| Internet Engineering Task Force | D. Eremin-Solenikov, Ed. |
| Internet-Draft | Mentor Graphics (Ireland) Ltd. |
| Updates: 3279, 4491 (if approved) | V. Nikolaev |
| Intended status: Informational | CryptoPro |
| Expires: May 23, 2020 | A. Chelpanov |
| InfoTeCS JSC | |
| November 20, 2019 |
Using GOST R 34.10-2012 and GOST R 34.11-2012 algorithms with the Internet X.509 Public Key Infrastructure
draft-deremin-rfc4491-bis-02
This document updates RFC 3279 and RFC 4491. It describes encoding formats, identifiers, and parameter formats for the algorithms GOST R 34.10-2012 and GOST R 34.11-2012 for use in Internet X.509 Public Key Infrastructure (PKI).
This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at https://datatracker.ietf.org/drafts/current/.
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This Internet-Draft will expire on May 23, 2020.
Copyright (c) 2019 IETF Trust and the persons identified as the document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (https://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License.
This document supplements [RFC3279]. It describes the conventions for using the GOST R 34.10-2012 (see [RFC7091]) signature algorithm and GOST R 34.11-2012 (see [RFC6986]) hash function in the Internet X.509 Public Key Infrastructure (PKI) [RFC5280].
This specification defines the contents of the signatureAlgorithm, signatureValue, signature, and subjectPublicKeyInfo fields within X.509 Certificates and CRLs. For each algorithm, the appropriate alternatives for the keyUsage certificate extension are provided.
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 [RFC2119].
Conforming CAs MAY use GOST R 34.10-2012 signature algorithm to sign certificates and CRLs. This signature algorithm MUST always be used with GOST R 34.11-2012 hash function. It may use keys length of either 256 bits or 512 bits.
The ASN.1 object identifier used to identify GOST R 34.10-2012 signature algorithm with 256-bit key length and GOST R 34.11-2012 hash function with 256-bit hash code is:
id-tc26-signwithdigest-gost3410-12-256 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) ru(643) rosstandart(7) tc26(1)
algorithms(1) signwithdigest(3) gost3410-12-256(2)}.
GOST R 34.10-2012 signature algorithm with 256-bit key length generates a digital signature in the form of two 256-bit numbers, r and s. Its octet string representation consists of 64 octets, where the first 32 octets contain the big-endian representation of s and the second 32 octets contain the big-endian representation of r.
The ASN.1 object identifier used to identify GOST R 34.10-2012 signature algorithm with 512-bit key length and GOST R 34.11-2012 hash function with 512-bit hash code is:
id-tc26-signwithdigest-gost3410-12-512 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) ru(643) rosstandart(7) tc26(1)
algorithms(1) signwithdigest(3) gost3410-12-512(3)}.
GOST R 34.10-2012 signature algorithm with 512-bit key length generates a digital signature in the form of two 512-bit numbers, r and s. Its octet string representation consists of 128 octets, where the first 64 octets contain the big-endian representation of s and the second 64 octets contain the big-endian representation of r.
When either of these OID is used as the algorithm field in an AlgorithmIdentifier structure, the encoding MUST omit the parameters field.
The described definition of a signature value is directly usable in CMS [RFC5652], where such values are represented as octet strings. However, signature values in certificates and CRLs [RFC5280] are represented as bit strings, and thus the octet string representation must be converted.
To convert an octet string signature value to a bit string, the most significant bit of the first octet of the signature value SHALL become the first bit of the bit string, and so on through the least significant bit of the last octet of the signature value, which SHALL become the last bit of the bit string.
The ASN.1 object identifier used to identify GOST R 34.11-2012 hash function with 256-bit hash code is:
id-tc26-digest-gost3411-12-256 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) ru(643) rosstandart(7) tc26(1)
algorithms(1) digest(2) gost3411-12-256(2)}.
The ASN.1 object identifier used to identify GOST R 34.11-2012 hash function with 512-bit hash code is:
id-tc26-digest-gost3411-12-512 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) ru(643) rosstandart(7) tc26(1)
algorithms(1) digest(2) gost3411-12-512(3)}.
When either of these OID is used as the algorithm field in an AlgorithmIdentifier structure, the encoding MUST omit the parameters field.
GOST R 34.10-2012 public keys with 256 bits private key length are identified by the following OID:
id-tc26-gost3410-12-256 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) ru(643) rosstandart(7) tc26(1)
algorithms(1) sign(1) gost3410-12-256(1)}.
GOST R 34.10-2012 public keys with 512 bits private key length are identified by the following OID:
id-tc26-gost3410-12-512 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) ru(643) rosstandart(7) tc26(1)
algorithms(1) sign(1) gost3410-12-512(2)}.
When either of these identifiers appears as algorithm field in SubjectPublicKeyInfo.algorithm.algorithm field, parameters field MUST have the following structure:
GostR3410-2012-PublicKeyParameters ::= SEQUENCE
{
publicKeyParamSet OBJECT IDENTIFIER,
digestParamSet OBJECT IDENTIFIER OPTIONAL
}
where:
The field digestParamSet:
The GOST R 34.10-2012 public key MUST be ASN.1 DER encoded as an OCTET STRING. This encoding SHALL be used as the content (i.e., the value) of the subjectPublicKey field (a BIT STRING) of SubjectPublicKeyInfo structure.
GostR3410-2012-256-PublicKey ::= OCTET STRING (64), GostR3410-2012-512-PublicKey ::= OCTET STRING (128).
GostR3410-2012-256-PublicKey MUST contain 64 octets, where the first 32 octets contain the little-endian representation of x and the second 32 octets contains the little-endian representation of y coordinates of the public key.
