Network Working Group H. Prafullchandra
Request for Comments: 2875 Critical Path Inc
Category: Standards Track J. Schaad
July 2000
Diffie-Hellman Proof-of-Possession Algorithms
Status of this Memo
This document specifies an Internet standards track protocol for the
Internet community, and requests discussion and suggestions for
improvements. Please refer to the current edition of the "Internet
Official Protocol Standards" (STD 1) for the standardization state
and status of this protocol. Distribution of this memo is unlimited.
Copyright Notice
Copyright (C) The Internet Society (2000). All Rights Reserved.
Abstract
This document describes two methods for producing an integrity check
value from a Diffie-Hellman key pair. This behavior is needed for
such operations as creating the signature of a PKCS #10 certification
request. These algorithms are designed to provide a proof-of-
possession rather than general purpose signing.
1. Introduction
PKCS #10 [RFC2314] defines a syntax for certification requests. It
assumes that the public key being requested for certification
corresponds to an algorithm that is capable of signing/encrypting.
Diffie-Hellman (DH) is a key agreement algorithm and as such cannot
be directly used for signing or encryption.
This document describes two new proof-of-possession algorithms using
the Diffie-Hellman key agreement process to provide a shared secret
as the basis of an integrity check value. In the first algorithm,
the value is constructed for a specific recipient/verifier by using a
public key of that verifier. In the second algorithm, the value is
constructed for arbitrary verifiers.
Prafullchandra & Schaad Standards Track [Page 1]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 2. Terminology The following definitions will be used in this document DH certificate = a certificate whose SubjectPublicKey is a DH public value and is signed with any signature algorithm (e.g. RSA or DSA). 3. Static DH Proof-of-Possession Process The steps for creating a DH POP are: 1. An entity (E) chooses the group parameters for a DH key agreement. This is done simply by selecting the group parameters from a certificate for the recipient of the POP process. A certificate with the correct group parameters has to be available. Let these common DH parameters be g and p; and let this DH key-pair be known as the Recipient key pair (Rpub and Rpriv). Rpub = g^x mod p (where x=Rpriv, the private DH value and ^ denotes exponentiation) 2. The entity generates a DH public/private key-pair using the parameters from step 1. For an entity E: Epriv = DH private value = y Epub = DH public value = g^y mod p 3. The POP computation process will then consist of: a) The value to be signed is obtained. (For a RFC2314 object, the value is the DER encoded certificationRequestInfo field represented as an octet string.) This will be the `text' referred to in [RFC2104], the data to which HMAC-SHA1 is applied. b) A shared DH secret is computed, as follows, shared secret = ZZ = g^xy mod p Prafullchandra & Schaad Standards Track [Page 2]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 [This is done by the entity E as Rpub^y and by the Recipient as Epub^x, where Rpub is retrieved from the Recipient's DH certificate (or is the one that was locally generated by the Entity) and Epub is retrieved from the actual certification request.] c) A temporary key K is derived from the shared secret ZZ as follows: K = SHA1(LeadingInfo | ZZ | TrailingInfo), where "|" means concatenation. LeadingInfo ::= Subject Distinguished Name from certificate TrailingInfo ::= Issuer Distinguished Name from certificate d) Compute HMAC-SHA1 over the data `text' as per [RFC2104] as: SHA1(K XOR opad, SHA1(K XOR ipad, text)) where, opad (outer pad) = the byte 0x36 repeated 64 times and ipad (inner pad) = the byte 0x5C repeated 64 times. Namely, (1) Append zeros to the end of K to create a 64 byte string (e.g., if K is of length 16 bytes it will be appended with 48 zero bytes 0x00). (2) XOR (bitwise exclusive-OR) the 64 byte string computed in step (1) with ipad. (3) Append the data stream `text' to the 64 byte string resulting from step (2). (4) Apply SHA1 to the stream generated in step (3). (5) XOR (bitwise exclusive-OR) the 64 byte string computed in step (1) with opad. (6) Append the SHA1 result from step (4) to the 64 byte string resulting from step (5). (7) Apply SHA1 to the stream generated in step (6) and output the result. Sample code is also provided