key b and associated data
       (AD) that is authenticated but not encrypted c.

2.  Properties

   Subversion of PKEX involves an adversary being able to insert its own
   public key into the exchange without the exchange failing, resulting
   in one of the parties to the exchange believing the adversary's
   public key actually belongs to the protocol peer.

   PKEX has the following properties:

   o  An adversary is unable to subvert the exchange without knowing the

   o  An adversary is unable to discover the password through passive

   o  The only information exposed by an active attack is whether a
      single guess of the password is correct or not.

   o  Proof-of-possession of the private key is provided.

   o  At the end of the protocol, either trust is established in the
      peer's public key and the public key is bound to the peer's
      identity, or the exchange fails.

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3.  Assumptions

   Due to the nature of the exchange, only DSA ([DSS]) and ECDSA
   ([X9.62]) keys can be exchanged with PKEX.

   PKEX requires fixed elements that are unique to the particular role
   in the protocol, an initiator-specific element and a responder-
   specific element.  They need not be secret.  It is assumed that both
   parties know the role-specific elements for the particular group in
   which their key pairs were derived.  Techniques to generate role-
   specific elements, and generated elements for popular groups, are
   listed in Appendix A.1 and Appendix A.2.

   The authenticated-encryption algorithm provides deterministic "key
   wrapping".  To achieve this the AE scheme used in PKEX is AES-SIV as
   defined in [RFC5297].

   The KDF provides for the generation of a cryptographically strong
   secret key from an "imperfect" source of randomness.  To achieve this
   the KDF used in PKEX is the unsalted version of [RFC5869].

   The keyed MAC function is HMAC per [RFC2104].

   The following assumptions are made on PKEX:

   o  Only the peers involved in the exchange know the password.

   o  The peers' public keys are from the same group.

   o  The discrete logarithms of the public role-specific elements are
      unknown, and determining them is computationally infeasible.

4.  Cryptographic Primitives

   HKDF and HMAC require an underlying hash function and AES-SIV
   requires a key length.  To provide for consistent security the hash
   algorithm and key length depend on the group chosen to use with PKEX.

   For ECC, the hash algorithm and key length depends on the size of the
   prime defining the curve, p:

   o  SHA-256 and 256 bits: when len(p) <= 256

   o  SHA-384 and 384 bits: when 256 < len(p) <= 384

   o  SHA-512 and 512 bits: when 384 < len(p)

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   For FFC, the hash algorithm depends on the prime, p, defining the
   finite field:

   o  SHA-256 and 256 bits: when len(p) <= 2048

   o  SHA-384 and 384 bits: when 2048 < len(p) <= 3072

   o  SHA-512 and 512 bits: when 3072 < len(p)

5.  Protocol Definition

   PKEX is a balanced PAKE.  The identical version of the password is
   used by both parties.

   PKEX consists of two phases: exchange and commit/reveal.  It is
   described using the popular protocol participants, Alice (an
   initiator of PKEX), and Bob (a responder of PKEX).

   We denote Alice's role-specific element a Pi and Bob's as Pr.  The
   password is pw.  For simplicity, Alice's identity is "Alice" and
   Bob's identity is "Bob".  Alice's public key she wants to share with
   Bob is A and her private key is a, while Bob's public key he wants to
   share with Alice is B and his private key is b.

5.1.  Exchange Phase

   The Exchange phase is essentially the SPAKE2 key exchange.  The peers
   derive ephemeral public keys, encrypt, and exchange them.  Each party
   hashes a concatentation of his or her identity and the password and
   operates on the role-specific element to obtain a secret encrypting
   element.  The group operation is then performed with the ephemeral
   key and the secret encrypting element to produce an encrypted
   ephmeral key.

         Alice:                           Bob:
         ------                           ----
     x, X = x*G                         y, Y = y*G
     Qa = H(Alice|pw)*Pi                Qr = H(Bob|pw)*Pr
     M = X + Qa
                           M ------>
                                        Qa = H(Alice|pw)*Pi
                                        X' = M - Qa
                                        N = Y + Qr
                           <------ N
     Qr = H(Bob|pw)*Pr
     Y' = N - Qr

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   Both M and N MUST be verified to be valid elements in the selected
   group.  If either one is not valid the protocol fails.

   At this point the peers have exchanged ephemeral elements that will
   be unknown except by someone with knowledge of the password.  Given
   our assumptions that means only Alice and Bob can know the elements X
   and Y.

   The secret encrypting elements Qa and Qb are irretrievably deleted at
   this point.

5.2.  Commit/Reveal Phase

   In the Commit/Reveal phase the peers commit to the particular public
   key they wish to exchange and reveal it to the peer.  Proof-of-
   possession of the private key is accomplished by "signing" the public
   key, the identity to which the public key is bound, the receipient's
   ephemeral public key, and the sender's ephemeral public key.

   The messages exchanged in the Commit/Reveal phase are encrypted and
   authenticated with AES-SIV using a key derived from the SPAKE2 key
   exchange in Section 5.1.  Successful construction and validation of
   these messages authenticates the SPAKE2 exchange by proving
   possession of the SPAKE2 shared secret and therefore knowledge of the
   password.  A single octet of the value zero (0) is used as AD when
   encrypting Alice's message to Bob and a single octet of the value one
   (1) is used as AD when constructing Bob's response.  The AD is not
   transferred as part of the either message.

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         Alice:                              Bob:
         ------                              ----
     z = KDF-n(F(x*Y'), Alice | Bob |
               F(M) | F(N) | pw)
     u = HMAC(F(a*Y'), Alice | F(A) |
              F(Y') | F(X))

                      {A, u}z[0] ------>

                                    z = KDF-n(F(y*X'), Alice | Bob |
                                        F(M) | F(N) | pw)
                                    if (SIV-decrypt returns fail) fail
                                    if (A not valid element) fail
                                    u' = HMAC(F(y*A), Alice | F(A) |
                                              F(Y) | F(X'))
                                    if (u' != u) fail
                                    v = HMAC(F(b*X'), Bob | F(B) |
                                             F(X') | F(Y))

                            <------ {B, v}z[1]

     if (SIV-decrypt returns fail) fail
     if (B not valid element) fail
     v' = HMAC(F(x*B), Bob | F(B) |
               F(X) | F(Y))
     if (v'!= v) fail

   where 0 and 1 are single octets of the value zero and one,
   respectively, n is the key length from Section 4, and both the KDF
   and HMAC use the hash algorithm from Section 4.

   If the parties didn't fail they have each other's public key,
   knowledge that the peer possesses the corresponding private key, and
   trust that the public key belongs to the peer's stated identity.

6.  IANA Considerations

   This memo could create a registry of the fixed public elements for a
   nice cross section of popular groups.  Or not.  Once published this
   document will be a stable reference and a registry might not be

7.  Security Considerations

   The encrypted shares exchanged in the Exchange phase MUST be
   ephemeral.  Reuse of these keys, even with a different password,
   voids the security of the exchange.

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   If fixed elements other than those in Appendix A.1 and Appendix A.2
   are used, their discrete logarithm MUST not be known.  Knowledge of
   of the discrete logarithm of either of the fixed elements voids the
   security of the exchange.

   The public keys exchanged in PKEX are never disclosed to an attacker,
   either passive or active.  While they are, as the name implies,
   public, PKEX provides for secrecy of the exchanged keys for any
   protocol that might need such a capability.

   PKEX has forward secrecy in the sense that exposure of the password
   used in a previous run of the protocol will not affect the security
   of that run.  This also means that once PKEX has finished, the
   password can be exposed to a third party with out loss of security--
   the public keys exchanged are still trusted and still bound to the
   entities that performed the exchange originally.

   There is no proof of security of PKEX at this time but the Exchange
   phase is SPAKE2 and the security proof for that protocol can be used
   to help prove the security of PKEX.

8.  References

8.1.  Normative References

   [DSS]      U.S. Department of Commerce/National Institute of
              Standards and Technology, "Digital Signature Standard
              (DSS)", Federal Information Processing Standards FIPS PUB
              186-4, July 2013.

   [RFC2104]  Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
              Hashing for Message Authentication", RFC 2104, DOI
              10.17487/RFC2104, February 1997,

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

   [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,

   [RFC5297]  Harkins, D., "Synthetic Initialization Vector (SIV)
              Authenticated Encryption Using the Advanced Encryption
              Standard (AES)", RFC 5297, DOI 10.17487/RFC5297, October
              2008, <>.

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   [RFC5869]  Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
              Key Derivation Function (HKDF)", RFC 5869, DOI 10.17487/
              RFC5869, May 2010,

   [X9.62]    American National Standards Institute, "X9.62-2005",
              Public Key Cryptography for the Financial Services
              Industry (ECDSA), 2005.

8.2.  Informative References

   [RFC7250]  Wouters, P., Ed., Tschofenig, H., Ed., Gilmore, J.,
              Weiler, S., and T. Kivinen, "Using Raw Public Keys in
              Transport Layer Security (TLS) and Datagram Transport
              Layer Security (DTLS)", RFC 7250, DOI 10.17487/RFC7250,
              June 2014, <>.

   [RFC7670]  Kivinen, T., Wouters, P., and H. Tschofenig, "Generic Raw
              Public-Key Support for IKEv2", RFC 7670, DOI 10.17487/
              RFC7670, January 2016,

Appendix A.  Role-specific Elements

   Role-specific elements for six popular elliptic curves and four
   popular modp groups from [RFC3526] have been generated using the
   following technique.

   A loop is performed to generate role-specific elements by generating
   a candidate, testing the candidate, and exiting the loop once the
   test succeeds.  A single octet counter is incremented each time
   through the loop (first time through the loop, the counter is one).

   To find a candidate, a hash of an identifier (the concatenation of
   the ASN.1 of the OID of the curve or the name of the FFC group), a
   constant string, and the counter is produced.  If the length of the
   hash's digest is less than the desired bits, the digest is pre-pended
   to the inputs and the result is fed back into the hash (this time it
   is a hash of a concatentation of the old digest, asn.1, constant
   string, counter) to produce the next length-of-digest bits.  This is
   repeated until the number of bits has been produced.  Excess octets
   are stripped off.  The resulting string is interpreted as an integer
   with the first octet of (the first) hash being the high-order octet
   of the integer.  For curves whose prime is not an integral number of
   octets, the bitstring is right-shifted, pre-pending with zero bits,
   in order to make a big-endian bitstring of the appropriate length.
   If that resulting number is larger than the prime defining the group
   the counter is incremented and the loop continues.  Once an candidate

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   has been produced it is checked to see whether it is a valid element
   in the group (for ECC it is treated as an x-coordinate and checked
   whether it produces a valid point on the curve, for FFC it is checked
   by seeing whether the exponentiation of the candidate to the power of
   the prime minus one divided by the order, modulo the prime, is one).
   If it is not, the counter is incremented and the whole loop is
   performed again.  This process is repeated until an element is found.
   The hash algorithm used to generate candidates is determined by
   Section 4.

   The loop is performed twice for each elliptic curve and FFC group to
   produce initiator- and responder-specific elements.  The string
   passed for the initiator-specific element is "PKEX Initiator", the
   string passed for the responder-specific element is "PKEX Responder".

   For FFC groups, the identifier is "group X" (including the space
   character and excluding the quotation marks) where X is the id
   assigned to the group, e.g. the 2048-bit group is named "group 14".
   For ECC groups, the identifier is the DER-encoded ASN.1
   representation of the OID of the curve.