GostR3410-2012-512-PublicKey MUST contain 128 octets, where the first 64 octets contain the little-endian representation of x and the second 64 octets contains the little-endian representation of y coordinates of the public key.
If the KeyUsage extension is present in a certificate with GOST R 34.10-2012 public key, the following values MAY be present:
Note that contentCommitment was named nonRepudiation in previous versions of X.509.
If the key is going to be used for key agreement, flag keyAgreement MUST be present in KeyUsage extension with encipherOnly and decipherOnly flags being optional. However flags encipherOnly and decipherOnly flags MUST NOT be present simultaneously.
This section defines additional object identifiers (OIDs) for use in qualified certificates for checking digital signatures.
OGRN is the main state registration number of juridical entities.
OGRN ::= NUMERIC STRING 13
Corresponding OID is 1.2.643.100.1.
SNILS is the individual insurance account number.
SNILS ::= NUMERIC STRING 11
Corresponding OID is 1.2.643.100.3.
OGRNIP is the main state registration number of individual enterpreneurs.
OGRNIP ::= NUMERIC STRING 15
Corresponding OID is 1.2.643.100.5.
INN is the individual taxpayer number (ITN).
INN ::= NUMERIC STRING 12
Corresponding OID is 1.2.643.3.131.1.1.
Russian national regulation body for cryptography defines several security levels of cryptographic tools. Depending on the class of cryptographic token used by certificate owner the following OIDs must be included into certificate policies. Certificate should include OIDs starting from the lowest one (KC1) up to the strongest applicable.
To denote the token or software type used by certificate owner following non-critical SubjectSignTool extension with OID 1.2.643.100.111 should be included. It is defined as
SubjectSignTool ::= UTF8String SIZE(1..200) .
To denote the tools used to generate key pair and tools used by CA to sign certificate following non-critical IssuerSignTool extension with OID 1.2.643.100.112 should be included. It is defined as
IssuerSignTool ::= SEQUENCE {
signTool UTF8String SIZE(1..200),
cATool UTF8String SIZE(1..200),
signToolCert UTF8String SIZE(1..100),
cAToolCert UTF8String SIZE(1..100) },
where:
Note that for the significant period of time there were no documents describing GostR3410-2012-PublicKeyParameters. Several old implementations have used GostR3410-2001-PublicKeyParameters instead. These implementations will return an error if digestParamSet field is not included into public key parameters. Thus an implementation wishing to collaborate with old implementations might want to include digestParamSet equal to id-tc26-digest-gost3411-12-512 if one of the following values is used as publicKeyParamSet:
This memo includes no request to IANA.
It is RECOMMENDED that applications verify signature values and subject public keys to conform to [RFC7091] standard prior to their use.
It is RECOMMENDED that CAs and applications make sure that the private key for creating signatures is not used for more than its allowed validity period (typically 15 months for GOST R 34.10-2012 algorithm).
For security discussion concerning use of algorithm parameters, see [ANS17] and the Security Considerations sections in [RFC4357], [RFC7836].
| [ANS17] | Alekseev, E., Nikolaev, V. and S. Smyshlyaev, "On the security properties of Russian standardized elliptic curves.", Mathematical Aspects of Cryptography 9:3. P. 5-32., DOI 10.4213/mvk260, 2018. |
| [GOSTR3410-2012] | Federal Agency on Technical Regulating and Metrology, "Information technology. Cryptographic data security. Signature and verification processes of [electronic] digital signature", GOST R 34.10-2012, 2012. |
| [GOSTR3411-2012] | Federal Agency on Technical Regulating and Metrology, "Information technology. Cryptographic Data Security. Hashing function", GOST R 34.11-2012, 2012. |
GostR3410-2012-PKISyntax
{ iso(1) member-body(2) ru(643) rosstandart(7)
tc26(1) modules(0) gostR3411-2012-PKISyntax(2) }
DEFINITIONS ::=
BEGIN
-- EXPORTS All --
-- ASN.1 TC 26 root
id-tc26 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) ru(643) rosstandart(7) tc26(1) }
-- Signature algorithm
id-tc26-sign OBJECT IDENTIFIER ::=
{ id-tc26 algorithms(1) sign(1) }
-- Signature algorithm parameters
id-tc26-sign-constants OBJECT IDENTIFIER ::=
{ id-tc26 constants(2) sign(1) }