in [RFC2104]. e) The output of (d) is encoded as a BIT STRING (the Signature value). Prafullchandra & Schaad Standards Track [Page 3]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 The POP verification process requires the Recipient to carry out steps (a) through (d) and then simply compare the result of step (d) with what it received as the signature component. If they match then the following can be concluded: a) The Entity possesses the private key corresponding to the public key in the certification request because it needed the private key to calculate the shared secret; and b) Only the Recipient that the entity sent the request to could actually verify the request because they would require their own private key to compute the same shared secret. In the case where the recipient is a Certification Authority, this protects the Entity from rogue CAs. ASN Encoding The ASN.1 structures associated with the static Diffie-Hellman POP algorithm are: id-dhPop-static-HMAC-SHA1 OBJECT IDENTIFIER ::= { id-pkix id-alg(6) 3} DhPopStatic ::= SEQUENCE { issuerAndSerial IssuerAndSerialNumber OPTIONAL, hashValue MessageDigest } issuerAndSerial is the issuer name and serial number of the certificate from which the public key was obtained. The issuerAndSerial field is omitted if the public key did not come from a certificate. hashValue contains the result of the SHA-1 HMAC operation in step 3d. DhPopStatic is encoded as a BIT STRING and is the signature value (i.e. encodes the above sequence instead of the raw output from 3d). 4. Discrete Logarithm Signature The use of a single set of parameters for an entire public key infrastructure allows all keys in the group to be attacked together. For this reason we need to create a proof of possession for Diffie- Hellman keys that does not require the use of a common set of parameters. Prafullchandra & Schaad Standards Track [Page 4]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 This POP is based on the Digital Signature Algorithm, but we have removed the restrictions imposed by the [FIPS-186] standard. The use of this method does impose some additional restrictions on the set of keys that may be used, however if the key generation algorithm documented in [DH-X9.42] is used the required restrictions are met. The additional restrictions are the requirement for the existence of a q parameter. Adding the q parameter is generally accepted as a good practice as it allows for checking of small group attacks. The following definitions are used in the rest of this section: p is a large prime g = h(p-1)/q mod p , where h is any integer 1 < h < p-1 such that h(p-1) mod q > 1 (g has order q mod p) q is a large prime j is a large integer such that p = qj + 1 x is a randomly or pseudo-randomly generated integer with 1 < x < q y = g^x mod p Note: These definitions match the ones in [DH-X9.42]. 4.1 Expanding the Digest Value Besides the addition of a q parameter, [FIPS-186] also imposes size restrictions on the parameters. The length of q must be 160-bits (matching output of the SHA-1 digest algorithm) and length of p must be 1024-bits. The size restriction on p is eliminated in this document, but the size restriction on q is replaced with the requirement that q must be at least 160-bits. (The size restriction on q is identical with that in [DH-X9.42].) Given that there is not a random length-hashing algorithm, a hash value of the message will need to be derived such that the hash is in the range from 0 to q-1. If the length of q is greater than 160-bits then a method must be provided to expand the hash length. The method for expanding the digest value used in this section does not add any additional security beyond the 160-bits provided by SHA- 1. The value being signed is increased mainly to enhance the difficulty of reversing the signature process. Prafullchandra & Schaad Standards Track [Page 5]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 This algorithm produces m the value to be signed. Let L = the size of q (i.e. 2^L <= q < 2^(L+1)). Let M be the original message to be signed. 1. Compute d = SHA-1(M), the SHA-1 digest of the original message. 