A.1.  ECC Role-specific Elements

A.1.1.  Role-specific Elements for NIST p256

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   unsigned char nist_p256_initiator_x_coord[32] = {
   0x56, 0x26, 0x12, 0xcf, 0x36, 0x48, 0xfe, 0x0b,
   0x07, 0x04, 0xbb, 0x12, 0x22, 0x50, 0xb2, 0x54,
   0xb1, 0x94, 0x64, 0x7e, 0x54, 0xce, 0x08, 0x07,
   0x2e, 0xec, 0xca, 0x74, 0x5b, 0x61, 0x2d, 0x25
   unsigned char nist_p256_initiator_y_coord[32] = {
   0x3e, 0x44, 0xc7, 0xc9, 0x8c, 0x1c, 0xa1, 0x0b,
   0x20, 0x09, 0x93, 0xb2, 0xfd, 0xe5, 0x69, 0xdc,
   0x75, 0xbc, 0xad, 0x33, 0xc1, 0xe7, 0xc6, 0x45,
   0x4d, 0x10, 0x1e, 0x6a, 0x3d, 0x84, 0x3c, 0xa4

   unsigned char nist_p256_responder_x_coord[32] = {
   0x1e, 0xa4, 0x8a, 0xb1, 0xa4, 0xe8, 0x42, 0x39,
   0xad, 0x73, 0x07, 0xf2, 0x34, 0xdf, 0x57, 0x4f,
   0xc0, 0x9d, 0x54, 0xbe, 0x36, 0x1b, 0x31, 0x0f,
   0x59, 0x91, 0x52, 0x33, 0xac, 0x19, 0x9d, 0x76
   unsigned char nist_p256_responder_y_coord[32] = {
   0x26, 0x04, 0x09, 0x45, 0x0a, 0x05, 0x20, 0xe7,
   0xa7, 0x27, 0xc1, 0x36, 0x76, 0x85, 0xca, 0x3e,
   0x42, 0x16, 0xf4, 0x89, 0x85, 0x34, 0x6e, 0xd5,
   0x17, 0xde, 0xc0, 0xb8, 0xad, 0xfd, 0xb2, 0x98

A.1.2.  Role-specific Elements for NIST p384

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   unsigned char nist_p384_initiator_x_coord[48] = {
   0x95, 0x3f, 0x42, 0x9e, 0x50, 0x7f, 0xf9, 0xaa,
   0xac, 0x1a, 0xf2, 0x85, 0x2e, 0x64, 0x91, 0x68,
   0x64, 0xc4, 0x3c, 0xb7, 0x5c, 0xf8, 0xc9, 0x53,
   0x6e, 0x58, 0x4c, 0x7f, 0xc4, 0x64, 0x61, 0xac,
   0x51, 0x8a, 0x6f, 0xfe, 0xab, 0x74, 0xe6, 0x12,
   0x81, 0xac, 0x38, 0x5d, 0x41, 0xe6, 0xb9, 0xa3
   unsigned char nist_p384_initiator_y_coord[48] = {
   0x89, 0xd0, 0x97, 0x7b, 0x59, 0x4f, 0xa6, 0xd6,
   0x7c, 0x5d, 0x93, 0x5b, 0x93, 0xc4, 0x07, 0xa9,
   0x89, 0xee, 0xd5, 0xcd, 0x6f, 0x42, 0xf8, 0x38,
   0xc8, 0xc6, 0x62, 0x24, 0x69, 0x0c, 0xd4, 0x48,
   0xd8, 0x44, 0xd6, 0xc2, 0xe8, 0xcc, 0x62, 0x6b,
   0x3c, 0x25, 0x53, 0xba, 0x4f, 0x71, 0xf8, 0xe7

   unsigned char nist_p384_responder_x_coord[48] = {
   0xad, 0xbe, 0xd7, 0x1d, 0x3a, 0x71, 0x64, 0x98,
   0x5f, 0xb4, 0xd6, 0x4b, 0x50, 0xd0, 0x84, 0x97,
   0x4b, 0x7e, 0x57, 0x70, 0xd2, 0xd9, 0xf4, 0x92,
   0x2a, 0x3f, 0xce, 0x99, 0xc5, 0x77, 0x33, 0x44,
   0x14, 0x56, 0x92, 0xcb, 0xae, 0x46, 0x64, 0xdf,
   0xe0, 0xbb, 0xd7, 0xb1, 0x29, 0x20, 0x72, 0xdf
   unsigned char nist_p384_responder_y_coord[48] = {
   0x54, 0x58, 0x20, 0xad, 0x55, 0x1d, 0xca, 0xf3,
   0x1c, 0x8a, 0xcd, 0x19, 0x40, 0xf9, 0x37, 0x83,
   0xc7, 0xd6, 0xb3, 0x13, 0x7d, 0x53, 0x28, 0x5c,
   0xf6, 0x2d, 0xf1, 0xdd, 0xa5, 0x8b, 0xad, 0x5d,
   0x81, 0xab, 0xb1, 0x00, 0x39, 0xd6, 0xcc, 0x9c,
   0xea, 0x1e, 0x84, 0x1d, 0xbf, 0xe3, 0x35, 0xf9

A.1.3.  Role-specific Elements for NIST p521

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   unsigned char nist_p521_initiator_x_coord[66] = {
   0x00, 0x16, 0x20, 0x45, 0x19, 0x50, 0x95, 0x23,
   0x0d, 0x24, 0xbe, 0x00, 0x87, 0xdc, 0xfa, 0xf0,
   0x58, 0x9a, 0x01, 0x60, 0x07, 0x7a, 0xca, 0x76,
   0x01, 0xab, 0x2d, 0x5a, 0x46, 0xcd, 0x2c, 0xb5,
   0x11, 0x9a, 0xff, 0xaa, 0x48, 0x04, 0x91, 0x38,
   0xcf, 0x86, 0xfc, 0xa4, 0xa5, 0x0f, 0x47, 0x01,
   0x80, 0x1b, 0x30, 0xa3, 0xae, 0xe8, 0x1c, 0x2e,
   0xea, 0xcc, 0xf0, 0x03, 0x9f, 0x77, 0x4c, 0x8d,
   0x97, 0x76
   unsigned char nist_p521_initiator_y_coord[66] = {
   0x01, 0x4c, 0x71, 0xfd, 0x1b, 0xd5, 0x9c, 0xa6,
   0xed, 0x39, 0xef, 0x45, 0xc5, 0x06, 0xfd, 0x66,
   0xc0, 0xeb, 0x0f, 0xbf, 0x21, 0xa3, 0x36, 0x74,
   0xfd, 0xaa, 0x05, 0x6e, 0x4e, 0x33, 0x95, 0x42,
   0x1a, 0x9d, 0x3f, 0x3a, 0x1c, 0x5e, 0xa8, 0x60,
   0xf7, 0xe5, 0x59, 0x1d, 0x07, 0xaa, 0x6f, 0x40,
   0x0a, 0x59, 0x3c, 0x27, 0xad, 0xe0, 0x48, 0xfd,
   0xd1, 0x83, 0x37, 0x4c, 0xdf, 0xe1, 0x86, 0x72,
   0xfc, 0x57

   unsigned char nist_p521_responder_x_coord[66] = {
   0x00, 0x79, 0xe4, 0x4d, 0x6b, 0x5e, 0x12, 0x0a,
   0x18, 0x2c, 0xb3, 0x05, 0x77, 0x0f, 0xc3, 0x44,
   0x1a, 0xcd, 0x78, 0x46, 0x14, 0xee, 0x46, 0x3f,
   0xab, 0xc9, 0x59, 0x7c, 0x85, 0xa0, 0xc2, 0xfb,
   0x02, 0x32, 0x99, 0xde, 0x5d, 0xe1, 0x0d, 0x48,
   0x2d, 0x71, 0x7d, 0x8d, 0x3f, 0x61, 0x67, 0x9e,
   0x2b, 0x8b, 0x12, 0xde, 0x10, 0x21, 0x55, 0x0a,
   0x5b, 0x2d, 0xe8, 0x05, 0x09, 0xf6, 0x20, 0x97,
   0x84, 0xb4
   unsigned char nist_p521_responder_y_coord[66] = {
   0x01, 0xb9, 0x9c, 0xc6, 0x41, 0x32, 0x5b, 0xd2,
   0x35, 0xd8, 0x8b, 0x2b, 0xe4, 0x6e, 0xcc, 0xdf,
   0x7c, 0x38, 0xc4, 0x5b, 0xf6, 0x74, 0x71, 0x5c,
   0x77, 0x16, 0x8a, 0x80, 0xa9, 0x84, 0xc7, 0x7b,
   0x9d, 0xfd, 0x83, 0x6f, 0xae, 0xf8, 0x24, 0x16,
   0x2f, 0x21, 0x25, 0x65, 0xa2, 0x1a, 0x6b, 0x2d,
   0x30, 0x62, 0xb3, 0xcc, 0x6e, 0x59, 0x3c, 0x7f,
   0x58, 0x91, 0x81, 0x72, 0x07, 0x8c, 0x91, 0xac,
   0x31, 0x1e

Harkins                   Expires July 6, 2017                 [Page 14]

Internet-Draft                    PKEX                      January 2017

A.1.4.  Role-specific Elements for brainpool p256r1

   unsigned char brainpool_p256r1_initiator_x_coord[32] = {
   0x46, 0x98, 0x18, 0x6c, 0x27, 0xcd, 0x4b, 0x10,
   0x7d, 0x55, 0xa3, 0xdd, 0x89, 0x1f, 0x9f, 0xca,
   0xc7, 0x42, 0x5b, 0x8a, 0x23, 0xed, 0xf8, 0x75,
   0xac, 0xc7, 0xe9, 0x8d, 0xc2, 0x6f, 0xec, 0xd8
   unsigned char brainpool_p256r1_initiator_y_coord[32] = {
   0x16, 0x30, 0x68, 0x32, 0x3b, 0xb0, 0x21, 0xee,
   0xeb, 0xf7, 0xb6, 0x7c, 0xae, 0x52, 0x26, 0x42,
   0x59, 0x28, 0x58, 0xb6, 0x14, 0x90, 0xed, 0x69,
   0xd0, 0x67, 0xea, 0x25, 0x60, 0x0f, 0xa9, 0x6c

   unsigned char brainpool_p256r1_responder_x_coord[32] = {
   0x90, 0x18, 0x84, 0xc9, 0xdc, 0xcc, 0xb5, 0x2f,
   0x4a, 0x3f, 0x4f, 0x18, 0x0a, 0x22, 0x56, 0x6a,
   0xa9, 0xef, 0xd4, 0xe6, 0xc3, 0x53, 0xc2, 0x1a,
   0x23, 0x54, 0xdd, 0x08, 0x7e, 0x10, 0xd8, 0xe3
   unsigned char brainpool_p256r1_responder_y_coord[32] = {
   0x2a, 0xfa, 0x98, 0x9b, 0xe3, 0xda, 0x30, 0xfd,
   0x32, 0x28, 0xcb, 0x66, 0xfb, 0x40, 0x7f, 0xf2,
   0xb2, 0x25, 0x80, 0x82, 0x44, 0x85, 0x13, 0x7e,
   0x4b, 0xb5, 0x06, 0xc0, 0x03, 0x69, 0x23, 0x64