-- GOST R 34.10-2012 / 256 bits signature algorithm parameters
id-tc26-gost-3410-2012-256-constants OBJECT IDENTIFIER ::=
{ id-tc26-sign-constants gost-3410-2012-256(1) }
-- GOST R 34.10-2012 / 512 bits signature algorithm parameters
id-tc26-gost-3410-2012-512-constants OBJECT IDENTIFIER ::=
{ id-tc26-sign-constants gost-3410-2012-512(2) }
-- GOST R 34.10-2012 / 256 bits signature algorithm
id-tc26-gost3410-2012-256 OBJECT IDENTIFIER ::=
{ id-tc26-sign gost3410-2012-256(1) }
-- GOST R 34.10-2012 / 512 bits signature algorithm
id-tc26-gost3410-2012-512 OBJECT IDENTIFIER ::=
{ id-tc26-sign gost3410-2012-512(2) }
-- Signature & hash algorithm GOST R 34.10-2012 / 256 bits
-- with GOST R 34.11-2012
id-tc26-signwithdigest-gost3410-2012-256 OBJECT IDENTIFIER ::=
{ id-tc26-signwithdigest gost3410-2012-256(2) }
-- Signature & hash algorithm GOST R 34.10-2012 / 512 bits
-- with GOST R 34.11-2012
id-tc26-signwithdigest-gost3410-2012-512 OBJECT IDENTIFIER ::=
{ id-tc26-signwithdigest gost3410-2012-512(3) }
-- GOST R 34.10-2012 / 256 bits Signature algorithm parameters ID:
-- "Set A"
id-tc26-gost-3410-2012-256-paramSetA OBJECT IDENTIFIER ::=
{ id-tc26-gost-3410-2012-256-constants paramSetA(1) }
-- GOST R 34.10-2012 / 256 bits signature algorithm parameters ID:
-- "Set B"
id-tc26-gost-3410-2012-256-paramSetB OBJECT IDENTIFIER ::=
{ id-tc26-gost-3410-2012-256-constants paramSetB(2) }
-- GOST R 34.10-2012 / 256 bits signature algorithm parameters ID:
-- "Set C"
id-tc26-gost-3410-2012-256-paramSetC OBJECT IDENTIFIER ::=
{ id-tc26-gost-3410-2012-256-constants paramSetC(3) }
-- GOST R 34.10-2012 / 256 bits signature algorithm parameters ID:
-- "Set D"
id-tc26-gost-3410-2012-256-paramSetD OBJECT IDENTIFIER ::=
{ id-tc26-gost-3410-2012-256-constants paramSetD(4) }
-- GOST R 34.10-2012 / 512 bits signature algorithm parameters ID:
-- "Test set"
id-tc26-gost-3410-2012-512-paramSetTest OBJECT IDENTIFIER ::=
{ id-tc26-gost-3410-2012-512-constants paramSetTest(0) }
-- GOST R 34.10-2012 / 512 bits signature algorithm parameters ID:
-- "Set A"
id-tc26-gost-3410-2012-512-paramSetA OBJECT IDENTIFIER ::=
{ id-tc26-gost-3410-2012-512-constants paramSetA(1) }
-- GOST R 34.10-2012 / 512 bits signature algorithm parameters ID:
-- "Set B"
id-tc26-gost-3410-2012-512-paramSetB OBJECT IDENTIFIER ::=
{ id-tc26-gost-3410-2012-512-constants paramSetB(2) }
-- GOST R 34.10-2012 / 512 bits signature algorithm parameters ID:
-- "Set C"
id-tc26-gost-3410-2012-512-paramSetC OBJECT IDENTIFIER ::=
{ id-tc26-gost-3410-2012-512-constants paramSetC(3) }
-- Public key GOST R 34.10-2012 / 256 bits
GostR3410-2012-256-PublicKey ::= OCTET STRING (SIZE (64))
-- Public key GOST R 34.10-2012 / 512 bits
GostR3410-2012-512-PublicKey ::= OCTET STRING (SIZE (128))
-- Public key GOST R 34.10-2012
GostR3410-PublicKey ::= OCTET STRING (SIZE (64 | 128))
-- Public key parameters GOST R 34.10-2012
GostR3410-2012-PublicKeyParameters ::=
SEQUENCE {
publicKeyParamSet OBJECT IDENTIFIER,
digestParamSet OBJECT IDENTIFIER OPTIONAL
}
END -- GostR3410-2012-PKISyntax
Here we define three new object identifiers for three existing public key parameter sets defined in [RFC4357]. These object identifiers MUST be used with GOST R 34.10-2012 public keys only.
id-tc26-gost-3410-2012-256-paramSetB OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) ru(643) rosstandart(7) tc26(1)
ru(643) rosstandart(7) tc26(1) constants(2) sign-constants(1)
gost-3410-12-256-constants(1) paramSetB(2)}.
The elliptic curve of this parameter set is the same as of id-GostR3410-2001-CryptoPro-A-ParamSet which can be found in [RFC4357].
id-tc26-gost-3410-2012-256-paramSetC OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) ru(643) rosstandart(7) tc26(1)
ru(643) rosstandart(7) tc26(1) constants(2) sign-constants(1)
gost-3410-12-256-constants(1) paramSetC(3)}.
The elliptic curve of this parameter set is the same as of id-GostR3410-2001-CryptoPro-B-ParamSet which can be found in [RFC4357].
id-tc26-gost-3410-2012-256-paramSetD OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) ru(643) rosstandart(7) tc26(1)
ru(643) rosstandart(7) tc26(1) constants(2) sign-constants(1)
gost-3410-12-256-constants(1) paramSetD(4)}.
The elliptic curve of this parameter set is the same as of id-GostR3410-2001-CryptoPro-C-ParamSet which can be found in [RFC4357].
This example uses curve defined in Section 7.1 of [RFC7091].