2. If L == 160 then m = d. 3. If L > 160 then follow steps (a) through (d) below. a) Set n = L / 160, where / represents integer division, consequently, if L = 200, n = 1. b) Set m = d, the initial computed digest value. c) For i = 0 to n - 1 m = m | SHA(m), where "|" means concatenation. d) m = LEFTMOST(m, L-1), where LEFTMOST returns the L-1 left most bits of m. Thus the final result of the process meets the criteria that 0 <= m < q. 4.2 Signature Computation Algorithm The signature algorithm produces the pair of values (r, s), which is the signature. The signature is computed as follows: Given m, the value to be signed, as well as the parameters defined earlier in section 5. 1. Generate a random or pseudorandom integer k, such that 0 < k^-1 < q. 2. Compute r = (g^k mod p) mod q. 3. If r is zero, repeat from step 1. 4. Compute s = (k^-1 (m + xr)) mod q. 5. If s is zero, repeat from step 1. 4.3 Signature Verification Algorithm The signature verification process is far more complicated than is normal for the Digital Signature Algorithm, as some assumptions about the validity of parameters cannot be taken for granted. Prafullchandra & Schaad Standards Track [Page 6]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 Given a message m to be validated, the signature value pair (r, s) and the parameters for the key. 1. Perform a strong verification that p is a prime number. 2. Perform a strong verification that q is a prime number. 3. Verify that q is a factor of p-1, if any of the above checks fail then the signature cannot be verified and must be considered a failure. 4. Verify that r and s are in the range [1, q-1]. 5. Compute w = (s^-1) mod q. 6. Compute u1 = m*w mod q. 7. Compute u2 = r*w mod q. 8. Compute v = ((g^u1 * y^u2) mod p) mod q. 9. Compare v and r, if they are the same then the signature verified correctly. 4.4 ASN Encoding The signature is encoded using id-alg-dhPOP OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 4} The parameters for id-alg-dhPOP are encoded as DomainParameters (imported from [PROFILE]). The parameters may be omitted in the signature, as they must exist in the associated key request. The signature value pair r and s are encoded using Dss-Sig-Value (imported from [PROFILE]). 5. Security Considerations In the static DH POP algorithm, an appropriate value can be produced by either party. Thus this algorithm only provides integrity and not origination service. The Discrete Logarithm algorithm provides both integrity checking and origination checking. Prafullchandra & Schaad Standards Track [Page 7]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 All the security in this system is provided by the secrecy of the private keying material. If either sender or recipient private keys are disclosed, all messages sent or received using that key are compromised. Similarly, loss of the private key results in an inability to read messages sent using that key. Selection of parameters can be of paramount importance. In the selection of parameters one must take into account the community/group of entities that one wishes to be able to communicate with. In choosing a set of parameters one must also be sure to avoid small groups. [FIPS-186] Appendixes 2 and 3 contain information on the selection of parameters. The practices outlined in this document will lead to better selection of parameters. 6. References [FIPS-186] Federal Information Processing Standards Publication (FIPS PUB) 186, "Digital Signature Standard", 1994 May 19. [RFC2314] Kaliski, B., "PKCS #10: Certification Request Syntax v1.5", RFC 2314, October 1997. [RFC2104] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed- Hashing for Message Authentication", RFC 2104, February 1997. [PROFILE] Housley, R., Ford, W., Polk, W., and D. Solo, "Internet X.509 Public Key Infrastructure: Certificate and CRL Profile", RFC 2459, January 1999. [DH-X9.42] Rescorla, E., "Diffie-Hellman Key Agreement Method", RFC 2631, June 1999. 7. Authors' Addresses Hemma Prafullchandra Critical Path Inc. 5150 El Camino Real, #A-32 Los Altos, CA 94022 Phone: (640) 694-6812 EMail: hemma@cp.net Jim Schaad EMail: jimsch@exmsft.com Prafullchandra & Schaad Standards Track [Page 8]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 Appendix A. ASN.1 Module DH-Sign DEFINITIONS IMPLICIT TAGS ::= BEGIN --EXPORTS ALL -- The types and values defined in this module are exported for use -- in the other ASN.1 modules. Other applications may use them -- for their own purposes. IMPORTS IssuerAndSerialNumber, MessageDigest FROM CryptographicMessageSyntax { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-9(9) smime(16) modules(0) cms(1) } Dss-Sig-Value, DomainParameters FROM PKIX1Explicit88 {iso(1) identified-organization(3) dod(6) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) id-pkix1-explicit-88(1)}; id-dh-sig-hmac-sha1 OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 3} DhSigStatic ::= SEQUENCE { IssuerAndSerial IssuerAndSerialNumber OPTIONAL, hashValue MessageDigest } id-alg-dh-pop OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 4} END Prafullchandra & Schaad Standards Track [Page 9]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 Appendix B. Example of Static DH Proof-of-Possession The following example follows the steps described earlier in section 3. Step 1: Establishing common Diffie-Hellman parameters. Assume the parameters are as in the DER encoded certificate. The certificate contains a DH public key signed by a CA with a DSA signing key. 0 30 939: SEQUENCE { 4 30 872: SEQUENCE { 8 A0 3: [0] { 10 02 1: INTEGER 2 : } 13 02 6: INTEGER : 00 DA 39 B6 E2 CB 21 30 11: SEQUENCE { 23 06 7: OBJECT IDENTIFIER dsaWithSha1 (1 2 840 10040 4 3) 32 05 0: NULL : } 34 30 72: SEQUENCE { 36 31 11: SET { 38 30 9: SEQUENCE { 40 06 3: OBJECT IDENTIFIER countryName (2 5 4 6) 45 13 2: PrintableString 'US' : } : } 49 31 17: SET { 51 30 15: SEQUENCE { 53 06 3: OBJECT IDENTIFIER organizationName (2 5 4 10) 58 13 8: PrintableString 'XETI Inc' : } : } 68 31 16: SET { 70 30 14: SEQUENCE { 72 06 3: OBJECT IDENTIFIER organizationalUnitName (2 5 4 11) 77 13 7: PrintableString 'Testing' : } : } 86 31 20: SET { 88 30 18: SEQUENCE { 90 06 3: OBJECT IDENTIFIER commonName (2 5 4 3) 95 13 11: PrintableString 'Root DSA CA' : } : } : } 108 30 30: SEQUENCE { Prafullchandra & Schaad Standards Track [Page 10]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 110 17 13: UTCTime '990914010557Z' 125 17 13: UTCTime '991113010557Z' : } 140 30 70: SEQUENCE { 142 31 11: SET { 144 30 9: SEQUENCE { 146 06 3: OBJECT IDENTIFIER countryName (2 5 4 6) 151 13 2: PrintableString 'US' : } : } 155 31 17: SET { 157 30 15: SEQUENCE { 159 06 3: OBJECT IDENTIFIER organizationName (2 5 4 10) 164 13 8: PrintableString 'XETI Inc' : } : } 174 31 16: SET { 176 30 14: SEQUENCE { 178 06 3: OBJECT IDENTIFIER organizationalUnitName (2 5 4 11) 183 13 7: PrintableString 'Testing' : } : } 192 31 18: SET { 194 30 16: SEQUENCE { 196 06 3: OBJECT IDENTIFIER commonName (2 5 4 3) 201 13 9: PrintableString 'DH TestCA' : } : } : } 212 30 577: SEQUENCE { 216 30 438: SEQUENCE { 220 06 7: OBJECT IDENTIFIER dhPublicKey (1 2 840 10046 2 1) 229 30 425: SEQUENCE { 233 02 129: INTEGER : 00 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7 : C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82 : F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21 : 51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68 : 5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72 : 8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2 : 32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02 : D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85 : 27 365 02 128: INTEGER : 26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90 : 06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4 : 64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57 Prafullchandra & Schaad Standards Track [Page 11]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 : 86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6 : 4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE : 47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1 : 39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48 : 95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD 496 02 33: INTEGER : 00 E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94 : B1 85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30 : FB 531 02 97: INTEGER : 00 A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7 : B0 CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D : AB 83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39 : 40 9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76 : B4 61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56 : 68 47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2 : 92 630 30 26: SEQUENCE { 632 03 21: BIT STRING 0 unused bits : 1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E DB : 09 E4 98 34 655 02 1: INTEGER 55 : } : } : } 658 03 132: BIT STRING 0 unused bits : 02 81 80 5F CF 39 AD 62 CF 49 8E D1 CE 66 E2 B1 : E6 A7 01 4D 05 C2 77 C8 92 52 42 A9 05 A4 DB E0 : 46 79 50 A3 FC 99 3D 3D A6 9B A9 AD BC 62 1C 69 : B7 11 A1 C0 2A F1 85 28 F7 68 FE D6 8F 31 56 22 : 4D 0A 11 6E 72 3A 02 AF 0E 27 AA F9 ED CE 05 EF : D8 59 92 C0 18 D7 69 6E BD 70 