A.1.5.  Role-specific Elements for brainpool p384r1

Harkins                   Expires July 6, 2017                 [Page 15]

Internet-Draft                    PKEX                      January 2017

   unsigned char brainpool_p384r1_initiator_x_coord[48] = {
   0x0a, 0x2c, 0xeb, 0x49, 0x5e, 0xb7, 0x23, 0xbd,
   0x20, 0x5b, 0xe0, 0x49, 0xdf, 0xcf, 0xcf, 0x19,
   0x37, 0x36, 0xe1, 0x2f, 0x59, 0xdb, 0x07, 0x06,
   0xb5, 0xeb, 0x2d, 0xae, 0xc2, 0xb2, 0x38, 0x62,
   0xa6, 0x73, 0x09, 0xa0, 0x6c, 0x0a, 0xa2, 0x30,
   0x99, 0xeb, 0xf7, 0x1e, 0x47, 0xb9, 0x5e, 0xbe
   unsigned char brainpool_p384r1_initiator_y_coord[48] = {
   0x54, 0x76, 0x61, 0x65, 0x75, 0x5a, 0x2f, 0x99,
   0x39, 0x73, 0xca, 0x6c, 0xf9, 0xf7, 0x12, 0x86,
   0x54, 0xd5, 0xd4, 0xad, 0x45, 0x7b, 0xbf, 0x32,
   0xee, 0x62, 0x8b, 0x9f, 0x52, 0xe8, 0xa0, 0xc9,
   0xb7, 0x9d, 0xd1, 0x09, 0xb4, 0x79, 0x1c, 0x3e,
   0x1a, 0xbf, 0x21, 0x45, 0x66, 0x6b, 0x02, 0x52

   unsigned char brainpool_p384r1_responder_x_coord[48] = {
   0x03, 0xa2, 0x57, 0xef, 0xe8, 0x51, 0x21, 0xa0,
   0xc8, 0x9e, 0x21, 0x02, 0xb5, 0x9a, 0x36, 0x25,
   0x74, 0x22, 0xd1, 0xf2, 0x1b, 0xa8, 0x9a, 0x9b,
   0x97, 0xbc, 0x5a, 0xeb, 0x26, 0x15, 0x09, 0x71,
   0x77, 0x59, 0xec, 0x8b, 0xb7, 0xe1, 0xe8, 0xce,
   0x65, 0xb8, 0xaf, 0xf8, 0x80, 0xae, 0x74, 0x6c
   unsigned char brainpool_p384r1_responder_y_coord[48] = {
   0x2f, 0xd9, 0x6a, 0xc7, 0x3e, 0xec, 0x76, 0x65,
   0x2d, 0x38, 0x7f, 0xec, 0x63, 0x26, 0x3f, 0x04,
   0xd8, 0x4e, 0xff, 0xe1, 0x0a, 0x51, 0x74, 0x70,
   0xe5, 0x46, 0x63, 0x7f, 0x5c, 0xc0, 0xd1, 0x7c,
   0xfb, 0x2f, 0xea, 0xe2, 0xd8, 0x0f, 0x84, 0xcb,
   0xe9, 0x39, 0x5c, 0x64, 0xfe, 0xcb, 0x2f, 0xf1

A.1.6.  Role-specific Elements for brainpool p512r1

Harkins                   Expires July 6, 2017                 [Page 16]

Internet-Draft                    PKEX                      January 2017

   unsigned char brainpool_p512r1_initiator_x_coord[64] = {
   0x4c, 0xe9, 0xb6, 0x1c, 0xe2, 0x00, 0x3c, 0x9c,
   0xa9, 0xc8, 0x56, 0x52, 0xaf, 0x87, 0x3e, 0x51,
   0x9c, 0xbb, 0x15, 0x31, 0x1e, 0xc1, 0x05, 0xfc,
   0x7c, 0x77, 0xd7, 0x37, 0x61, 0x27, 0xd0, 0x95,
   0x98, 0xee, 0x5d, 0xa4, 0x3d, 0x09, 0xdb, 0x3d,
   0xfa, 0x89, 0x9e, 0x7f, 0xa6, 0xa6, 0x9c, 0xff,
   0x83, 0x5c, 0x21, 0x6c, 0x3e, 0xf2, 0xfe, 0xdc,
   0x63, 0xe4, 0xd1, 0x0e, 0x75, 0x45, 0x69, 0x0f
   unsigned char brainpool_p512r1_initiator_y_coord[64] = {
   0x5a, 0x28, 0x01, 0xbe, 0x96, 0x82, 0x4e, 0xf6,
   0xfa, 0xed, 0x7d, 0xfd, 0x48, 0x8b, 0x48, 0x4e,
   0xd1, 0x97, 0x87, 0xc4, 0x05, 0x5d, 0x15, 0x2a,
   0xf4, 0x91, 0x4b, 0x75, 0x90, 0xd9, 0x34, 0x2c,
   0x3c, 0x12, 0xf2, 0xf5, 0x25, 0x94, 0x24, 0x34,
   0xa7, 0x6d, 0x66, 0xbc, 0x27, 0xa4, 0xa0, 0x8d,
   0xd5, 0xe1, 0x54, 0xa3, 0x55, 0x26, 0xd4, 0x14,
   0x17, 0x0f, 0xc1, 0xc7, 0x3d, 0x68, 0x7f, 0x5a

   unsigned char brainpool_p512r1_responder_x_coord[64] = {
   0x2a, 0x60, 0x32, 0x27, 0xa1, 0xe6, 0x94, 0x72,
   0x1c, 0x48, 0xbe, 0xc5, 0x77, 0x14, 0x30, 0x76,
   0xe4, 0xbf, 0xf7, 0x7b, 0xc5, 0xfd, 0xdf, 0x19,
   0x1e, 0x0f, 0xdf, 0x1c, 0x40, 0xfa, 0x34, 0x9e,
   0x1f, 0x42, 0x24, 0xa3, 0x2c, 0xd5, 0xc7, 0xc9,
   0x7b, 0x47, 0x78, 0x96, 0xf1, 0x37, 0x0e, 0x88,
   0xcb, 0xa6, 0x52, 0x29, 0xd7, 0xa8, 0x38, 0x29,
   0x8e, 0x6e, 0x23, 0x47, 0xd4, 0x4b, 0x70, 0x3e
   unsigned char brainpool_p512r1_responder_y_coord[64] = {
   0x2a, 0xbe, 0x59, 0xe6, 0xc4, 0xb3, 0xd8, 0x09,
   0x66, 0x89, 0x0a, 0x2d, 0x19, 0xf0, 0x9c, 0x9f,
   0xb4, 0xab, 0x8f, 0x50, 0x68, 0x3c, 0x74, 0x64,
   0x4e, 0x19, 0x55, 0x81, 0x9b, 0x48, 0x5c, 0xf4,
   0x12, 0x8d, 0xb9, 0xd8, 0x02, 0x5b, 0xe1, 0x26,
   0x7e, 0x19, 0x5c, 0xfd, 0x70, 0xf7, 0x4b, 0xdc,
   0xb5, 0x5d, 0xc1, 0x7a, 0xe9, 0xd1, 0x05, 0x2e,
   0xd1, 0xfd, 0x2f, 0xce, 0x63, 0x77, 0x48, 0x2c

A.2.  FFC Role-specific Elements

Harkins                   Expires July 6, 2017                 [Page 17]

Internet-Draft                    PKEX                      January 2017

A.2.1.  Role-specific Elements for 2048-bit FFC group

   unsigned char group14_initiator[256] = {
   0x97, 0x15, 0x52, 0x05, 0x89, 0xdf, 0xeb, 0x3d,
   0xd6, 0x50, 0xe1, 0x96, 0xd4, 0x30, 0x81, 0x04,
   0x3a, 0x4d, 0x6c, 0xae, 0xe5, 0x81, 0xb6, 0x1d,
   0x53, 0xca, 0x65, 0xfa, 0x19, 0x59, 0xfd, 0xe4,
   0xa4, 0xf0, 0x7b, 0xc5, 0xc7, 0xc4, 0xa9, 0xd6,
   0xdf, 0x79, 0x54, 0x04, 0x5d, 0x64, 0xdc, 0x3c,
   0xec, 0x0a, 0xa0, 0xd3, 0x2f, 0xef, 0xf3, 0xf5,
   0x2c, 0x51, 0xe6, 0x6d, 0x1c, 0xdc, 0xac, 0x09,
   0x3c, 0x00, 0x62, 0x41, 0xe7, 0x0b, 0x0d, 0xba,
   0x1b, 0xf2, 0xb9, 0x22, 0xe9, 0x11, 0xea, 0xc7,
   0xb1, 0xb2, 0x15, 0xc5, 0x19, 0x46, 0x2e, 0x15,
   0x88, 0x41, 0xe0, 0x24, 0x16, 0x13, 0xc1, 0x0e,
   0x27, 0xd3, 0x5f, 0x71, 0x12, 0xc6, 0x6f, 0x75,
   0x1e, 0xe8, 0xa4, 0xaa, 0x57, 0xa3, 0x22, 0x32,
   0xdc, 0xd4, 0xe3, 0xb5, 0xa3, 0xd0, 0x87, 0xb1,
   0x3d, 0x1c, 0x2a, 0xcf, 0xe5, 0x87, 0x1f, 0xea,
   0x98, 0xdd, 0xd6, 0x8f, 0xce, 0x0b, 0xdd, 0xba,
   0xae, 0x85, 0x81, 0xd6, 0x89, 0x27, 0x71, 0xc9,
   0x9f, 0xf9, 0xea, 0x5a, 0x89, 0xa6, 0xaa, 0x0a,
   0xc2, 0x76, 0xd6, 0x6d, 0x89, 0xd3, 0xd2, 0x4c,
   0xc0, 0xad, 0xb0, 0xf6, 0x4d, 0x2b, 0x7c, 0xbf,
   0xd2, 0x4e, 0xe3, 0x2b, 0x4f, 0xd7, 0xc5, 0x3a,
   0x4b, 0x1c, 0xc0, 0x17, 0xbe, 0x1e, 0x7b, 0x81,
   0x1c, 0x77, 0xd4, 0xc2, 0xf6, 0xca, 0xb8, 0x51,
   0xa8, 0x94, 0xe9, 0xe5, 0xe9, 0xa5, 0x46, 0x60,
   0xb5, 0x36, 0x10, 0xcf, 0xc8, 0x2a, 0xe7, 0x7f,
   0x94, 0x49, 0x96, 0xeb, 0xff, 0x7b, 0x62, 0xa9,
   0x95, 0x35, 0x5c, 0xad, 0xcd, 0x52, 0x06, 0xa1,
   0x9c, 0xa1, 0xb7, 0xe0, 0xcd, 0xd3, 0x13, 0x43,
   0xee, 0xe7, 0xf1, 0xb1, 0x4d, 0x76, 0x51, 0x53,
   0x24, 0x4f, 0xb4, 0xbd, 0x8b, 0x0c, 0x73, 0xd1,
   0x6f, 0xf5, 0x27, 0x3f, 0xb9, 0x60, 0xa6, 0x17

   unsigned char group14_responder[256] = {
   0x3c, 0x86, 0x96, 0x8a, 0xb0, 0x4b, 0x14, 0xdd,
   0x27, 0xf0, 0x6f, 0x51, 0xa2, 0xb2, 0xbd, 0x7d,
   0x27, 0x34, 0xf2, 0x21, 0x3c, 0x6a, 0x63, 0xcf,
   0x15, 0xd8, 0xeb, 0x21, 0xc2, 0x2d, 0xe5, 0x75,
   0xbb, 0x7e, 0x09, 0x2e, 0xba, 0xa2, 0xd7, 0x04,
   0x7c, 0x81, 0x82, 0x07, 0x09, 0x15, 0x28, 0x35,
   0xf7, 0x0a, 0xd6, 0xa9, 0xaf, 0x0d, 0xb1, 0x97,
   0x71, 0x76, 0x74, 0x66, 0xa3, 0x54, 0x9e, 0xd9,
   0xa9, 0x13, 0xa8, 0xcf, 0xec, 0xce, 0x60, 0xd8,
   0xea, 0x18, 0x67, 0xb7, 0x15, 0x17, 0xf7, 0xe6,