Private key is
d = 0x7A929ADE789BB9BE10ED359DD39A72C11B60961F49397EEE1D19CE9891EC3B28
Public key is
X = 0x7F2B49E270DB6D90D8595BEC458B50C58585BA1D4E9B788F6689DBD8E56FD80B Y = 0x26F1B489D6701DD185C8413A977B3CBBAF64D1C593D26627DFFB101A87FF77DA
-----BEGIN CERTIFICATE REQUEST-----
MIHTMIGBAgEAMBIxEDAOBgNVBAMTB0V4YW1wbGUwZjAfBggqhQMHAQEBATATBgcq
hQMCAiMABggqhQMHAQECAgNDAARAC9hv5djbiWaPeJtOHbqFhcVQi0XsW1nYkG3b
cOJJK3/ad/+HGhD73ydm0pPF0WSvuzx7lzpByIXRHXDWibTxJqAAMAoGCCqFAwcB
AQMCA0EAaqqzjjXUqqUXlAMBeZEi2FVIT1efTLuW1jzf3zrMQypBqijS8asUgoDN
ntVv7aQZdAU1VKQnZ7g60EP9OdwEkw==
-----END CERTIFICATE REQUEST-----
0 211: SEQUENCE {
3 129: SEQUENCE {
6 1: INTEGER 0
9 18: SEQUENCE {
11 16: SET {
13 14: SEQUENCE {
15 3: OBJECT IDENTIFIER commonName (2 5 4 3)
20 7: PrintableString 'Example'
: }
: }
: }
29 102: SEQUENCE {
31 31: SEQUENCE {
33 8: OBJECT IDENTIFIER '1 2 643 7 1 1 1 1'
43 19: SEQUENCE {
45 7: OBJECT IDENTIFIER testSignParams (1 2 643 2 2 35 0)
54 8: OBJECT IDENTIFIER '1 2 643 7 1 1 2 2'
: }
: }
64 67: BIT STRING, encapsulates {
67 64: OCTET STRING
: 0B D8 6F E5 D8 DB 89 66 8F 78 9B 4E 1D BA 85 85
: C5 50 8B 45 EC 5B 59 D8 90 6D DB 70 E2 49 2B 7F
: DA 77 FF 87 1A 10 FB DF 27 66 D2 93 C5 D1 64 AF
: BB 3C 7B 97 3A 41 C8 85 D1 1D 70 D6 89 B4 F1 26
: }
: }
133 0: [0] {}
: }
135 10: SEQUENCE {
137 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 2'
: }
147 65: BIT STRING
: 6A AA B3 8E 35 D4 AA A5 17 94 03 01 79 91 22 D8
: 55 48 4F 57 9F 4C BB 96 D6 3C DF DF 3A CC 43 2A
: 41 AA 28 D2 F1 AB 14 82 80 CD 9E D5 6F ED A4 19
: 74 05 35 54 A4 27 67 B8 3A D0 43 FD 39 DC 04 93
: }
-----BEGIN CERTIFICATE-----
MIIBLTCB26ADAgECAgEKMAoGCCqFAwcBAQMCMBIxEDAOBgNVBAMTB0V4YW1wbGUw
IBcNMDEwMTAxMDAwMDAwWhgPMjA1MDEyMzEwMDAwMDBaMBIxEDAOBgNVBAMTB0V4
YW1wbGUwZjAfBggqhQMHAQEBATATBgcqhQMCAiMABggqhQMHAQECAgNDAARAC9hv
5djbiWaPeJtOHbqFhcVQi0XsW1nYkG3bcOJJK3/ad/+HGhD73ydm0pPF0WSvuzx7
lzpByIXRHXDWibTxJqMTMBEwDwYDVR0TAQH/BAUwAwEB/zAKBggqhQMHAQEDAgNB
AE1T8BL+CBd2UH1Nm7gfAO/bTu/Uq4O6xLrPc1Fzz6gcQaoo0vGrFIKAzZ7Vb+2k
GXQFNVSkJ2e4OtBD/TncBJM=
-----END CERTIFICATE-----
0 301: SEQUENCE {
4 219: SEQUENCE {
7 3: [0] {
9 1: INTEGER 2
: }
12 1: INTEGER 10
15 10: SEQUENCE {
17 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 2'
: }
27 18: SEQUENCE {
29 16: SET {
31 14: SEQUENCE {