B6 21 D1 77 39 21 : E1 AF 7A 3A CF 20 0A B4 2C 69 5F CF 79 67 20 31 : 4D F2 C6 ED 23 BF C4 BB 1E D1 71 40 2C 07 D6 F0 : 8F C5 1A : } 793 A3 85: [3] { 795 30 83: SEQUENCE { 797 30 29: SEQUENCE { 799 06 3: OBJECT IDENTIFIER subjectKeyIdentifier (2 5 29 14) 804 04 22: OCTET STRING : 04 14 80 DF 59 88 BF EB 17 E1 AD 5E C6 40 A3 42 : E5 AC D3 B4 88 78 : } 828 30 34: SEQUENCE { 830 06 3: OBJECT IDENTIFIER authorityKeyIdentifier (2 5 29 35) Prafullchandra & Schaad Standards Track [Page 12]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 835 01 1: BOOLEAN TRUE 838 04 24: OCTET STRING : 30 16 80 14 6A 23 37 55 B9 FD 81 EA E8 4E D3 C9 : B7 09 E5 7B 06 E3 68 AA : } 864 30 14: SEQUENCE { 866 06 3: OBJECT IDENTIFIER keyUsage (2 5 29 15) 871 01 1: BOOLEAN TRUE 874 04 4: OCTET STRING : 03 02 03 08 : } : } : } : } 880 30 11: SEQUENCE { 882 06 7: OBJECT IDENTIFIER dsaWithSha1 (1 2 840 10040 4 3) 891 05 0: NULL : } 893 03 48: BIT STRING 0 unused bits : 30 2D 02 14 7C 6D D2 CA 1E 32 D1 30 2E 29 66 BC : 06 8B 60 C7 61 16 3B CA 02 15 00 8A 18 DD C1 83 : 58 29 A2 8A 67 64 03 92 AB 02 CE 00 B5 94 6A : } Step 2. End Entity/User generates a Diffie-Hellman key-pair using the parameters from the CA certificate. EE DH public key: SunJCE Diffie-Hellman Public Key: Y: 13 63 A1 85 04 8C 46 A8 88 EB F4 5E A8 93 74 AE FD AE 9E 96 27 12 65 C4 4C 07 06 3E 18 FE 94 B8 A8 79 48 BD 2E 34 B6 47 CA 04 30 A1 EC 33 FD 1A 0B 2D 9E 50 C9 78 0F AE 6A EC B5 6B 6A BE B2 5C DA B2 9F 78 2C B9 77 E2 79 2B 25 BF 2E 0B 59 4A 93 4B F8 B3 EC 81 34 AE 97 47 52 E0 A8 29 98 EC D1 B0 CA 2B 6F 7A 8B DB 4E 8D A5 15 7E 7E AF 33 62 09 9E 0F 11 44 8C C1 8D A2 11 9E 53 EF B2 E8 EE DH private key: X: 32 CC BD B4 B7 7C 44 26 BB 3C 83 42 6E 7D 1B 00 86 35 09 71 07 A0 A4 76 B8 DB 5F EC 00 CE 6F C3 Step 3. Compute K and the signature. LeadingInfo: DER encoded Subject/Requestor DN (as in the generated Certificate Signing Request) Prafullchandra & Schaad Standards Track [Page 13]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 30 4E 31 0B 30 09 06 03 55 04 06 13 02 55 53 31 11 30 0F 06 03 55 04 0A 13 08 58 45 54 49 20 49 6E 63 31 10 30 0E 06 03 55 04 0B 13 07 54 65 73 74 69 6E 67 31 1A 30 18 06 03 55 04 03 13 11 50 4B 49 58 20 45 78 61 6D 70 6C 65 20 55 73 65 72 TrailingInfo: DER encoded Issuer/Recipient DN (from the certificate described in step 1) 30 46 31 0B 30 09 06 03 55 04 06 13 02 55 53 31 11 30 0F 06 03 55 04 0A 13 08 58 45 54 49 20 49 6E 63 31 10 30 0E 06 03 55 04 0B 13 07 54 65 73 74 69 6E 67 31 12 30 10 06 03 55 04 03 13 09 44 48 20 54 65 73 74 43 41 K: F4 D7 BB 6C C7 2D 21 7F 1C 38 F7 DA 74 2D 51 AD 14 40 66 75 TBS: the ôtextö for computing the SHA-1 HMAC. 30 82 02 98 02 01 00 30 4E 31 0B 30 09 06 03 55 04 06 13 02 55 53 31 11 30 0F 06 03 55 04 0A 13 08 58 45 54 49 20 49 6E 63 31 10 30 0E 06 03 55 04 0B 13 07 54 65 73 74 69 6E 67 31 1A 30 18 06 03 55 04 03 13 11 50 4B 49 58 20 45 78 61 6D 70 6C 65 20 55 73 65 72 30 82 02 41 30 82 01 B6 06 07 2A 86 48 CE 3E 02 01 30 82 01 A9 02 81 81 00 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7 C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82 F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21 51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68 5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72 8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2 32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02 D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85 27 02 81 80 26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90 06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4 64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57 86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6 4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE 47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1 39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48 95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD 02 21 00 E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94 B1 85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30 FB 02 61 00 A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7 B0 CD 0F 94 87 0C 25 BE Prafullchandra & Schaad Standards Track [Page 14]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 97 76 8D EB E5 A4 09 5D AB 83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39 40 9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76 B4 61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56 68 47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2 