Harkins                   Expires July 6, 2017                 [Page 18]

Internet-Draft                    PKEX                      January 2017

   0x23, 0xc8, 0x30, 0x02, 0xb9, 0x9e, 0x0e, 0xe6,
   0x64, 0x3e, 0x1a, 0x61, 0xb9, 0xbf, 0xd8, 0x7a,
   0x0e, 0xbe, 0x1e, 0x58, 0xdc, 0xba, 0x9e, 0x31,
   0xab, 0xcc, 0x6b, 0x03, 0xcc, 0x08, 0xf8, 0xa2,
   0xcb, 0x9d, 0xd5, 0x1a, 0xb8, 0x6a, 0x1f, 0x4b,
   0xab, 0xe8, 0x2a, 0x0c, 0x44, 0xde, 0x2a, 0xfd,
   0x0f, 0x6d, 0x2f, 0xe4, 0xc4, 0x41, 0x61, 0xed,
   0x4a, 0x85, 0x2a, 0x06, 0x9d, 0x3a, 0x27, 0xf0,
   0x30, 0x6e, 0xf8, 0xb1, 0xc8, 0xde, 0x1f, 0xe0,
   0xfb, 0xb6, 0xd0, 0x51, 0xee, 0x7d, 0x3a, 0x05,
   0x0c, 0xbb, 0xa0, 0x41, 0xc5, 0x5d, 0x25, 0xb4,
   0x48, 0xd6, 0x4f, 0x08, 0x85, 0x96, 0xa3, 0xa6,
   0xf5, 0x1b, 0xa1, 0xb3, 0x13, 0x50, 0x06, 0xb2,
   0xef, 0xf8, 0x2f, 0xe8, 0x7b, 0xe0, 0x5a, 0xe1,
   0x42, 0x16, 0xfc, 0xdf, 0xad, 0x53, 0x95, 0x43,
   0xb0, 0x73, 0x33, 0xa9, 0x08, 0x29, 0xcd, 0x6c,
   0x14, 0x98, 0x5e, 0x98, 0xe6, 0xca, 0x92, 0x55,
   0xd9, 0x3e, 0xc3, 0x51, 0x83, 0xda, 0x1e, 0x6d,
   0x16, 0x88, 0x3f, 0xd1, 0xa5, 0xd1, 0xc5, 0x43,
   0xcf, 0x8a, 0xd7, 0x29, 0xaa, 0xa6, 0x4f, 0x6b,
   0x4f, 0xee, 0x36, 0x65, 0xd6, 0x71, 0xef, 0x71,
   0xc5, 0x5b, 0x7c, 0x6d, 0x90, 0x9d, 0xf5, 0x74

A.2.2.  Role-specific Elements for 3072-bit FFC group

   unsigned char group15_initiator[384] = {
   0x12, 0xce, 0x47, 0xcf, 0xa9, 0xc4, 0xfc, 0x5e,
   0x99, 0xf6, 0xd2, 0x43, 0x5c, 0x60, 0x39, 0xb0,
   0x06, 0xe9, 0x4a, 0xec, 0x21, 0x60, 0x9f, 0x5a,
   0x25, 0xb1, 0x22, 0xf2, 0x53, 0x2b, 0x44, 0xe3,
   0x6c, 0xfb, 0x9c, 0x46, 0x3c, 0x8f, 0x88, 0xaa,
   0x60, 0xfd, 0x3a, 0x51, 0xf1, 0x19, 0x8d, 0x88,
   0xee, 0xa4, 0xc2, 0x21, 0x3c, 0xbb, 0xc5, 0x53,
   0x12, 0x16, 0xfb, 0xd3, 0xa9, 0x4d, 0x85, 0x5d,
   0x17, 0x9d, 0x92, 0x15, 0x30, 0xc7, 0x97, 0x0c,
   0x68, 0x62, 0x91, 0xff, 0xce, 0x81, 0x97, 0x25,
   0x54, 0x94, 0x0e, 0x3a, 0x14, 0x36, 0x4e, 0xc2,
   0xda, 0xc2, 0xaa, 0xa3, 0x58, 0x49, 0xca, 0xa4,
   0xa4, 0x0b, 0x2a, 0x26, 0x35, 0x0d, 0x72, 0x4f,
   0x10, 0x3c, 0x5f, 0x4d, 0xbc, 0x7c, 0x09, 0xcb,
   0xef, 0x99, 0xdd, 0x73, 0x1c, 0x23, 0x69, 0xa7,
   0xc9, 0xc4, 0x1a, 0x4c, 0x7c, 0xf2, 0xca, 0x48,
   0x15, 0xf4, 0xd6, 0x30, 0x25, 0x44, 0x9f, 0xcd,
   0xc0, 0x23, 0x72, 0x4a, 0x4f, 0x83, 0x3c, 0xba,
   0x88, 0x1c, 0x5a, 0xcc, 0x3f, 0xf6, 0x5e, 0x68,
   0x5a, 0x38, 0x10, 0xa1, 0xd2, 0x99, 0x5f, 0x4d,
   0x48, 0xec, 0xb1, 0x2f, 0x9a, 0x08, 0xcf, 0x59,

Harkins                   Expires July 6, 2017                 [Page 19]

Internet-Draft                    PKEX                      January 2017

   0x0f, 0xeb, 0x35, 0x0b, 0xf5, 0xab, 0x6e, 0xc9,
   0x69, 0x44, 0xbd, 0x9a, 0x62, 0x3b, 0x53, 0x4e,
   0x59, 0xc9, 0x38, 0x1d, 0x9e, 0x61, 0x5b, 0xdb,
   0x72, 0x4e, 0xb9, 0x35, 0xb5, 0xc3, 0x9f, 0x47,
   0x4f, 0x70, 0xfa, 0xff, 0x95, 0x45, 0xf9, 0x4a,
   0xf4, 0xc3, 0xcc, 0x8e, 0xf4, 0x89, 0x0b, 0x73,
   0x08, 0x97, 0x0d, 0x22, 0xe2, 0x97, 0xc8, 0xf8,
   0x45, 0x83, 0x8f, 0xea, 0x68, 0x4b, 0xe0, 0xed,
   0x71, 0xdb, 0x73, 0x62, 0x57, 0xab, 0x03, 0x69,
   0x93, 0x66, 0x0e, 0xc1, 0x29, 0x2d, 0x01, 0x7c,
   0x7d, 0x50, 0x14, 0x03, 0x9f, 0xdb, 0x5c, 0x4c,
   0xf4, 0xdf, 0xa4, 0x9c, 0xda, 0x80, 0xd9, 0xbe,
   0x0d, 0xdc, 0xb8, 0x0b, 0xc2, 0x19, 0x28, 0xaf,
   0xf0, 0x98, 0x1a, 0xec, 0x26, 0xf0, 0x15, 0x1b,
   0xa1, 0xa1, 0x11, 0x8f, 0x9f, 0x5a, 0x1e, 0x8a,
   0x8e, 0x57, 0x84, 0x60, 0xc5, 0xda, 0xa2, 0x74,
   0x3d, 0xe8, 0xc0, 0x08, 0x0f, 0x7e, 0xdd, 0x11,
   0xd6, 0xbf, 0x5b, 0x2e, 0xde, 0x81, 0x1a, 0xfd,
   0x33, 0x9c, 0x07, 0xcc, 0x1d, 0x0f, 0x63, 0xc8,
   0x3e, 0x1d, 0xbb, 0x16, 0x5e, 0x70, 0x4c, 0x82,
   0x8e, 0x72, 0xb6, 0x35, 0x69, 0xc6, 0xe4, 0xa7,
   0xae, 0x6e, 0xa2, 0x23, 0xe8, 0x86, 0x99, 0x3a,
   0x0b, 0x64, 0xec, 0xe2, 0xdb, 0xb2, 0xaa, 0xc4,
   0x59, 0xe1, 0x23, 0x3d, 0xa5, 0x46, 0x92, 0x8f,
   0x04, 0x34, 0x5f, 0x7a, 0x13, 0x55, 0x75, 0xd5,
   0x6d, 0x0f, 0x5a, 0xc2, 0x0d, 0x16, 0xf9, 0xc0,
   0xf3, 0xac, 0x0a, 0xa8, 0x62, 0x20, 0x09, 0x4e

   unsigned char group15_responder[384] = {
   0x9f, 0x17, 0xe0, 0xf9, 0x3d, 0x23, 0x36, 0x6e,
   0x7d, 0xa6, 0x34, 0x75, 0xb7, 0xb4, 0x22, 0xb1,
   0x87, 0x7a, 0x00, 0x4e, 0x02, 0x14, 0x4e, 0xe6,
   0x96, 0xd4, 0x2c, 0x61, 0x00, 0x97, 0x7d, 0x99,
   0xad, 0x18, 0x1c, 0xc4, 0x1b, 0xed, 0x6f, 0xd3,
   0x9f, 0x85, 0xef, 0xfd, 0x1e, 0xcd, 0x13, 0xa0,
   0x61, 0x2f, 0xf8, 0xa7, 0x11, 0xab, 0x83, 0xfc,
   0xae, 0xad, 0xb6, 0xed, 0x6b, 0x7f, 0x34, 0x81,
   0x30, 0xa2, 0x1c, 0x38, 0xb3, 0x31, 0x7b, 0x74,
   0xc1, 0x0f, 0xf4, 0x29, 0x4b, 0xdd, 0x2b, 0x09,
   0x32, 0xb7, 0x8f, 0x84, 0xab, 0x89, 0x9d, 0x64,
   0xea, 0xec, 0x00, 0xa9, 0x0c, 0x82, 0x1c, 0x35,
   0x75, 0x3b, 0x7f, 0x35, 0x28, 0xb8, 0xcc, 0xb1,
   0x62, 0xc2, 0xd0, 0x74, 0x83, 0xb6, 0xf7, 0x76,
   0x10, 0x2a, 0x7e, 0xce, 0xd0, 0x0a, 0x68, 0x46,
   0xac, 0x78, 0x26, 0x90, 0xc7, 0x0e, 0xaa, 0x21,
   0x59, 0xb1, 0x8d, 0x8e, 0xc8, 0xfb, 0x5c, 0x60,
   0xec, 0x53, 0x9c, 0x40, 0xd9, 0x42, 0xab, 0xa3,

Harkins                   Expires July 6, 2017                 [Page 20]