33 3: OBJECT IDENTIFIER commonName (2 5 4 3)
38 7: PrintableString 'Example'
: }
: }
: }
47 32: SEQUENCE {
49 13: UTCTime 01/01/2001 00:00:00 GMT
64 15: GeneralizedTime 31/12/2050 00:00:00 GMT
: }
81 18: SEQUENCE {
83 16: SET {
85 14: SEQUENCE {
87 3: OBJECT IDENTIFIER commonName (2 5 4 3)
92 7: PrintableString 'Example'
: }
: }
: }
101 102: SEQUENCE {
103 31: SEQUENCE {
105 8: OBJECT IDENTIFIER '1 2 643 7 1 1 1 1'
115 19: SEQUENCE {
117 7: OBJECT IDENTIFIER testSignParams (1 2 643 2 2 35 0)
126 8: OBJECT IDENTIFIER '1 2 643 7 1 1 2 2'
: }
: }
136 67: BIT STRING, encapsulates {
139 64: OCTET STRING
: 0B D8 6F E5 D8 DB 89 66 8F 78 9B 4E 1D BA 85 85
: C5 50 8B 45 EC 5B 59 D8 90 6D DB 70 E2 49 2B 7F
: DA 77 FF 87 1A 10 FB DF 27 66 D2 93 C5 D1 64 AF
: BB 3C 7B 97 3A 41 C8 85 D1 1D 70 D6 89 B4 F1 26
: }
: }
205 19: [3] {
207 17: SEQUENCE {
209 15: SEQUENCE {
211 3: OBJECT IDENTIFIER basicConstraints (2 5 29 19)
216 1: BOOLEAN TRUE
219 5: OCTET STRING, encapsulates {
221 3: SEQUENCE {
223 1: BOOLEAN TRUE
: }
: }
: }
: }
: }
: }
226 10: SEQUENCE {
228 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 2'
: }
238 65: BIT STRING
: 4D 53 F0 12 FE 08 17 76 50 7D 4D 9B B8 1F 00 EF
: DB 4E EF D4 AB 83 BA C4 BA CF 73 51 73 CF A8 1C
: 41 AA 28 D2 F1 AB 14 82 80 CD 9E D5 6F ED A4 19
: 74 05 35 54 A4 27 67 B8 3A D0 43 FD 39 DC 04 93
: }
-----BEGIN X509 CRL-----
MIGSMEECAQEwCgYIKoUDBwEBAwIwEjEQMA4GA1UEAxMHRXhhbXBsZRcNMTQwMTAx
MDAwMDAwWhcNMTQwMTAyMDAwMDAwWjAKBggqhQMHAQEDAgNBAEK/OSoU0+vpV68+
RstQv19CIaADrT0XJ1PJSpw3ox0gQaoo0vGrFIKAzZ7Vb+2kGXQFNVSkJ2e4OtBD
/TncBJM=
-----END X509 CRL-----
0 146: SEQUENCE {
3 65: SEQUENCE {
5 1: INTEGER 1
8 10: SEQUENCE {
10 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 2'
: }
20 18: SEQUENCE {
22 16: SET {
24 14: SEQUENCE {
26 3: OBJECT IDENTIFIER commonName (2 5 4 3)
31 7: PrintableString 'Example'
: }
: }
: }
40 13: UTCTime 01/01/2014 00:00:00 GMT
55 13: UTCTime 02/01/2014 00:00:00 GMT
: }
70 10: SEQUENCE {
72 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 2'
: }
82 65: BIT STRING
: 42 BF 39 2A 14 D3 EB E9 57 AF 3E 46 CB 50 BF 5F
: 42 21 A0 03 AD 3D 17 27 53 C9 4A 9C 37 A3 1D 20
: 41 AA 28 D2 F1 AB 14 82 80 CD 9E D5 6F ED A4 19
: 74 05 35 54 A4 27 67 B8 3A D0 43 FD 39 DC 04 93
: }
This example uses curve defined in Section A.2 of [RFC7836].