92 30 1A 03 15 00 1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E DB 09 E4 98 34 02 01 37 03 81 84 00 02 81 80 13 63 A1 85 04 8C 46 A8 88 EB F4 5E A8 93 74 AE FD AE 9E 96 27 12 65 C4 4C 07 06 3E 18 FE 94 B8 A8 79 48 BD 2E 34 B6 47 CA 04 30 A1 EC 33 FD 1A 0B 2D 9E 50 C9 78 0F AE 6A EC B5 6B 6A BE B2 5C DA B2 9F 78 2C B9 77 E2 79 2B 25 BF 2E 0B 59 4A 93 4B F8 B3 EC 81 34 AE 97 47 52 E0 A8 29 98 EC D1 B0 CA 2B 6F 7A 8B DB 4E 8D A5 15 7E 7E AF 33 62 09 9E 0F 11 44 8C C1 8D A2 11 9E 53 EF B2 E8 Certification Request: 0 30 793: SEQUENCE { 4 30 664: SEQUENCE { 8 02 1: INTEGER 0 11 30 78: SEQUENCE { 13 31 11: SET { 15 30 9: SEQUENCE { 17 06 3: OBJECT IDENTIFIER countryName (2 5 4 6) 22 13 2: PrintableString 'US' : } : } 26 31 17: SET { 28 30 15: SEQUENCE { 30 06 3: OBJECT IDENTIFIER organizationName (2 5 4 10) 35 13 8: PrintableString 'XETI Inc' : } : } 45 31 16: SET { 47 30 14: SEQUENCE { 49 06 3: OBJECT IDENTIFIER organizationalUnitName (2 5 4 11) 54 13 7: PrintableString 'Testing' : } : } 63 31 26: SET { 65 30 24: SEQUENCE { 67 06 3: OBJECT IDENTIFIER commonName (2 5 4 3) 72 13 17: PrintableString 'PKIX Example User' : } : } Prafullchandra & Schaad Standards Track [Page 15]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 : } 91 30 577: SEQUENCE { 95 30 438: SEQUENCE { 99 06 7: OBJECT IDENTIFIER dhPublicKey (1 2 840 10046 2 1) 108 30 425: SEQUENCE { 112 02 129: INTEGER : 00 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7 : C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82 : F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21 : 51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68 : 5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72 : 8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2 : 32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02 : D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85 : 27 244 02 128: INTEGER : 26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90 : 06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4 : 64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57 : 86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6 : 4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE : 47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1 : 39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48 : 95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD 375 02 33: INTEGER : 00 E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94 : B1 85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30 : FB 410 02 97: INTEGER : 00 A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7 : B0 CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D : AB 83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39 : 40 9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76 : B4 61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56 : 68 47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2 : 92 509 30 26: SEQUENCE { 511 03 21: BIT STRING 0 unused bits : 1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E DB : 09 E4 98 34 534 02 1: INTEGER 55 : } : } : } 537 03 132: BIT STRING 0 unused bits : 02 81 80 13 63 A1 85 04 8C 46 A8 88 EB F4 5E A8 : 93 74 AE FD AE 9E 96 27 12 65 C4 4C 07 06 3E 18 Prafullchandra & Schaad Standards Track [Page 16]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 : FE 94 B8 A8 79 48 BD 2E 34 B6 47 CA 04 30 A1 EC : 33 FD 1A 0B 2D 9E 50 C9 78 0F AE 6A EC B5 6B 6A : BE B2 5C DA B2 9F 78 2C B9 77 E2 79 2B 25 BF 2E : 0B 59 4A 93 4B F8 B3 EC 81 34 AE 97 47 52 E0 A8 : 29 98 EC D1 B0 CA 2B 6F 7A 8B DB 4E 8D A5 15 7E : 7E AF 33 62 09 9E 0F 11 44 8C C1 8D A2 11 9E 53 : EF B2 E8 : } : } 672 30 12: SEQUENCE { 674 06 8: OBJECT IDENTIFIER dh-sig-hmac-sha1 (1 3 6 1 5 5 7 6 3) 684 05 0: NULL : } 686 03 109: BIT STRING 0 unused bits : 30 6A 30 52 30 48 31 0B 30 09 06 03 55 04 06 13 : 02 55 53 31 11 30 0F 06 03 55 04 0A 13 08 58 45 : 54 49 20 49 6E 63 31 10 30 0E 06 03 55 04 0B 13 : 07 54 65 73 74 69 6E 67 31 14 30 12 06 03 55 04 : 03 13 0B 52 6F 6F 74 20 44 53 41 20 43 41 02 06 : 00 DA 39 B6 E2 CB 04 14 1B 17 AD 4E 65 86 1A 6C : 7C 85 FA F7 95 DE 48 93 C5 9D C5 24 : } Signature verification requires CAÆs private key, the CA certificate and the generated Certification Request. CA DH private key: x: 3E 5D AD FD E5 F4 6B 1B 61 5E 18 F9 0B 84 74 a7 52 1E D6 92 BC 34 94 56 F3 0C BE DA 67 7A DD 7D Prafullchandra & Schaad Standards Track [Page 17]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 Appendix C. Example of