Internet-Draft                    PKEX                      January 2017

   0xd8, 0x45, 0x81, 0x04, 0x6c, 0x13, 0x79, 0x66,
   0x51, 0x1f, 0xa4, 0x81, 0x38, 0x0d, 0x48, 0x06,
   0xef, 0x25, 0x89, 0x26, 0x5d, 0x09, 0x0e, 0xbe,
   0xba, 0xe2, 0xca, 0x2c, 0xa6, 0x3e, 0x36, 0xd7,
   0xef, 0x46, 0xe3, 0x8a, 0x1d, 0x85, 0x59, 0xc4,
   0x89, 0x5e, 0x36, 0xea, 0xb2, 0x44, 0x79, 0xc8,
   0x91, 0x80, 0x2c, 0x89, 0xfc, 0x55, 0x81, 0x62,
   0x40, 0x82, 0x1a, 0x66, 0xf1, 0x1c, 0x10, 0xf0,
   0x34, 0xdd, 0x52, 0x9f, 0xff, 0x63, 0x62, 0xe2,
   0xec, 0x68, 0x75, 0xa0, 0x2e, 0x72, 0x44, 0xf3,
   0x66, 0x33, 0x2a, 0x65, 0x61, 0x79, 0x91, 0x13,
   0x4f, 0x73, 0x8f, 0x38, 0xef, 0xa6, 0x65, 0x88,
   0xf9, 0x03, 0x35, 0x57, 0xed, 0xb9, 0x05, 0x7f,
   0xe8, 0xfb, 0x90, 0xac, 0x19, 0x2e, 0xff, 0x9c,
   0xaf, 0x76, 0x5f, 0x40, 0x74, 0x49, 0x11, 0xee,
   0x18, 0xb5, 0x6e, 0xa4, 0x91, 0xbc, 0x42, 0x1c,
   0x0e, 0x2e, 0x0d, 0x6f, 0xc3, 0x6a, 0x7b, 0x8b,
   0xf4, 0x1a, 0x30, 0x52, 0x54, 0x99, 0xae, 0x8a,
   0x8c, 0x33, 0x5e, 0x5c, 0xa8, 0xc2, 0x49, 0xf3,
   0xbd, 0x0e, 0x85, 0x22, 0x9b, 0x5d, 0x92, 0xbc,
   0x42, 0x8b, 0x60, 0x38, 0xd7, 0x14, 0x24, 0xaa,
   0x36, 0xc7, 0x8f, 0xd7, 0xc2, 0x14, 0x20, 0x72,
   0x0a, 0xba, 0x28, 0x95, 0x65, 0x53, 0x30, 0x0f,
   0xc8, 0x17, 0xc2, 0x02, 0x58, 0x08, 0x7b, 0x93,
   0x36, 0xcc, 0x80, 0x19, 0x9c, 0x1f, 0xad, 0x1f,
   0x8e, 0x8e, 0x2e, 0x3a, 0xbf, 0x0f, 0xab, 0x76,
   0x7a, 0xac, 0xce, 0x1a, 0x57, 0xe6, 0x7c, 0x64,
   0x93, 0x5f, 0x92, 0x5d, 0xbe, 0xe2, 0x11, 0xf6,
   0x58, 0x90, 0xd8, 0x87, 0xe4, 0x17, 0x8b, 0x61,
   0xf6, 0x11, 0xe2, 0x0a, 0x99, 0xe8, 0x55, 0xcc

A.2.3.  Role-specific Elements for 4096-bit FFC group

   unsigned char group16_initiator[512] = {
   0x79, 0x8f, 0xfe, 0xed, 0x53, 0x08, 0x41, 0x73,
   0xba, 0x89, 0x66, 0x8d, 0xf0, 0x18, 0xee, 0xe0,
   0x76, 0xda, 0x5f, 0xf8, 0x55, 0x36, 0x53, 0x71,
   0xd3, 0xfd, 0xf5, 0x30, 0xd9, 0xa0, 0xd2, 0x30,
   0x2c, 0x16, 0x38, 0x0a, 0x2b, 0x91, 0x6e, 0x02,
   0xc9, 0x27, 0x52, 0xf2, 0x51, 0x0e, 0xe3, 0x1f,
   0xbb, 0x2b, 0x8b, 0xad, 0xa8, 0xc3, 0xf4, 0xc0,
   0xba, 0x45, 0xf5, 0xf7, 0x4c, 0x91, 0x6f, 0x86,
   0x9a, 0xb8, 0xb1, 0xea, 0x7d, 0x89, 0x91, 0x39,
   0xd0, 0xb0, 0x95, 0x98, 0xf1, 0xa9, 0x03, 0x8d,
   0xc5, 0x7a, 0x75, 0x36, 0x7a, 0xf8, 0x0b, 0xf6,
   0xbf, 0x5c, 0x33, 0xde, 0x7f, 0xed, 0xec, 0x1a,
   0x1e, 0xbc, 0x54, 0xf1, 0x5f, 0x5c, 0xfa, 0x2f,

Harkins                   Expires July 6, 2017                 [Page 21]

Internet-Draft                    PKEX                      January 2017

   0x98, 0x85, 0xe0, 0x6f, 0xb8, 0x2b, 0x16, 0xe9,
   0x48, 0x6e, 0xe4, 0xb3, 0x3f, 0x20, 0x66, 0x3b,
   0x3d, 0xcf, 0x62, 0xc6, 0xed, 0xe5, 0x2e, 0x7a,
   0xac, 0x0b, 0x15, 0x6d, 0x15, 0x4e, 0xcb, 0x23,
   0xcd, 0x5a, 0xed, 0x51, 0xf4, 0xbe, 0x52, 0x6b,
   0x55, 0x30, 0xe3, 0x57, 0x91, 0x1f, 0xf3, 0xbd,
   0x07, 0xd9, 0x8b, 0x32, 0x9d, 0xfb, 0x99, 0xbb,
   0x17, 0x81, 0x24, 0xd1, 0x82, 0x10, 0xce, 0x34,
   0x77, 0x4f, 0xbc, 0x4d, 0xe6, 0x23, 0xdf, 0x2c,
   0x24, 0x8d, 0xf5, 0xf5, 0xf9, 0x93, 0x3d, 0x08,
   0x55, 0x31, 0xc8, 0xe5, 0xf3, 0x5b, 0x4c, 0xe2,
   0x4a, 0xdf, 0x88, 0x83, 0xc7, 0x84, 0x1b, 0xfa,
   0x99, 0x72, 0x1b, 0x13, 0x9e, 0xf6, 0x76, 0xca,
   0xa9, 0xa2, 0x7f, 0xd8, 0xc0, 0x9a, 0x46, 0x15,
   0x0b, 0x20, 0x4e, 0x53, 0x09, 0xe5, 0x16, 0x67,
   0xaf, 0xe5, 0x07, 0xe9, 0x57, 0x2f, 0xdc, 0x38,
   0xde, 0x33, 0x19, 0x49, 0x08, 0x05, 0x6f, 0xb9,
   0xb0, 0xce, 0x97, 0xab, 0xb5, 0xac, 0x88, 0x4e,
   0x7a, 0xbe, 0xd0, 0xaa, 0x74, 0x67, 0x73, 0xe3,
   0xd5, 0x04, 0x18, 0x41, 0x51, 0xcd, 0xf5, 0x59,
   0x85, 0xb6, 0x4b, 0x63, 0x1f, 0x24, 0x27, 0x18,
   0x02, 0x1d, 0xb7, 0x95, 0x45, 0xae, 0x60, 0x3a,
   0xcc, 0xcb, 0xca, 0x6f, 0xb8, 0x6f, 0x1b, 0x95,
   0xba, 0x46, 0x76, 0x8d, 0xc3, 0x61, 0xd0, 0x86,
   0xc3, 0x6c, 0x9a, 0xd9, 0x33, 0xde, 0xce, 0x97,
   0x28, 0x69, 0xa3, 0xd4, 0xbc, 0x49, 0x6d, 0x10,
   0x8d, 0x31, 0x77, 0x53, 0x94, 0xe3, 0xc5, 0xf9,
   0xea, 0xcd, 0xb3, 0x5b, 0xbf, 0x51, 0x6f, 0x57,
   0x8b, 0x9f, 0x40, 0x8b, 0x47, 0xa8, 0x77, 0xbe,
   0x44, 0x3d, 0x8b, 0x54, 0x63, 0xc3, 0xbb, 0xdc,
   0xeb, 0x9e, 0xec, 0xf5, 0x7c, 0x31, 0x69, 0x45,
   0xf5, 0x48, 0x2c, 0x84, 0x57, 0x53, 0xe1, 0x20,
   0x25, 0x2b, 0x70, 0x3a, 0x4e, 0x9f, 0x36, 0xc3,
   0x16, 0xf8, 0x4f, 0xa3, 0x21, 0x66, 0x51, 0x49,
   0xc6, 0x6d, 0xac, 0xd0, 0x2a, 0x8e, 0xd4, 0x5d,
   0x55, 0x11, 0x1a, 0x31, 0x77, 0xdb, 0xa8, 0xf4,
   0x7a, 0xb9, 0x32, 0xe8, 0x54, 0xaf, 0xed, 0x55,
   0x6e, 0x87, 0xd0, 0x5c, 0x6d, 0xb9, 0x19, 0x0f,
   0xbf, 0x16, 0xa6, 0xc7, 0x7c, 0xa2, 0xd3, 0x95,
   0x34, 0xad, 0xfc, 0xc2, 0x0a, 0xfc, 0x23, 0x2f,
   0xc7, 0xe9, 0x98, 0x92, 0x90, 0x11, 0x1d, 0xd5,
   0xf5, 0xbc, 0xd2, 0x8f, 0x09, 0xb0, 0x43, 0x63,
   0x65, 0x51, 0x17, 0xfd, 0x11, 0xee, 0xd2, 0x23,
   0xff, 0x9f, 0x4e, 0x39, 0xda, 0xfe, 0x89, 0xc1,
   0x9d, 0xf3, 0xe0, 0x31, 0xdd, 0x74, 0x36, 0xb2,
   0x9f, 0xfa, 0xd2, 0xd0, 0xfc, 0xc4, 0x37, 0x83,
   0xf0, 0x13, 0x1f, 0x8d, 0x80, 0x47, 0x53, 0x93,
   0x0c, 0x84, 0x1f, 0x69, 0x08, 0x74, 0x33, 0x29,

Harkins                   Expires July 6, 2017                 [Page 22]