Private key is
d = 0x7A929ADE789BB9BE10ED359DD39A72C11B60961F49397EEE1D19CE9891EC3B28
Public key is
X = 0x99C3DF265EA59350640BA69D1DE04418AF3FEA03EC0F85F2DD84E8BED4952774 Y = 0xE218631A69C47C122E2D516DA1C09E6BD19344D94389D1F16C0C4D4DCF96F578
-----BEGIN CERTIFICATE REQUEST-----
MIHKMHkCAQAwEjEQMA4GA1UEAxMHRXhhbXBsZTBeMBcGCCqFAwcBAQEBMAsGCSqF
AwcBAgEBAQNDAARAdCeV1L7ohN3yhQ/sA+o/rxhE4B2dpgtkUJOlXibfw5l49ZbP
TU0MbPHRiUPZRJPRa57AoW1RLS4SfMRpGmMY4qAAMAoGCCqFAwcBAQMCA0EAG9wq
Exdnm2YjL2PqFv98ZMyqua2FX8bhgJFmHbedSBIdDh2lvjR8bxtSVseurCAK1krH
em9bOg4Jcxjnrm7naQ==
-----END CERTIFICATE REQUEST-----
0 202: SEQUENCE {
3 121: SEQUENCE {
5 1: INTEGER 0
8 18: SEQUENCE {
10 16: SET {
12 14: SEQUENCE {
14 3: OBJECT IDENTIFIER commonName (2 5 4 3)
19 7: PrintableString 'Example'
: }
: }
: }
28 94: SEQUENCE {
30 23: SEQUENCE {
32 8: OBJECT IDENTIFIER '1 2 643 7 1 1 1 1'
42 11: SEQUENCE {
44 9: OBJECT IDENTIFIER '1 2 643 7 1 2 1 1 1'
: }
: }
55 67: BIT STRING, encapsulates {
58 64: OCTET STRING
: 74 27 95 D4 BE E8 84 DD F2 85 0F EC 03 EA 3F AF
: 18 44 E0 1D 9D A6 0B 64 50 93 A5 5E 26 DF C3 99
: 78 F5 96 CF 4D 4D 0C 6C F1 D1 89 43 D9 44 93 D1
: 6B 9E C0 A1 6D 51 2D 2E 12 7C C4 69 1A 63 18 E2
: }
: }
124 0: [0] {}
: }
126 10: SEQUENCE {
128 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 2'
: }
138 65: BIT STRING
: 1B DC 2A 13 17 67 9B 66 23 2F 63 EA 16 FF 7C 64
: CC AA B9 AD 85 5F C6 E1 80 91 66 1D B7 9D 48 12
: 1D 0E 1D A5 BE 34 7C 6F 1B 52 56 C7 AE AC 20 0A
: D6 4A C7 7A 6F 5B 3A 0E 09 73 18 E7 AE 6E E7 69
: }
-----BEGIN CERTIFICATE-----
MIIBJTCB06ADAgECAgEKMAoGCCqFAwcBAQMCMBIxEDAOBgNVBAMTB0V4YW1wbGUw
IBcNMDEwMTAxMDAwMDAwWhgPMjA1MDEyMzEwMDAwMDBaMBIxEDAOBgNVBAMTB0V4
YW1wbGUwXjAXBggqhQMHAQEBATALBgkqhQMHAQIBAQEDQwAEQHQnldS+6ITd8oUP
7APqP68YROAdnaYLZFCTpV4m38OZePWWz01NDGzx0YlD2UST0WuewKFtUS0uEnzE
aRpjGOKjEzARMA8GA1UdEwEB/wQFMAMBAf8wCgYIKoUDBwEBAwIDQQAUC02pEksJ
yw1c6Sjuh0JzoxASlJLsDik2njt5EkhXjB0OHaW+NHxvG1JWx66sIArWSsd6b1s6
DglzGOeubudp
-----END CERTIFICATE-----
0 293: SEQUENCE {
4 211: SEQUENCE {
7 3: [0] {
9 1: INTEGER 2
: }
12 1: INTEGER 10
15 10: SEQUENCE {
17 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 2'
: }
27 18: SEQUENCE {
29 16: SET {
31 14: SEQUENCE {
33 3: OBJECT IDENTIFIER commonName (2 5 4 3)
38 7: PrintableString 'Example'
: }
: }
: }
47 32: SEQUENCE {
49 13: UTCTime 01/01/2001 00:00:00 GMT
64 15: GeneralizedTime 31/12/2050 00:00:00 GMT
: }
81 18: SEQUENCE {
83 16: SET {
85 14: SEQUENCE {
87 3: OBJECT IDENTIFIER commonName (2 5 4 3)
92 7: PrintableString 'Example'
: }
: }
: }
101 94: SEQUENCE {
103 23: SEQUENCE {
105 8: OBJECT IDENTIFIER '1 2 643 7 1 1 1 1'
115 11: SEQUENCE {
117 9: OBJECT IDENTIFIER '1 2 643 7 1 2 1 1 1'
: }
: }
128 67: BIT STRING, encapsulates {
131 64: OCTET STRING
: 74 27 95 D4 BE E8 84 DD F2 85 0F EC 03 EA 3F AF
: 18 44 E0 1D 9D A6 0B 64 50 93 A5 5E 26 DF C3 99
: 78 F5 96 CF 4D 4D 0C 6C F1 D1 89 43 D9 44 93 D1
: 6B 9E C0 A1 6D 51 2D 2E 12 7C C4 69 1A 63 18 E2
: }
: }
197 19: [3] {
199 17: SEQUENCE {
201 15: SEQUENCE {
203 3: OBJECT IDENTIFIER basicConstraints (2 5 29 19)
208 1: BOOLEAN TRUE
211 5: OCTET STRING, encapsulates {
213 3: SEQUENCE {
215 1: BOOLEAN TRUE
: }
: }
: }
: }
: }
: }
218 10: SEQUENCE {
220 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 2'
: }
230 65: BIT STRING
: 14 0B 4D A9 12 4B 09 CB 0D 5C E9 28 EE 87 42 73
: A3 10 12 94 92 EC 0E 29 36 9E 3B 79 12 48 57 8C
: 1D 0E 1D A5 BE 34 7C 6F 1B 52 56 C7 AE AC 20 0A
: D6 4A C7 7A 6F 5B 3A 0E 09 73 18 E7 AE 6E E7 69
: }
-----BEGIN X509 CRL-----
MIGSMEECAQEwCgYIKoUDBwEBAwIwEjEQMA4GA1UEAxMHRXhhbXBsZRcNMTQwMTAx
MDAwMDAwWhcNMTQwMTAyMDAwMDAwWjAKBggqhQMHAQEDAgNBABS9aAh8O5A8eqKL
B/6y571v4JY/VjJnNZ9c2Oq0UFmtHQ4dpb40fG8bUlbHrqwgCtZKx3pvWzoOCXMY
565u52k=
-----END X509 CRL-----
0 146: SEQUENCE {
3 65: SEQUENCE {
5 1: INTEGER 1
8 10: SEQUENCE {
10 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 2'
: }
20 18: SEQUENCE {
22 16: SET {
24 14: SEQUENCE {
26 3: OBJECT IDENTIFIER commonName (2 5 4 3)
31 7: PrintableString 'Example'
: }
: }
: }
40 13: UTCTime 01/01/2014 00:00:00 GMT
55 13: UTCTime 02/01/2014 00:00:00 GMT
: }
70 10: SEQUENCE {
72 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 2'
: }
82 65: BIT STRING
: 14 BD 68 08 7C 3B 90 3C 7A A2 8B 07 FE B2 E7 BD
: 6F E0 96 3F 56 32 67 35 9F 5C D8 EA B4 50 59 AD
: 1D 0E 1D A5 BE 34 7C 6F 1B 52 56 C7 AE AC 20 0A
: D6 4A C7 7A 6F 5B 3A 0E 09 73 18 E7 AE 6E E7 69
: }
This example uses curve defined in Appendix D.