Discrete Log Signature Step 1. Generate a Diffie-Hellman Key with length of q being 256- bits. p: 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7 C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82 F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21 51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68 5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72 8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2 32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02 D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85 27 q: E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94 B1 85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30 FB g: 26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90 06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4 64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57 86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6 4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE 47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1 39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48 95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD j: A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7 B0 CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D AB 83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39 40 9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76 B4 61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56 68 47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2 92 y: 5F CF 39 AD 62 CF 49 8E D1 CE 66 E2 B1 E6 A7 01 4D 05 C2 77 C8 92 52 42 A9 05 A4 DB E0 46 79 50 A3 FC 99 3D 3D A6 9B A9 AD BC 62 1C 69 B7 11 A1 C0 2A F1 85 28 F7 68 FE D6 8F 31 56 22 4D 0A 11 6E 72 3A 02 AF 0E 27 AA F9 ED CE 05 EF D8 59 92 C0 18 D7 69 6E BD 70 B6 21 D1 77 39 21 E1 AF 7A 3A CF 20 0A B4 2C 69 5F CF 79 67 20 31 4D F2 C6 ED 23 BF C4 BB 1E D1 71 40 2C 07 D6 F0 8F C5 1A seed: Prafullchandra & Schaad Standards Track [Page 18]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E DB 09 E4 98 34 C: 00000037 x: 3E 5D AD FD E5 F4 6B 1B 61 5E 18 F9 0B 84 74 a7 52 1E D6 92 BC 34 94 56 F3 0C BE DA 67 7A DD 7D Step 2. Form the value to be signed and hash with SHA1. The result of the hash for this example is: 5f a2 69 b6 4b 22 91 22 6f 4c fe 68 ec 2b d1 c6 d4 21 e5 2c Step 3. The hash value needs to be expanded since |q| = 256. This is done by hashing the hash with SHA1 and appending it to the original hash. The value after this step is: 5f a2 69 b6 4b 22 91 22 6f 4c fe 68 ec 2b d1 c6 d4 21 e5 2c 64 92 8b c9 5e 34 59 70 bd 62 40 ad 6f 26 3b f7 1c a3 b2 cb Next the first 255 bits of this value are taken to be the resulting "hash" value. Note in this case a shift of one bit right is done since the result is to be treated as an integer: 2f d1 34 db 25 91 48 91 37 a6 7f 34 76 15 e8 e3 6a 10 f2 96 32 49 45 e4 af 1a 2c b8 5e b1 20 56 Step 4. The signature value is computed. In this case you get the values R: A1 B5 B4 90 01 34 6B A0 31 6A 73 F5 7D F6 5C 14 43 52 D2 10 BF 86 58 87 F7 BC 6E 5A 77 FF C3 4B S: 59 40 45 BC 6F 0D DC FF 9D 55 40 1E C4 9E 51 3D 66 EF B2 FF 06 40 9A 39 68 75 81 F7 EC 9E BE A1 The encoded signature values is then: 30 45 02 21 00 A1 B5 B4 90 01 34 6B A0 31 6A 73 F5 7D F6 5C 14 43 52 D2 10 BF 86 58 87 F7 BC 6E 5A 77 FF C3 4B 02 20 59 40 45 BC 6F 0D DC FF 9D 55 40 1E C4 9E 51 3D 66 EF B2 FF 06 40 9A 39 68 75 81 F7 EC 9E BE A1 Prafullchandra & Schaad Standards Track [Page 19]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 Result: 30 82 02 c2 30 82 02 67 02 01 00 30 1b 31 19 30 17 06 03 55 04 03 13 10 49 45 54 46 20 50 4b 49 58 20 53 41 4d 50 4c 45 30 82 02 41 30 82 01 b6 06 07 2a 86 48 ce 3e 02 01 30 82 01 a9 02 81 81 00 94 84 e0 45 6c 7f 69 51 62 3e 56 80 7c 68 e7 c5 a9 9e 9e 74 74 94 ed 90 8c 1d c4 e1 4a 14 82 f5 d2 94 0c 19 e3 b9 10 bb 11 b9 e5 a5 fb 8e 21 51 63 02 86 aa 06 b8 21 36 b6 7f 36 df d1 d6 68 5b 79 7c 1d 5a 14 75 1f 6a 93 75 93 ce bb 97 72 8a f0 0f 23 9d 47 f6 d4 b3 c7 f0 f4 e6 f6 2b c2 32 e1 89 67 be 7e 06 ae f8 d0 01 6b 8b 2a f5 02 d7 b6 a8 63 94 83 b0 1b 31 7d 52 1a de e5 03 85 27 02 81 80 26 a6 32 2c 5a 2b d4 33 2b 5c dc 06 87 53 3f 90 06 61 50 38 3e d2 b9 7d 81 1c 12 10 c5 0c 53 d4 64 d1 8e 30 07 08 8c dd 3f 0a 2f 2c d6 1b 7f 57 86 d0 da bb 6e 36 2a 18 e8 d3 bc 70 31 7a 48 b6 4e 18 6e dd 1f 22 06 eb 3f ea d4 41 69 d9 9b de 47 95 7a 72 91 d2 09 7f 49 5c 3b 03 33 51 c8 f1 39 9a ff 04 d5 6e 7e 94 3d 03 b8 f6 31 15 26 48 95 a8 5c de 47 88 b4 69 3a 00 a7 86 9e da d1 cd 02 21 00 e8 72 fa 96 f0 11 40 f5 f2 