Internet-Draft                    PKEX                      January 2017

   0x59, 0x5f, 0x62, 0x7d, 0xe2, 0x59, 0x1c, 0x56,
   0x52, 0x75, 0xc2, 0x83, 0xad, 0xc0, 0xd4, 0x66,
   0x71, 0x6a, 0x1a, 0x61, 0x94, 0xa4, 0xa5, 0x73

   unsigned char group16_responder[512] = {
   0x06, 0x85, 0x8b, 0x2e, 0x0c, 0x05, 0xfd, 0x1b,
   0x1f, 0x93, 0xd3, 0xc2, 0xe6, 0x70, 0xc8, 0xe1,
   0x17, 0x39, 0xe6, 0x38, 0x75, 0xfd, 0xdd, 0xe6,
   0x4a, 0xfe, 0x95, 0x5e, 0xd6, 0x80, 0x17, 0x2c,
   0x1d, 0xbb, 0x8c, 0xf7, 0x2d, 0x9b, 0x17, 0x93,
   0x4d, 0x92, 0xd3, 0x57, 0xa0, 0xcd, 0x44, 0x37,
   0x1d, 0xdf, 0xd3, 0x80, 0x25, 0xa0, 0xa8, 0x51,
   0x13, 0xb9, 0x63, 0xec, 0xda, 0xa2, 0x8b, 0xdb,
   0x2e, 0x09, 0x9c, 0x93, 0x09, 0x02, 0x64, 0xb4,
   0xee, 0xa2, 0x3c, 0x75, 0x0e, 0xbb, 0x31, 0x44,
   0xff, 0xf0, 0x7e, 0x99, 0x86, 0x17, 0xe5, 0xc4,
   0xf9, 0x39, 0xe1, 0xec, 0xed, 0xd5, 0x13, 0xe9,
   0x97, 0xda, 0x2b, 0xb5, 0x1e, 0x23, 0x88, 0x1a,
   0xb5, 0x10, 0xda, 0x24, 0x05, 0xe7, 0xdf, 0xc3,
   0xc2, 0x24, 0xd2, 0xf4, 0x14, 0x6c, 0xfd, 0x2e,
   0x62, 0xa8, 0x00, 0x4e, 0xa9, 0x96, 0x3d, 0x48,
   0x4f, 0xcf, 0x62, 0xfe, 0x16, 0x06, 0x56, 0x81,
   0x1b, 0x58, 0xca, 0x84, 0xd2, 0x86, 0xad, 0xc6,
   0x66, 0xb4, 0x6f, 0x49, 0x91, 0x2a, 0xb5, 0x3b,
   0x39, 0xec, 0x88, 0xdf, 0x31, 0x24, 0x44, 0x04,
   0x30, 0x4e, 0x91, 0xdd, 0x1f, 0xf7, 0x62, 0x0c,
   0x8a, 0xf1, 0xcd, 0xf1, 0xcf, 0x56, 0x42, 0x1d,
   0x1b, 0xb2, 0x47, 0x7f, 0x4c, 0x82, 0x88, 0xbe,
   0x99, 0x31, 0x96, 0x6e, 0x5f, 0xa0, 0x6a, 0xa0,
   0x53, 0x63, 0xdb, 0xb9, 0xe0, 0xe4, 0x8f, 0xa9,
   0x44, 0x32, 0x2e, 0x05, 0x70, 0x3b, 0x6e, 0xc3,
   0x82, 0x36, 0x51, 0x4c, 0xbe, 0x38, 0x61, 0x54,
   0x66, 0x5c, 0x88, 0x42, 0x50, 0x84, 0x1a, 0x69,
   0xdf, 0xc5, 0x2b, 0x00, 0x3d, 0xdb, 0xe1, 0x92,
   0x69, 0xb4, 0xda, 0xfa, 0x87, 0x43, 0x9e, 0xdd,
   0x03, 0x29, 0xd4, 0x06, 0xef, 0x63, 0x60, 0xe3,
   0x83, 0xe3, 0x28, 0xd7, 0xa3, 0x47, 0xeb, 0xb7,
   0x0a, 0x20, 0x5a, 0x9e, 0x61, 0x68, 0xcc, 0x0b,
   0x39, 0xdc, 0x7b, 0x8c, 0x22, 0x0f, 0xc8, 0xd4,
   0x0c, 0x44, 0x9c, 0xa2, 0xb4, 0xd2, 0xf4, 0x71,
   0xeb, 0xc6, 0x75, 0xb8, 0x53, 0x8c, 0x93, 0x9a,
   0xf2, 0xd7, 0xba, 0x45, 0x40, 0xef, 0x56, 0xaf,
   0xdd, 0x1b, 0xcc, 0x0e, 0xe0, 0x3b, 0x2f, 0xd5,
   0xc5, 0xc7, 0x36, 0x37, 0xc0, 0x5e, 0xff, 0xb1,
   0x31, 0xce, 0xce, 0xc3, 0x28, 0xb7, 0x84, 0x88,
   0xe2, 0x7f, 0x11, 0x62, 0xb1, 0x14, 0x41, 0xe2,
   0x7e, 0xfb, 0x31, 0x0e, 0x5b, 0xba, 0x27, 0xf7,

Harkins                   Expires July 6, 2017                 [Page 23]

Internet-Draft                    PKEX                      January 2017

   0xa0, 0xce, 0xa0, 0xb8, 0xdd, 0xbe, 0xc4, 0x74,
   0xe0, 0xc9, 0x50, 0x71, 0x16, 0x81, 0x42, 0x2a,
   0xa9, 0xda, 0x2e, 0x3a, 0x85, 0x0b, 0x62, 0x5a,
   0x55, 0x31, 0x31, 0xc4, 0xda, 0x4b, 0x36, 0x9a,
   0xa6, 0x0b, 0x78, 0x51, 0x50, 0xea, 0x44, 0x07,
   0x6d, 0xf7, 0x49, 0xb0, 0xea, 0x7e, 0x12, 0x92,
   0x88, 0x5e, 0xb8, 0xee, 0x0b, 0xa9, 0xd8, 0x04,
   0xbe, 0xd8, 0x5d, 0x8e, 0x0a, 0xea, 0x5c, 0xce,
   0xf5, 0x2d, 0x80, 0xff, 0x57, 0x07, 0x0c, 0x06,
   0x20, 0xaf, 0xb5, 0x32, 0x16, 0xb5, 0x79, 0x60,
   0xce, 0x3b, 0xb8, 0x55, 0x4c, 0xf5, 0x58, 0x90,
   0xeb, 0xae, 0x48, 0x04, 0x8b, 0x76, 0xfc, 0x66,
   0x18, 0x70, 0x13, 0x5c, 0x85, 0xa4, 0x18, 0xf1,
   0xbb, 0x06, 0x4e, 0x59, 0x19, 0x75, 0x4d, 0xaf,
   0x97, 0x6b, 0x1c, 0x82, 0x2f, 0xbf, 0x91, 0xbb,
   0xb7, 0x93, 0x21, 0xf2, 0xca, 0xf7, 0xec, 0x31,
   0xf2, 0x05, 0x73, 0x1e, 0x69, 0x30, 0xd1, 0xd9,
   0xef, 0x4f, 0x57, 0xc5, 0xf2, 0x46, 0xbf, 0xe8,
   0x81, 0xb6, 0x24, 0xdb, 0xf3, 0x67, 0x27, 0x97,
   0xb8, 0x04, 0x8c, 0xa3, 0xfe, 0xda, 0x6b, 0x9d,
   0x51, 0xba, 0xbd, 0xb5, 0xca, 0xfe, 0x73, 0xce,
   0x48, 0x9d, 0x28, 0x30, 0x7d, 0x53, 0x63, 0xc7

A.2.4.  Role-specific Elements for 8192-bit FFC group

   unsigned char group18_initiator[1024] = {
   0x5b, 0x92, 0xc0, 0x76, 0x71, 0x48, 0x5e, 0x4d,
   0x9d, 0xdf, 0xde, 0xc3, 0xcc, 0x32, 0x6e, 0xf1,
   0x90, 0xef, 0x71, 0x86, 0xde, 0x55, 0x60, 0x3e,
   0x24, 0x3e, 0xc2, 0x38, 0x09, 0x65, 0x56, 0xfb,
   0x2b, 0x8b, 0x97, 0x07, 0x19, 0xac, 0xaf, 0x59,
   0x32, 0xd7, 0x65, 0x19, 0xa2, 0x02, 0x83, 0xa3,
   0x72, 0xc2, 0x2c, 0xe8, 0x15, 0x58, 0x0d, 0xb8,
   0x1a, 0xad, 0xe3, 0xbc, 0xc0, 0x82, 0xab, 0x42,
   0x9a, 0x7e, 0x0d, 0x39, 0x6a, 0x81, 0x3e, 0x72,
   0xee, 0xba, 0x58, 0x01, 0xe6, 0x36, 0x9f, 0x82,
   0x49, 0xa3, 0x6a, 0x88, 0x59, 0x0f, 0x77, 0x6b,
   0x4d, 0x6a, 0x36, 0x25, 0xf0, 0xbc, 0x75, 0x53,
   0x45, 0x1b, 0x02, 0x4c, 0x99, 0x5d, 0x51, 0x87,
   0x41, 0x3c, 0xcc, 0x54, 0x6a, 0xdc, 0x6e, 0x22,
   0xb5, 0x7d, 0xa9, 0x65, 0x90, 0xd3, 0x38, 0x4c,
   0xa8, 0x26, 0x22, 0x57, 0xd8, 0x55, 0xc0, 0xc9,
   0x9a, 0x62, 0x08, 0x71, 0x2b, 0x55, 0xde, 0x89,
   0xd4, 0xf8, 0xab, 0x5f, 0x55, 0x42, 0xc0, 0x40,
   0x60, 0x61, 0x1b, 0x68, 0x01, 0x80, 0x67, 0x27,
   0x95, 0x8e, 0x6b, 0xcd, 0xc1, 0x04, 0x35, 0x96,
   0x8e, 0x15, 0x1e, 0xd3, 0x01, 0x7d, 0x81, 0x38,

Harkins                   Expires July 6, 2017                 [Page 24]

