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Internet Draft HemmaNetwork Working Group H. Prafullchandra(XETI) Expires in 6 months JimRequest for Comments: 2875 Critical Path Inc Category: Standards Track J. Schaad(Microsoft) November 19,July 2000 Diffie-Hellman Proof-of-Possession Algorithms<draft-ietf-pkix-dhpop-03.txt>Status of this Memo This documentisspecifies anInternet-Draft and is in full conformance with all provisions of Section 10 of RFC2026. Internet-Drafts are working documents of theInternetEngineering Task Force (IETF), its areas, and its working groups. Internet-Drafts are working documents ofstandards track protocol for the InternetEngineering Task Force (IETF), its areas,community, andits working groups. Note that other groups MAY also distribute working documents as Internet-Drafts. Internet-Drafts are draft documents valid for a maximum of six monthsrequests discussion andMAY be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material orsuggestions for improvements. Please refer tocite them other than as "work in progress." The list of current Internet-Drafts can be accessed at" http://www.ietf.org/ietf/1id-abstracts.txt" The list of Internet-Draft Shadow Directories can be accessed at" http://www.ietf.org/shadow.html." To learnthe currentstatusedition ofany Internet-Draft, please checkthe"1id-abstracts.txt" listing contained in"Internet Official Protocol Standards" (STD 1) for theInternet-Drafts Shadow Directories on ftp.is.co.za (Africa), nic.nordu.net (Europe), munari.oz.au Pacific Rim), ds.internic.net (US East Coast), or ftp.isi.edu (US West Coast).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 aproof-of-possessionproof-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.2. Terminology Prafullchandra,Prafullchandra & Schaad1 Internet Draft MayStandards 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 certificationrequest. ] Prafullchandra, Schaad 2 Internet Draft May 2000request.] 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.Prafullchandra, Schaad 3 Internet Draft May 2000ASN 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.The method outlined in this documentPrafullchandra & Schaad Standards Track [Page 4] RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 This POP isthe same as used bybased 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][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 withPrafullchandra, Schaad 4 Internet Draft May 20001 < 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 than160- bits160-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 bySHA.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.Prafullchandra, Schaad 5 Internet Draft May 20001. 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]).Prafullchandra, Schaad 6 Internet Draft May 20005. 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 thecommunity/ groupcommunity/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]B.Kaliski, B., "PKCS #10: Certification Request Syntax v1.5", RFC 2314, October19971997. [RFC2104]H.Krawczyk,M.H., Bellare, M., and R. Canetti, "HMAC: Keyed- Hashing for Message Authentication", RFC 2104, February 1997. [PROFILE]R.Housley,W.R., Ford,W.W., Polk, W., and D. Solo, "Internet X.509 Public Key Infrastructure: Certificate and CRL Profile", RFC 2459, January 1999. [DH-X9.42]E.Rescorla, E., "Diffie-Hellman Key AgreementMethod".Method", RFC 2631, June 1999. 7.Author'sAuthors' Addresses Hemma PrafullchandraXETICritical Path Inc. 5150 El Camino Real, #A-32 Los Altos, CA 94022 Phone: (640) 694-6812hemma@xeti.comEMail: hemma@cp.net Jim Schaad EMail: jimsch@exmsft.comPrafullchandra,Prafullchandra & Schaad7 Internet Draft MayStandards 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 usein-- 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} ENDPrafullchandra,Prafullchandra & Schaad8 Internet Draft MayStandards 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 {Prafullchandra, Schaad 9 Internet Draft May 2000144 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 A7Prafullchandra, Schaad 10 Internet Draft May 2000: 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: NULLPrafullchandra, Schaad 11 Internet Draft May 2000: } 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.Prafullchandra, Schaad 12 Internet Draft May 200030 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'Prafullchandra, Schaad 13 Internet Draft May 2000: } : } 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 76Prafullchandra, Schaad 14 Internet Draft May 2000: 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 7DPrafullchandra,Prafullchandra & Schaad15 Internet Draft MayStandards 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: 00000037Prafullchandra, Schaad 16 Internet Draft May 2000x: 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 72Prafullchandra, Schaad 17 Internet Draft May 20008a 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 {Prafullchandra, Schaad 18 Internet Draft May 200048 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]Prafullchandra, Schaad 19 Internet Draft May 2000: } 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,Prafullchandra & Schaad20 http://www.nwlink.comStandards Track [Page 22] RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000 Full Copyright Statement Copyright (C) The Internet Society (2000). All Rights Reserved. This document and translations of it may be copied and furnished to others, and derivative works that comment on or otherwise explain it or assist in its implementation may be prepared, copied, published and distributed, in whole or in part, without restriction of any kind, provided that the above copyright notice and this paragraph are included on all such copies and derivative works. However, this document itself may not be modified in any way, such as by removing the copyright notice or references to the Internet Society or other Internet organizations, except as needed for the purpose of developing Internet standards in which case the procedures for copyrights defined in the Internet Standards process must be followed, or as required to translate it into languages other than English. The limited permissions granted above are perpetual and will not be revoked by the Internet Society or its successors or assigns. This document and the information contained herein is provided on an "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Acknowledgement Funding for the RFC Editor function is currently provided by the Internet Society. Prafullchandra & Schaad Standards Track [Page 23] ----