Private key is
d = 0x0BA6048AADAE241BA40936D47756D7C93091A0E8514669700EE7508E508B1020\\
72E8123B2200A0563322DAD2827E2714A2636B7BFD18AADFC62967821FA18DD4
Public key is
X = 0x115DC5BC96760C7B48598D8AB9E740D4C4A85A65BE33C1815B5C320C854621DD\\
5A515856D13314AF69BC5B924C8B4DDFF75C45415C1D9DD9DD33612CD530EFE1
Y = 0x37C7C90CD40B0F5621DC3AC1B751CFA0E2634FA0503B3D52639F5D7FB72AFD61\\
EA199441D943FFE7F0C70A2759A3CDB84C114E1F9339FDF27F35ECA93677BEEC
-----BEGIN CERTIFICATE REQUEST-----
MIIBTzCBvAIBADASMRAwDgYDVQQDEwdFeGFtcGxlMIGgMBcGCCqFAwcBAQECMAsG
CSqFAwcBAgECAAOBhAAEgYDh7zDVLGEz3dmdHVxBRVz3302LTJJbvGmvFDPRVlhR
Wt0hRoUMMlxbgcEzvmVaqMTUQOe5io1ZSHsMdpa8xV0R7L53NqnsNX/y/TmTH04R
TLjNo1knCsfw5/9D2UGUGeph/Sq3f12fY1I9O1CgT2PioM9Rt8E63CFWDwvUDMnH
N6AAMAoGCCqFAwcBAQMDA4GBAEM7HWzkClHx5XN+sWqixoOCmkBbnZEn4hJg/J1q
wF2HvyTibEUnilwhkqdbqUmTq9YHTn/xvwP9L1OXr6HZRVgvhvpgoIEJGiPdeV4e
PGie5RKjyC7g3MJkPHjuqPys01SSVYSGsg8cnsGXyQaZhQJgyTvLzZxcMxfhk0Th
c642
-----END CERTIFICATE REQUEST-----
0 335: SEQUENCE {
4 188: SEQUENCE {
7 1: INTEGER 0
10 18: SEQUENCE {
12 16: SET {
14 14: SEQUENCE {
16 3: OBJECT IDENTIFIER commonName (2 5 4 3)
21 7: PrintableString 'Example'
: }
: }
: }
30 160: SEQUENCE {
33 23: SEQUENCE {
35 8: OBJECT IDENTIFIER '1 2 643 7 1 1 1 2'
45 11: SEQUENCE {
47 9: OBJECT IDENTIFIER '1 2 643 7 1 2 1 2 0'
: }
: }
58 132: BIT STRING, encapsulates {
62 128: OCTET STRING
: E1 EF 30 D5 2C 61 33 DD D9 9D 1D 5C 41 45 5C F7
: DF 4D 8B 4C 92 5B BC 69 AF 14 33 D1 56 58 51 5A
: DD 21 46 85 0C 32 5C 5B 81 C1 33 BE 65 5A A8 C4
: D4 40 E7 B9 8A 8D 59 48 7B 0C 76 96 BC C5 5D 11
: EC BE 77 36 A9 EC 35 7F F2 FD 39 93 1F 4E 11 4C
: B8 CD A3 59 27 0A C7 F0 E7 FF 43 D9 41 94 19 EA
: 61 FD 2A B7 7F 5D 9F 63 52 3D 3B 50 A0 4F 63 E2
: A0 CF 51 B7 C1 3A DC 21 56 0F 0B D4 0C C9 C7 37
: }
: }
193 0: [0] {}
: }
195 10: SEQUENCE {
197 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 3'
: }
207 129: BIT STRING
: 43 3B 1D 6C E4 0A 51 F1 E5 73 7E B1 6A A2 C6 83
: 82 9A 40 5B 9D 91 27 E2 12 60 FC 9D 6A C0 5D 87
: BF 24 E2 6C 45 27 8A 5C 21 92 A7 5B A9 49 93 AB
: D6 07 4E 7F F1 BF 03 FD 2F 53 97 AF A1 D9 45 58
: 2F 86 FA 60 A0 81 09 1A 23 DD 79 5E 1E 3C 68 9E
: E5 12 A3 C8 2E E0 DC C2 64 3C 78 EE A8 FC AC D3
: 54 92 55 84 86 B2 0F 1C 9E C1 97 C9 06 99 85 02
: 60 C9 3B CB CD 9C 5C 33 17 E1 93 44 E1 73 AE 36
: }
-----BEGIN CERTIFICATE-----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==
-----END CERTIFICATE-----
0 426: SEQUENCE {
4 278: SEQUENCE {
8 3: [0] {
10 1: INTEGER 2
: }
13 1: INTEGER 11
16 10: SEQUENCE {
18 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 3'
: }
28 18: SEQUENCE {
30 16: SET {
32 14: SEQUENCE {
34 3: OBJECT IDENTIFIER commonName (2 5 4 3)
39 7: PrintableString 'Example'
: }
: }
: }
48 32: SEQUENCE {
50 13: UTCTime 01/01/2001 00:00:00 GMT
65 15: GeneralizedTime 31/12/2050 00:00:00 GMT
: }
82 18: SEQUENCE {
84 16: SET {
86 14: SEQUENCE {
88 3: OBJECT IDENTIFIER commonName (2 5 4 3)
93 7: PrintableString 'Example'
: }
: }
: }
102 160: SEQUENCE {
105 23: SEQUENCE {
107 8: OBJECT IDENTIFIER '1 2 643 7 1 1 1 2'
117 11: SEQUENCE {
119 9: OBJECT IDENTIFIER '1 2 643 7 1 2 1 2 0'
: }
: }
130 132: BIT STRING, encapsulates {
134 128: OCTET STRING
: E1 EF 30 D5 2C 61 33 DD D9 9D 1D 5C 41 45 5C F7
: DF 4D 8B 4C 92 5B BC 69 AF 14 33 D1 56 58 51 5A
: DD 21 46 85 0C 32 5C 5B 81 C1 33 BE 65 5A A8 C4
: D4 40 E7 B9 8A 8D 59 48 7B 0C 76 96 BC C5 5D 11
: EC BE 77 36 A9 EC 35 7F F2 FD 39 93 1F 4E 11 4C
: B8 CD A3 59 27 0A C7 F0 E7 FF 43 D9 41 94 19 EA
: 61 FD 2A B7 7F 5D 9F 63 52 3D 3B 50 A0 4F 63 E2
: A0 CF 51 B7 C1 3A DC 21 56 0F 0B D4 0C C9 C7 37
: }
: }
265 19: [3] {
267 17: SEQUENCE {
269 15: SEQUENCE {
271 3: OBJECT IDENTIFIER basicConstraints (2 5 29 19)
276 1: BOOLEAN TRUE
279 5: OCTET STRING, encapsulates {
281 3: SEQUENCE {
283 1: BOOLEAN TRUE
: }
: }
: }
: }
: }
: }
286 10: SEQUENCE {
288 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 3'
