PKEX
draft-harkins-pkex-02
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| Last updated | 2016-11-28 | ||
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draft-harkins-pkex-02
Internet Research Task Force Harkins
Internet-Draft HP Enterprise
Intended status: Informational November 28, 2016
Expires: June 1, 2017
PKEX
draft-harkins-pkex-02
Abstract
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 June 1, 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
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the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. Requirements Language . . . . . . . . . . . . . . . . . . 3
1.2. Notation . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Properties . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 4
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 . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.1. Normative References . . . . . . . . . . . . . . . . . . 8
8.2. Informative References . . . . . . . . . . . . . . . . . 9
Appendix A. Generation of ECC Role-specific Elements . . . . . . 9
A.1. Role-specific Elements for NIST p256 . . . . . . . . . . 10
A.2. Role-specific Elements for NIST p384 . . . . . . . . . . 10
A.3. Role-specific Elements for NIST p521 . . . . . . . . . . 11
A.4. Role-specific Elements for brainpool p256r1 . . . . . . . 13
A.5. Role-specific Elements for brainpool p384r1 . . . . . . . 13
A.6. Role-specific Elements for brainpool p512r1 . . . . . . . 14
Appendix B. Generation of FFC Role-Specific Elements . . . . . . 15
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 16
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
public keys that can subsequently be used to faccilitate
authentication in other authentication and key exchange protocols.
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1.1. Requirements Language
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in 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.
a = H(b)
A cryptographic hash function that takes data b of indeterminate
length and returns a fixed sized digest a.
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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
function.
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.
c = a | b
Concatentation of data a with data b producing c.
{a}b
Authenticated-encryption of data a with key b.
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
password.
o An adversary is unable to discover the password through passive
attack.
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.
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
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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 and Appendix B.
The authenticated-encryption algorithm provides deterministic "key
wrapping". To achieve this the AE scheme used in PKEX is [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 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 requires 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)
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)
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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
Qi = H(Alice|pw)*Pi Qr = H(Bob|pw)*Pr
M = X + Qa
M ------>
Qi = H(Alice|pw)*Pi
X' = M - Qi
N = Y + Qr
<------ N
Qr = H(Bob|pw)*Pr
Y' = N - Qr
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 in time 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 are irretrievably deleted at this
point.
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5.2. Commit/Reveal Phase
In the Commit/Reveal phase the peers commit to the particular public
key they wish to exchange and then reveal it to the peer.
Alice: Bob:
------ ----
ka = KDF-n(F(a*Y'), F(M) | F(N) |
F(A) | F(Y') | pw)
u = HMAC(ka, F(X) | F(Y') |
F(A) | Alice | 0)
z = KDF-n(F(x*Y'), F(M) | F(N) |
F(X) | F(Y') | pw)
{A, u}z ------>
z = KDF-n(F(y*X'), F(M) | F(N) |
F(X') | F(Y) | pw)
if (SIV-decrypt returns fail) fail
if (A not valid element) fail
ka' = KDF-n(F(y*A), F(M) | F(N) |
F(A) | F(Y) | pw)
u' = HMAC(ka', F(X') | F(Y) |
F(A) | Alice | 0)
if (u' != u) fail
kb = KDF-n(F(b*X'), F(N) | F(M) |
F(B) | F(X') | pw)
v = HMAC(kb, F(Y) | F(X') |
F(B) | Bob | 1)
<------ {B, v}z
if (SIV-decrypt returns fail) fail
if (B not valid element) fail
kb' = KDF-n(F(x*B'), F(N) | F(M) |
F(B') | F(X) | pw)
v' = HMAC(kb', F(Y') | F(X) |
F(B') | Bob | 1)
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.
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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
needed.
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.
The discrete logaritm of the fixed public elements MUST not be known.
Knowledge of either of these values 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. Also, once PKEX has finished, exposing the password to
a third party would not change the fact that the public keys
exchanged in that run of PKEX are trusted and bound to the entities
that performed the exchange.
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.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
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[RFC5297] Harkins, D., "Synthetic Initialization Vector (SIV)
Authenticated Encryption Using the Advanced Encryption
Standard (AES)", RFC 5297, DOI 10.17487/RFC5297, October
2008, <http://www.rfc-editor.org/info/rfc5297>.
[RFC5869] Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
Key Derivation Function (HKDF)", RFC 5869, DOI 10.17487/
RFC5869, May 2010,
<http://www.rfc-editor.org/info/rfc5869>.
[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, <http://www.rfc-editor.org/info/rfc7250>.
[RFC7670] Kivinen, T., Wouters, P., and H. Tschofenig, "Generic Raw
Public-Key Support for IKEv2", RFC 7670, DOI 10.17487/
RFC7670, January 2016,
<http://www.rfc-editor.org/info/rfc7670>.
Appendix A. Generation of ECC Role-specific Elements
A loop is performed to generate role-specific elements by generating
a candidate point, testing the point, 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 x-coordinate, a hash of the concatenation of the
ASN.1 of the OID of the curve, 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. Excess octets are stripped off. The
resulting string is interpreted as an integer with the first octet of
(the first) hash being the low-order octet of the integer. Excess
bits are masked to zero. If that number is larger than the prime
defining the curve the counter is incremented and the loop continues.
Once an x-candidate has been produced it is checked to see whether it
can represent a point on the curve. If it does not, the counter is
incremented and the whole loop is performed again. This process is
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repeated until a point is found. The hash algorithm used to generate
candidate x-coordinates is determined by Section 4.
The loop is performed twice for each curve to produce initiator- and
responder-specific points. The string passed for the initiator-
specific point is "PKEX Initiator", the string passed for the
responder-specific point is "PKEX Responder".
Role-specific elements for popular elliptic curves are presented
here.
A.1. Role-specific Elements for NIST p256
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.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.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 June 1, 2017 [Page 12]
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A.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.5. Role-specific Elements for brainpool p384r1
Harkins Expires June 1, 2017 [Page 13]
Internet-Draft Public Key Exchange November 2016
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.6. Role-specific Elements for brainpool p512r1
Harkins Expires June 1, 2017 [Page 14]
Internet-Draft Public Key Exchange November 2016
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
};
Appendix B. Generation of FFC Role-Specific Elements
Haven't generated those yet. Use ECC.
Harkins Expires June 1, 2017 [Page 15]
Internet-Draft Public Key Exchange November 2016
Author's Address
Dan Harkins
HP Enterprise
1322 Crossman avenue
Sunnyvale, California 94089
USA
Phone: +1 415 997 9834
Email: dharkins@lounge.org
Harkins Expires June 1, 2017 [Page 16]