Internet-Draft                    PKEX                      January 2017

   0xe8, 0xbf, 0xd1, 0xa8, 0x31, 0xd5, 0x49, 0x11,
   0x0d, 0x78, 0x2f, 0x61, 0x31, 0xfc, 0xcc, 0x11,
   0x4f, 0x09, 0xa1, 0x13, 0x2b, 0x0e, 0x73, 0xbc,
   0x1f, 0xef, 0x01, 0x7d, 0xd3, 0x26, 0xe3, 0xda,
   0xa9, 0xaa, 0x15, 0xaf, 0x47, 0xe5, 0xc0, 0x39,
   0x29, 0xa3, 0x68, 0xfc, 0x03, 0xaa, 0x20, 0xc0,
   0xf8, 0xc5, 0xe2, 0xe3, 0x03, 0x0d, 0x3c, 0x20,
   0x7c, 0xbf, 0xa5, 0x1b, 0xd9, 0x92, 0x2d, 0x79,
   0x42, 0x42, 0xe8, 0x92, 0x25, 0x9a, 0x94, 0x54,
   0x40, 0xec, 0x8d, 0x55, 0x26, 0x71, 0xb3, 0x58,
   0x2c, 0x0b, 0x81, 0x4d, 0x53, 0xb8, 0x52, 0xf9,
   0x1b, 0xb1, 0x75, 0x60, 0xd4, 0x4b, 0x45, 0x72,
   0xa6, 0x61, 0x20, 0x96, 0xaa, 0x3b, 0xb9, 0x50,
   0x81, 0xe3, 0x93, 0xde, 0x4b, 0x80, 0xa2, 0xbd,
   0x20, 0x64, 0x63, 0xe2, 0x48, 0xc8, 0xec, 0x82,
   0x07, 0xa1, 0x7b, 0x45, 0x2a, 0xfb, 0xe9, 0x2f,
   0xa1, 0xf0, 0x69, 0x36, 0x2d, 0x4f, 0x1a, 0x85,
   0xf3, 0x58, 0x34, 0xe6, 0x0a, 0x9e, 0xe9, 0x9a,
   0x77, 0xe5, 0xf9, 0xa4, 0xc4, 0x14, 0xa2, 0x43,
   0xdd, 0xaa, 0x03, 0x17, 0x71, 0x55, 0x62, 0xf4,
   0xf5, 0x9c, 0x5f, 0x2f, 0xe7, 0x6f, 0xde, 0xa4,
   0x7a, 0xbb, 0x9d, 0xb5, 0x8d, 0xc3, 0x95, 0xf9,
   0x54, 0x06, 0xba, 0xd1, 0x31, 0xcf, 0x03, 0x6c,
   0x7a, 0x53, 0xd5, 0x76, 0x97, 0x4c, 0xbd, 0x23,
   0x59, 0xff, 0xfe, 0xea, 0xd3, 0xd1, 0x86, 0x10,
   0x2c, 0xf9, 0x9f, 0xc8, 0xd3, 0x45, 0x44, 0x2f,
   0x5a, 0xcf, 0x86, 0x8e, 0x1c, 0xc2, 0xb7, 0x04,
   0x75, 0x74, 0x78, 0xdf, 0x7a, 0x6f, 0xaf, 0x56,
   0x03, 0x93, 0x19, 0x4f, 0x4d, 0x73, 0x11, 0xc9,
   0x34, 0x90, 0x1a, 0x76, 0x18, 0x76, 0xa7, 0x19,
   0xe4, 0x5e, 0x66, 0x10, 0x2e, 0x0a, 0xbe, 0x7c,
   0x64, 0xd2, 0xd3, 0xbb, 0x18, 0x58, 0x86, 0xd9,
   0x54, 0x58, 0xf5, 0xeb, 0x86, 0xac, 0x61, 0x48,
   0xbc, 0x95, 0x1e, 0x13, 0xab, 0xef, 0x6e, 0xdf,
   0xbc, 0xa5, 0x78, 0x10, 0x87, 0x43, 0x9a, 0xd6,
   0xd6, 0x10, 0x30, 0xc0, 0xf5, 0x9b, 0x09, 0xc4,
   0x2c, 0xed, 0x8b, 0xeb, 0xc7, 0x3c, 0x12, 0xc5,
   0x1c, 0xf1, 0x88, 0xfd, 0x15, 0x45, 0xdb, 0xb3,
   0x35, 0x87, 0x40, 0xf8, 0x8a, 0xd1, 0x07, 0x32,
   0x2b, 0xf7, 0x4a, 0x77, 0xb5, 0x69, 0x4a, 0x20,
   0xdd, 0x69, 0x1e, 0x38, 0xac, 0x0b, 0x31, 0xda,
   0x43, 0x5d, 0xf0, 0x94, 0x22, 0x8d, 0x4a, 0x26,
   0xda, 0x91, 0xdf, 0xb7, 0xdd, 0xfb, 0x97, 0x88,
   0x7a, 0x43, 0x5e, 0xf3, 0x36, 0xbd, 0xef, 0xc0,
   0xe6, 0x7f, 0xd1, 0x81, 0x5b, 0xd6, 0x1b, 0x01,
   0x89, 0x19, 0x1d, 0x0e, 0xd0, 0x1a, 0x3a, 0x56,
   0x82, 0xf6, 0x2c, 0xdf, 0x6a, 0x42, 0xf5, 0x44,
   0x57, 0x61, 0x95, 0xdc, 0x9d, 0x4c, 0x15, 0xc0,

Harkins                   Expires July 6, 2017                 [Page 25]

Internet-Draft                    PKEX                      January 2017

   0x29, 0x42, 0x55, 0x77, 0x28, 0xc8, 0x7c, 0xe2,
   0xc8, 0x44, 0xbd, 0xdd, 0x8e, 0xe1, 0xb8, 0xa3,
   0xa6, 0xb1, 0xa5, 0xfc, 0x9f, 0xed, 0x5f, 0xd7,
   0x58, 0xee, 0xe9, 0xa8, 0x1e, 0x11, 0x1a, 0x8c,
   0xf6, 0xea, 0x45, 0x8f, 0x41, 0x4d, 0xb9, 0x7f,
   0xe9, 0xd2, 0x90, 0x8c, 0xed, 0x0a, 0xd1, 0x12,
   0x48, 0x9b, 0x5e, 0x8a, 0x98, 0xc8, 0x0e, 0x71,
   0xff, 0x35, 0xa3, 0xc0, 0x17, 0x1c, 0x29, 0xe7,
   0x30, 0x47, 0x5f, 0x22, 0x62, 0x1b, 0xde, 0xb9,
   0xeb, 0x20, 0xcc, 0xeb, 0xfc, 0x7d, 0x38, 0x1e,
   0xce, 0x8a, 0x4e, 0xa8, 0xfe, 0xba, 0xa9, 0xfc,
   0x44, 0x8a, 0xcf, 0x0a, 0xe3, 0xf1, 0x91, 0x63,
   0xaf, 0xf2, 0x7d, 0x52, 0x2a, 0x6d, 0x38, 0xcf,
   0x10, 0xd5, 0xa3, 0xa1, 0xb0, 0xcc, 0x74, 0x08,
   0xe9, 0x97, 0xe1, 0x7e, 0xd8, 0xd1, 0x3f, 0x4e,
   0x8d, 0x6d, 0x4e, 0x3e, 0x33, 0xc7, 0xae, 0x28,
   0xb6, 0x6a, 0xd0, 0x15, 0xf3, 0xd6, 0xfd, 0x11,
   0x3e, 0xbc, 0x65, 0xe6, 0xf7, 0xb4, 0xfe, 0x55,
   0x03, 0x4d, 0x1f, 0x4f, 0x8b, 0xef, 0x8d, 0x11,
   0xa2, 0x9b, 0x42, 0x58, 0xf4, 0xdf, 0x0c, 0xf2,
   0x80, 0x0e, 0x02, 0xff, 0xe8, 0x46, 0x0d, 0xae,
   0x50, 0x41, 0x14, 0x37, 0x5d, 0x82, 0x26, 0x96,
   0x9f, 0x1d, 0xff, 0x9e, 0xe0, 0x01, 0x24, 0x19,
   0xe8, 0xca, 0xe7, 0x7b, 0xaa, 0xef, 0x05, 0x4a,
   0x8a, 0xdd, 0x3b, 0xe8, 0x93, 0xf0, 0x21, 0xab,
   0x7f, 0x77, 0xcd, 0xc1, 0x71, 0x9f, 0x6b, 0x2b,
   0x64, 0xfb, 0x43, 0x9e, 0x92, 0x33, 0x68, 0xe6,
   0x51, 0xc1, 0x16, 0x3d, 0xde, 0xf8, 0x85, 0x8a,
   0xb6, 0x6c, 0x96, 0x7a, 0x6b, 0x12, 0xd8, 0x18,
   0x30, 0x5e, 0x0c, 0x82, 0xff, 0xff, 0xd0, 0xf7,
   0x9c, 0x23, 0x30, 0x61, 0x80, 0x5b, 0xde, 0xd9,
   0x35, 0x16, 0xdd, 0x6a, 0x5b, 0xbe, 0x5a, 0x1d,
   0x77, 0x37, 0x2b, 0xee, 0x00, 0x61, 0xef, 0xfe,
   0xa8, 0x3f, 0x2e, 0xd6, 0x8e, 0x3a, 0x0f, 0x03,
   0xae, 0x46, 0x01, 0x0c, 0x75, 0x8c, 0x42, 0x9b,
   0x24, 0x02, 0x4b, 0xdb, 0xb8, 0x98, 0x31, 0xc7,
   0xd0, 0xd9, 0xb1, 0x89, 0x4a, 0x54, 0x74, 0xc0,
   0x68, 0x5d, 0xe7, 0x62, 0xe4, 0x44, 0x44, 0x5e,
   0x17, 0x75, 0x34, 0x96, 0xbe, 0xf1, 0x94, 0x49,
   0x14, 0xe7, 0x17, 0x79, 0xf6, 0xab, 0xe8, 0xf4,
   0x47, 0x77, 0x74, 0x10, 0x51, 0x3b, 0x30, 0x8e,
   0x8e, 0x00, 0x4f, 0x0e, 0x75, 0x03, 0xc7, 0x48,
   0xfb, 0xf8, 0x50, 0xc7, 0xe5, 0xfc, 0xe2, 0x7d,
   0x07, 0x90, 0xd5, 0x91, 0x6a, 0xce, 0x14, 0x12,
   0xab, 0xe6, 0x65, 0x64, 0xfb, 0x03, 0xce, 0xdf,
   0xf1, 0x0b, 0x11, 0x82, 0x5a, 0x11, 0xf6, 0xf9,
   0xd6, 0xf2, 0xfe, 0xd4, 0x72, 0x60, 0x80, 0xd4,
   0x53, 0x86, 0xe6, 0xfc, 0xb7, 0xc0, 0x03, 0x4d,

Harkins                   Expires July 6, 2017                 [Page 26]

Internet-Draft                    PKEX                      January 2017

   0x3c, 0x32, 0xe9, 0xfd, 0x46, 0x9e, 0x81, 0x6a,
   0x72, 0xd6, 0x9c, 0x14, 0x70, 0x47, 0xbe, 0x35,
   0xef, 0xb2, 0xbb, 0x0a, 0xca, 0x84, 0xc9, 0x15,
   0xac, 0x83, 0x6b, 0x83, 0xe8, 0x36, 0x5d, 0x27,
   0xc0, 0x25, 0xc8, 0x92, 0x69, 0x6b, 0x51, 0x6a,
   0xc2, 0x8f, 0x9c, 0x8b, 0xf5, 0x35, 0x1e, 0x31,
   0x4b, 0xf7, 0xd6, 0x40, 0xa7, 0x1c, 0xe4, 0xa2,
   0x00, 0x3c, 0x78, 0x78, 0x8f, 0x27, 0x24, 0x7e,
   0x0b, 0x7f, 0xf6, 0xb0, 0x66, 0xf4, 0x79, 0x46,
   0x2e, 0x5b, 0x11, 0xca, 0x9b, 0x93, 0x4e, 0x99,
   0x2c, 0xd2, 0x2d, 0x88, 0x84, 0xf1, 0x1e, 0x0e