: }
298 129: BIT STRING
: 41 57 03 D8 92 F1 A5 F3 F6 8C 43 53 18 9A 7E E2
: 07 B8 0B 56 31 EF 9D 49 52 9A 4D 6B 54 2C 2C FA
: 15 AA 2E AC F1 1F 47 0F DE 7D 95 48 56 90 3C 35
: FD 8F 95 5E F3 00 D9 5C 77 53 4A 72 4A 0E EE 70
: 2F 86 FA 60 A0 81 09 1A 23 DD 79 5E 1E 3C 68 9E
: E5 12 A3 C8 2E E0 DC C2 64 3C 78 EE A8 FC AC D3
: 54 92 55 84 86 B2 0F 1C 9E C1 97 C9 06 99 85 02
: 60 C9 3B CB CD 9C 5C 33 17 E1 93 44 E1 73 AE 36
: }
-----BEGIN X509 CRL-----
MIHTMEECAQEwCgYIKoUDBwEBAwMwEjEQMA4GA1UEAxMHRXhhbXBsZRcNMTQwMTAx
MDAwMDAwWhcNMTQwMTAyMDAwMDAwWjAKBggqhQMHAQEDAwOBgQA6E/t67NtVYO72
E3z8XdZGkXMuv7NpCh/Ax+ik7uoIMH1kjU3AmGxGqHs/vkx69C6jQ1nHlZVMo5/z
q77ZBR9NL4b6YKCBCRoj3XleHjxonuUSo8gu4NzCZDx47qj8rNNUklWEhrIPHJ7B
l8kGmYUCYMk7y82cXDMX4ZNE4XOuNg==
-----END X509 CRL-----
0 211: SEQUENCE {
3 65: SEQUENCE {
5 1: INTEGER 1
8 10: SEQUENCE {
10 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 3'
: }
20 18: SEQUENCE {
22 16: SET {
24 14: SEQUENCE {
26 3: OBJECT IDENTIFIER commonName (2 5 4 3)
31 7: PrintableString 'Example'
: }
: }
: }
40 13: UTCTime 01/01/2014 00:00:00 GMT
55 13: UTCTime 02/01/2014 00:00:00 GMT
: }
70 10: SEQUENCE {
72 8: OBJECT IDENTIFIER '1 2 643 7 1 1 3 3'
: }
82 129: BIT STRING
: 3A 13 FB 7A EC DB 55 60 EE F6 13 7C FC 5D D6 46
: 91 73 2E BF B3 69 0A 1F C0 C7 E8 A4 EE EA 08 30
: 7D 64 8D 4D C0 98 6C 46 A8 7B 3F BE 4C 7A F4 2E
: A3 43 59 C7 95 95 4C A3 9F F3 AB BE D9 05 1F 4D
: 2F 86 FA 60 A0 81 09 1A 23 DD 79 5E 1E 3C 68 9E
: E5 12 A3 C8 2E E0 DC C2 64 3C 78 EE A8 FC AC D3
: 54 92 55 84 86 B2 0F 1C 9E C1 97 C9 06 99 85 02
: 60 C9 3B CB CD 9C 5C 33 17 E1 93 44 E1 73 AE 36
: }
The following parameters must be used for digital signature generation and verification.
The following value is assigned to parameter p in this example:
p = 36239861022290036359077887536838743060213209255346786050\\
8654615045085616662400248258848202227149685402509082360305\\
8735163734263822371964987228582907372403,
p = 0x4531ACD1FE0023C7550D267B6B2FEE80922B14B2FFB90F04D4EB7C09B5D2D15D\\
F1D852741AF4704A0458047E80E4546D35B8336FAC224DD81664BBF528BE6373.
Parameters a and b take the following values in this example:
a = 7,
a = 0x7,
b = 1518655069210828534508950034714043154928747527740206436\\
1940188233528099824437937328297569147859746748660416053978836775\\
96626326413990136959047435811826396,
b = 0x1CFF0806A31116DA29D8CFA54E57EB748BC5F377E49400FDD788B649ECA1AC4\\
361834013B2AD7322480A89CA58E0CF74BC9E540C2ADD6897FAD0A3084F302ADC.
Parameter m takes the following value in this example:
m = 36239861022290036359077887536838743060213209255346786050865461\\
504508561666239691648983050328630684999614040794379365854558651922\\
12970734808812618120619743,
m = 0x4531ACD1FE0023C7550D267B6B2FEE80922B14B2FFB90F04D4EB7C09B5D2D15D\\
A82F2D7ECB1DBAC719905C5EECC423F1D86E25EDBE23C595D644AAF187E6E6DF.
Parameter q takes the following value in this example:
q = 36239861022290036359077887536838743060213209255346786050865461\\
504508561666239691648983050328630684999614040794379365854558651922\\
12970734808812618120619743,
q = 0x4531ACD1FE0023C7550D267B6B2FEE80922B14B2FFB90F04D4EB7C09B5D2D15D\\
A82F2D7ECB1DBAC719905C5EECC423F1D86E25EDBE23C595D644AAF187E6E6DF.
Point P coordinates take the following values in this example:
x = 1928356944067022849399309401243137598997786635459507974357075491\\
307766592685835441065557681003184874819658004903212332884252335830\\
250729527632383493573274,
x = 0x24D19CC64572EE30F396BF6EBBFD7A6C5213B3B3D7057CC825F91093A68CD762\\
FD60611262CD838DC6B60AA7EEE804E28BC849977FAC33B4B530F1B120248A9A,
y = 22887286933719728599700121555294784163535623273295061803\\
144974259311028603015728141419970722717088070665938506503341523818\\
57347798885864807605098724013854,
y = 0x2BB312A43BD2CE6E0D020613C857ACDDCFBF061E91E5F2C3F32447C259F39B2\\
C83AB156D77F1496BF7EB3351E1EE4E43DC1A18B91B24640B6DBB92CB1ADD371E.