dc fd 3b 5d 78 94 b1 85 01 e5 69 37 21 f7 25 b9 ba 71 4a fc 60 30 fb 02 61 00 a3 91 01 c0 a8 6e a4 4d a0 56 fc 6c fe 1f a7 b0 cd 0f 94 87 0c 25 be 97 76 8d eb e5 a4 09 5d ab 83 cd 80 0b 35 67 7f 0c 8e a7 31 98 32 85 39 40 9d 11 98 d8 de b8 7f 86 9b af 8d 67 3d b6 76 b4 61 2f 21 e1 4b 0e 68 ff 53 3e 87 dd d8 71 56 68 47 dc f7 20 63 4b 3c 5f 78 71 83 e6 70 9e e2 92 30 1a 03 15 00 1c d5 3a 0d 17 82 6d 0a 81 75 81 46 10 8e 3e db 09 e4 98 34 02 01 37 03 81 84 00 02 81 80 5f cf 39 ad 62 cf 49 8e d1 ce 66 e2 b1 e6 a7 01 4d 05 c2 77 c8 92 52 42 a9 05 a4 db e0 46 79 50 a3 fc 99 3d 3d a6 9b a9 ad bc 62 1c 69 b7 11 a1 c0 2a f1 85 28 f7 68 fe d6 8f 31 56 22 4d 0a 11 6e 72 3a 02 af 0e 27 aa f9 ed ce 05 ef d8 59 92 c0 18 d7 69 6e bd 70 b6 21 d1 77 39 21 e1 af 7a 3a cf 20 0a b4 2c 69 5f cf 79 67 20 31 4d f2 c6 ed 23 bf c4 bb 1e d1 71 40 2c 07 d6 f0 8f c5 1a a0 00 30 0c 06 08 2b 06 01 05 05 07 06 04 05 00 03 47 00 30 44 02 20 54 d9 43 8d 0f 9d 42 03 d6 09 aa a1 9a 3c 17 09 ae bd ee b3 d1 a0 00 db 7d 8c b8 e4 56 e6 57 7b 02 20 44 89 b1 04 f5 40 2b 5f e7 9c f9 a4 97 50 0d ad c3 7a a4 2b b2 2d 5d 79 fb 38 8a b4 df bb 88 bc Prafullchandra & Schaad Standards Track [Page 20]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 Decoded Version of result: 0 30 707: SEQUENCE { 4 30 615: SEQUENCE { 8 02 1: INTEGER 0 11 30 27: SEQUENCE { 13 31 25: SET { 15 30 23: SEQUENCE { 17 06 3: OBJECT IDENTIFIER commonName (2 5 4 3) 22 13 16: PrintableString 'IETF PKIX SAMPLE' : } : } : } 40 30 577: SEQUENCE { 44 30 438: SEQUENCE { 48 06 7: OBJECT IDENTIFIER dhPublicNumber (1 2 840 10046 2 1) 57 30 425: SEQUENCE { 61 02 129: INTEGER : 00 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7 : C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82 : F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21 : 51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68 : 5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72 : 8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2 : 32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02 : D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85 : 27 193 02 128: INTEGER : 26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90 : 06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4 : 64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57 : 86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6 : 4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE : 47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1 : 39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48 : 95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD 324 02 33: INTEGER : 00 E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94 : B1 85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30 : FB 359 02 97: INTEGER : 00 A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7 : B0 CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D : AB 83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39 : 40 9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76 : B4 61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56 : 68 47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2 Prafullchandra & Schaad Standards Track [Page 21]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 : 92 458 30 26: SEQUENCE { 460 03 21: BIT STRING 0 unused bits : 1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E DB : 09 E4 98 34 483 02 1: INTEGER 55 : } : } : } 486 03 132: BIT STRING 0 unused bits : 02 81 80 5F CF 39 AD 62 CF 49 8E D1 CE 66 E2 B1 : E6 A7 01 4D 05 C2 77 C8 92 52 42 A9 05 A4 DB E0 : 46 79 50 A3 FC 99 3D 3D A6 9B A9 AD BC 62 1C 69 : B7 11 A1 C0 2A F1 85 28 F7 68 FE D6 8F 31 56 22 : 4D 0A 11 6E 72 3A 02 AF 0E 27 AA F9 ED CE 05 EF : D8 59 92 C0 18 D7 69 6E BD 70 B6 21 D1 77 39 21 : E1 AF 7A 3A CF 20 0A B4 2C 69 5F CF 79 67 20 31 : 4D F2 C6 ED 23 BF C4 BB 1E D1 71 40 2C 07 D6 F0 : 8F C5 1A : } 621 A0 0: [0] : } 623 30 12: SEQUENCE { 625 06 8: OBJECT IDENTIFIER '1 3 6 1 5 5 7 6 4' 635 05 0: NULL : } 637 03 72: BIT STRING 0 unused bits : 30 45 02 21 00 A1 B5 B4 90 01 34 6B A0 31 6A 73 : F5 7D F6 5C 14 43 52 D2 10 BF 86 58 87 F7 BC 6E : 5A 77 FF C3 4B 02 20 59 40 45 BC 6F 0D DC FF 9D : 55 40 1E C4 9E 51 3D 66 EF B2 FF 06 40 9A 39 68 : 75 81 F7 EC 9E BE A1 : } Prafullchandra & Schaad Standards Track [Page 22]
RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000
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Prafullchandra & Schaad Standards Track [Page 23]
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