   unsigned char group18_responder[1024] = {
   0xdf, 0x63, 0xdc, 0x3a, 0x74, 0xbd, 0x83, 0x8e,
   0x72, 0x90, 0x81, 0xf0, 0x85, 0x65, 0x86, 0x07,
   0x06, 0x05, 0xed, 0x93, 0x73, 0xa5, 0xbb, 0x88,
   0x42, 0x17, 0x8a, 0x10, 0x33, 0xc3, 0x6e, 0x9b,
   0x3b, 0x68, 0x33, 0x30, 0xa2, 0x3f, 0xb2, 0xa3,
   0x2d, 0x6b, 0xec, 0x34, 0x5a, 0xe7, 0x6a, 0xc1,
   0x11, 0xc8, 0xa5, 0x3d, 0x6c, 0xc5, 0xf7, 0x48,
   0xca, 0xac, 0xa6, 0x10, 0x0b, 0x7c, 0x93, 0xe9,
   0x45, 0x4d, 0xa7, 0x00, 0x30, 0xd2, 0xf5, 0xaf,
   0x93, 0xf1, 0xa5, 0x8a, 0x9f, 0x10, 0x14, 0xe6,
   0x6a, 0xe0, 0x5a, 0xe6, 0xea, 0x8b, 0x21, 0xbb,
   0x6a, 0x1f, 0x6c, 0x8c, 0x0b, 0x01, 0xda, 0xfd,
   0x4f, 0x0b, 0x7f, 0xe9, 0x46, 0x27, 0x8e, 0xaa,
   0x64, 0xd1, 0xd5, 0x40, 0xc9, 0xf7, 0x47, 0xef,
   0x9f, 0x7c, 0xce, 0x6c, 0x41, 0xd2, 0x9c, 0x47,
   0x09, 0x6e, 0xc7, 0xc2, 0xdc, 0x7d, 0x7e, 0xce,
   0x04, 0x6f, 0xf9, 0xc1, 0x86, 0x56, 0x1b, 0x88,
   0x7f, 0x62, 0x33, 0x3b, 0xca, 0xb9, 0xd4, 0x7d,
   0x24, 0xfa, 0x9f, 0xd8, 0xf8, 0x63, 0x91, 0x72,
   0x45, 0x82, 0x4d, 0x9f, 0xd7, 0x9d, 0xc8, 0x0b,
   0x4c, 0x6a, 0xc5, 0xf4, 0xec, 0x77, 0x3e, 0xfd,
   0xb7, 0x6b, 0xe0, 0x86, 0x32, 0x41, 0x25, 0xfe,
   0x43, 0x03, 0x0a, 0x07, 0x90, 0x75, 0xd5, 0xca,
   0x48, 0x23, 0xfb, 0x80, 0x5f, 0x22, 0xfe, 0x1c,
   0xba, 0x48, 0x2c, 0x28, 0x78, 0x5c, 0xc4, 0x98,
   0xad, 0xb7, 0xa6, 0x78, 0x5f, 0x84, 0x3a, 0xb6,
   0x96, 0xd5, 0xad, 0x88, 0x60, 0xb9, 0x09, 0x00,
   0xbb, 0x7d, 0x5c, 0xd6, 0x17, 0xfe, 0x18, 0x8e,
   0x07, 0x10, 0xc3, 0xe9, 0xd0, 0xb8, 0xe2, 0xfa,
   0x00, 0xae, 0xa1, 0xcd, 0x86, 0x33, 0xda, 0x4b,
   0x0c, 0x34, 0xa1, 0x6e, 0x19, 0x0b, 0xdb, 0xef,
   0xb0, 0xf6, 0x86, 0xc6, 0xe3, 0x8c, 0x9c, 0x53,
   0x15, 0x16, 0x04, 0xd9, 0xa8, 0xa7, 0x38, 0xc1,
   0x43, 0x9d, 0x7e, 0x33, 0x16, 0x1a, 0x8d, 0x33,

Harkins                   Expires July 6, 2017                 [Page 27]

Internet-Draft                    PKEX                      January 2017

   0xe8, 0x2b, 0x47, 0xaf, 0x4c, 0xd0, 0x96, 0x87,
   0x5b, 0x57, 0x27, 0xc3, 0x1a, 0xf7, 0x12, 0xfd,
   0x8a, 0x64, 0xa0, 0xc9, 0x51, 0xc9, 0x95, 0xcb,
   0x7b, 0x9d, 0x97, 0xda, 0x3c, 0xae, 0x87, 0x1c,
   0x08, 0xa8, 0xb2, 0x3b, 0x92, 0xb7, 0x52, 0x97,
   0x99, 0x9c, 0x52, 0x92, 0xcc, 0xba, 0xbe, 0x16,
   0xf7, 0xac, 0x08, 0xb5, 0x1a, 0x99, 0x99, 0xee,
   0x33, 0x3a, 0x2a, 0xea, 0x70, 0xbe, 0xcc, 0xfd,
   0xc7, 0x6b, 0xf3, 0xa9, 0x9d, 0x66, 0x87, 0x1b,
   0x26, 0x0e, 0xf5, 0x04, 0x33, 0x82, 0x25, 0x75,
   0x74, 0x37, 0xbd, 0xfe, 0x78, 0xa2, 0x4a, 0x77,
   0xda, 0xef, 0x84, 0xfd, 0x5c, 0x1d, 0x09, 0xc7,
   0xd8, 0xc2, 0x97, 0xf8, 0xd0, 0x96, 0x6f, 0xf0,
   0x54, 0xea, 0x5e, 0x14, 0xb6, 0x9c, 0x16, 0x96,
   0xcd, 0x56, 0x3e, 0x49, 0xef, 0x8f, 0xbf, 0xc1,
   0x59, 0xd6, 0x0c, 0xa0, 0xd6, 0x6b, 0xff, 0x34,
   0xe5, 0x68, 0x70, 0x6b, 0x00, 0x87, 0xac, 0x4e,
   0x7e, 0x44, 0xa2, 0x04, 0xa2, 0x96, 0xfc, 0x73,
   0xe7, 0xe2, 0x7f, 0xc6, 0x0b, 0x17, 0xdb, 0xa6,
   0x45, 0xa8, 0x72, 0x61, 0x08, 0xc8, 0x4c, 0x19,
   0x2d, 0x27, 0x0b, 0x4f, 0xb9, 0xc0, 0x55, 0xd6,
   0x6d, 0x11, 0xd7, 0x15, 0x0d, 0xef, 0x97, 0x08,
   0xd3, 0x22, 0xd8, 0x03, 0x7f, 0x91, 0xe0, 0x0e,
   0xe4, 0x70, 0x75, 0x47, 0x33, 0xd9, 0x80, 0x08,
   0x5f, 0xc9, 0xea, 0x91, 0xd4, 0x4e, 0x80, 0x08,
   0xb3, 0x83, 0x37, 0xba, 0xd2, 0xe0, 0x6d, 0x44,
   0x83, 0x9a, 0xf1, 0xa6, 0x83, 0xc4, 0x5a, 0xd2,
   0x3f, 0x50, 0x7a, 0x19, 0xed, 0x82, 0xda, 0x02,
   0x6f, 0xbe, 0x27, 0x91, 0xd6, 0x7e, 0x11, 0xc1,
   0x95, 0x3a, 0x6a, 0x61, 0x80, 0x6c, 0x23, 0x1f,
   0xcd, 0x8d, 0xac, 0x5c, 0x4c, 0x14, 0xee, 0xde,
   0x08, 0x15, 0x87, 0xae, 0x2d, 0xf4, 0x77, 0x81,
   0xcb, 0x39, 0x9a, 0x51, 0xb1, 0x3e, 0xc6, 0xd5,
   0xcd, 0xa2, 0x3a, 0x15, 0x6a, 0x73, 0x2e, 0x78,
   0x24, 0x16, 0xb8, 0xd2, 0x3e, 0xb4, 0x0c, 0xc2,
   0x0e, 0x67, 0xea, 0xe9, 0x9c, 0xce, 0x5c, 0x6a,
   0x29, 0x27, 0xe1, 0x3f, 0xac, 0x9d, 0x31, 0xb8,
   0xda, 0x2f, 0x94, 0x6e, 0xfc, 0x33, 0xab, 0x54,
   0xf9, 0x8e, 0xe8, 0xbf, 0x8e, 0x33, 0x62, 0xab,
   0x1f, 0xca, 0x17, 0x68, 0x89, 0x27, 0x19, 0x52,
   0xb1, 0x4c, 0xd1, 0x04, 0xb8, 0x8d, 0xfe, 0xc2,
   0xa4, 0xbf, 0xb8, 0x4e, 0x7c, 0x24, 0x2f, 0xaa,
   0x8c, 0x57, 0x3c, 0x60, 0xe8, 0xd5, 0x1e, 0x7f,
   0x8b, 0x85, 0x0e, 0xfb, 0x0e, 0xbd, 0xed, 0x75,
   0x3f, 0x35, 0xeb, 0xb7, 0x35, 0x60, 0x53, 0x8f,
   0x7d, 0x86, 0xbc, 0x98, 0x8b, 0x2e, 0x22, 0x33,
   0x5e, 0x60, 0x49, 0x6d, 0xc3, 0xe0, 0xaa, 0xec,
   0x5e, 0x67, 0x87, 0xd8, 0x20, 0x92, 0x71, 0x34,

Harkins                   Expires July 6, 2017                 [Page 28]

Internet-Draft                    PKEX                      January 2017

   0x46, 0xa4, 0xf4, 0x2d, 0x02, 0xaf, 0x64, 0x45,
   0xef, 0xea, 0xb3, 0x84, 0x39, 0xd6, 0x6b, 0xaf,
   0x7d, 0x63, 0xd3, 0x50, 0xf9, 0x95, 0xaf, 0xf7,
   0xf3, 0x8a, 0x6f, 0x59, 0xf1, 0x32, 0x37, 0x3d,
   0x6c, 0xd4, 0xaa, 0x17, 0xd7, 0x13, 0x19, 0xa7,
   0x51, 0x98, 0x21, 0x89, 0x26, 0x12, 0xe1, 0xed,
   0x78, 0x04, 0x33, 0xd7, 0xc6, 0xf4, 0xe2, 0x39,
   0x5c, 0x37, 0xdb, 0x16, 0x42, 0xf9, 0x0a, 0x3d,
   0xee, 0x4b, 0x96, 0xbd, 0x60, 0x1f, 0x36, 0xbb,
   0xe6, 0x15, 0x95, 0x47, 0x7f, 0x8f, 0x2e, 0xff,
   0x59, 0x9b, 0xfc, 0x99, 0x13, 0x87, 0xac, 0x85,
   0xd9, 0x84, 0x0c, 0x99, 0x95, 0xe8, 0x2b, 0xdf,
   0xae, 0x64, 0x7e, 0x24, 0x85, 0x67, 0x9c, 0x86,
   0x51, 0x8a, 0x61, 0x6c, 0x17, 0x24, 0x89, 0xba,
   0x2f, 0xfa, 0x9d, 0x3d, 0xa6, 0x51, 0xce, 0x85,
   0xf8, 0x95, 0x78, 0xeb, 0x00, 0x51, 0x06, 0xb4,
   0x8b, 0x02, 0x1b, 0x1c, 0xf7, 0x13, 0xcb, 0xee,
   0x83, 0x98, 0xdc, 0xab, 0xed, 0x57, 0x62, 0x78,
   0x1c, 0xc5, 0x5c, 0xac, 0xa6, 0x23, 0x68, 0xd0,
   0xa5, 0xda, 0x43, 0x2d, 0x61, 0x73, 0x66, 0x03,
   0xea, 0xc9, 0xad, 0x7e, 0xe3, 0x54, 0xa9, 0x53,
   0x3e, 0x23, 0x4c, 0x6a, 0x15, 0x70, 0xa5, 0x2c,
   0xee, 0xcd, 0x4d, 0x7e, 0x41, 0x6f, 0xa6, 0xc5,
   0x1c, 0x24, 0x37, 0x58, 0x00, 0x81, 0xd9, 0xb2,
   0xf7, 0x9a, 0x9c, 0xa3, 0xf5, 0xc6, 0x31, 0xc1,
   0xb2, 0x8b, 0x3d, 0xec, 0xbe, 0x21, 0xe7, 0x53,
   0x0f, 0xb8, 0x87, 0x76, 0xb5, 0x76, 0xcc, 0x50,
   0x03, 0x51, 0x8a, 0xa5, 0xb9, 0x50, 0xc7, 0x38,
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Harkins                   Expires July 6, 2017                 [Page 29]

Internet-Draft                    PKEX                      January 2017

Author's Address

   Dan Harkins
   HP Enterprise
   1322 Crossman avenue
   Sunnyvale, California  94089

   Phone: +1 415 997 9834

Harkins                   Expires July 6, 2017                 [Page 30]