ISO/IEC 14888-3:2016
(Main)Information technology — Security techniques — Digital signatures with appendix — Part 3: Discrete logarithm based mechanisms
Information technology — Security techniques — Digital signatures with appendix — Part 3: Discrete logarithm based mechanisms
ISO/IEC 14888-3:2016 specifies digital signature mechanisms with appendix whose security is based on the discrete logarithm problem. ISO/IEC 14888-3:2016 provides - a general description of a digital signature with appendix mechanism, and - a variety of mechanisms that provide digital signatures with appendix. For each mechanism, this part of ISO/IEC 14888 specifies - the process of generating a pair of keys, - the process of producing signatures, and - the process of verifying signatures.
Technologies de l'information — Techniques de sécurité — Signatures numériques avec appendice — Partie 3: Mécanismes basés sur un logarithme discret
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INTERNATIONAL ISO/IEC
STANDARD 14888-3
Third edition
2016-03-15
Corrected version
2017-09
Information technology — Security
techniques — Digital signatures with
appendix —
Part 3:
Discrete logarithm based mechanisms
Technologies de l'information — Techniques de sécurité — Signatures
numériques avec appendice —
Partie 3: Mécanismes basés sur un logarithme discret
Reference number
©
ISO/IEC 2016
© ISO/IEC 2016, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
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ii © ISO/IEC 2016 – All rights reserved
Contents Page
Foreword .vi
Introduction .vii
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms . 3
5 General model . 5
5.1 Parameter generation process . 5
5.1.1 Certificate-based mechanisms . 5
5.1.2 Identity-based mechanisms . 5
5.1.3 Parameter selection . 6
5.1.4 Validity of domain parameters and verification key . 7
5.2 Signature process . 7
5.2.1 General. 7
5.2.2 Producing the randomizer. 8
5.2.3 Producing the pre-signature . 8
5.2.4 Preparing the message for signing . 8
5.2.5 Computing the witness (the first part of the signature) . 8
5.2.6 Computing the assignment . 8
5.2.7 Computing the second part of the signature . 9
5.2.8 Constructing the appendix . 9
5.2.9 Constructing the signed message . 9
5.3 Verification process .10
5.3.1 General.10
5.3.2 Retrieving the witness .10
5.3.3 Preparing message for verification .11
5.3.4 Retrieving the assignment .11
5.3.5 Recomputing the pre-signature .11
5.3.6 Recomputing the witness .11
5.3.7 Verifying the witness .11
6 Certificate-based mechanisms .12
6.1 General .12
6.1 6.1 .
General .12
6.2 DSA .13
6.2.1 General.13
6.2.2 Parameters .13
6.2.3 Generation of signature key and verification key .14
6.2.4 Signature process .14
6.2.5 Verification process .15
6.3 KCDSA .16
6.3.1 General.16
6.3.2 Parameters .16
6.3.3 Generation of signature key and verification key .17
6.3.4 Signature process .17
6.3.5 Verification process .18
6.4 Pointcheval/Vaudenay algorithm .19
6.4.1 General.19
6.4.2 Parameters .19
6.4.3 Generation of signature key and verification key .19
6.4.4 Signature process .19
6.4.5 Verification process .20
© ISO/IEC 2016 – All rights reserved iii
6.5 SDSA .21
6.5.1 General.21
6.5.2 Parameters .22
6.5.3 Generation of signature key and verification key .22
6.5.4 Signature process .22
6.5.5 Verification process .23
6.6 EC-DSA .24
6.6.1 General.24
6.6.2 Parameters .24
6.6.3 Generation of signature key and verification key .25
6.6.4 Signature process .25
6.6.5 Verification process .26
6.7 EC-KCDSA.27
6.7.1 General.27
6.7.2 Parameters .27
6.7.3 Generation of signature key and verification key .28
6.7.4 Signature process .28
6.7.5 Verification process .29
6.8 EC-GDSA .30
6.8.1 General.30
6.8.2 Parameters .30
6.8.3 Generation of signature key and verification key .30
6.8.4 Signature process .
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© ISO/IEC 2015 – All rights reserved
ISO/IEC JTC 1/SC 27 N15619 Style Definition
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Information technology — Security techniques — Digital signatures with Formatted: French (Switzerland)
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Document type: International Standard
ISO/IEC 14888-3:2017(E)
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Contents Page
Foreword . 10
Introduction . 11
1 Scope . 14
2 Normative references . 14
3 Terms and definitions . 14
4 Symbols and abbreviated terms . 16
5 General model . 18
5.1 Parameter generation process . 18
5.2 Signature process . 20
5.3 Verification process . 23
6 Certificate-based mechanisms . 25
6.1 General . 25
6.2 DSA . 26
6.3 KCDSA . 29
6.4 Pointcheval/Vaudenay algorithm . 32
6.5 SDSA . 34
6.6 EC-DSA . 37
6.7 EC-KCDSA . 40
6.8 EC-GDSA . 43
6.9 EC-RDSA . 45
6.10 EC-SDSA . 47
6.11 EC-FSDSA . 50
7 Identity-based mechanisms . 52
7.1 General . 52
7.2 IBS-1 . 53
7.3 IBS-2 . 56
Annex A (normative) Object identifier . 59
Annex B (normative) Conversion functions (I) . 62
B.1 Conversion from a field element to an integer: FE2I(r, x) . 62
B.2 Conversion from an integer to a field element: I2FE(r, x) . 63
B.3 Conversion from a field element to a binary string: FE2BS(r, x) . 64
B.4 Conversion from a binary string to an integer: BS2I (g, x) . 65
B.5 Conversion from an integer to a binary string: I2BS(g, x) . 65
B.6 Conversion between an integer and an octet string: I2OS(h, x) & OS2I(h, M). 65
Annex C (informative) Conversion functions (II) . 67
Annex D (normative) Generation of DSA domain parameters . 69
D.1 Generation of the prime p and q . 69
D.2 Generation of the generator G . 70
D.2.1 Unverifiable generation of G . 70
D.2.2 Verifiable generation of G . 70
ii © ISO/IEC 2015 – All rights reserved
ISO/IEC 14888-3:2017(E)
Deleted: 2016
Annex E (informative) The Weil and Tate pairings . 71
E.1 General . 71
E.2 The functions f, g and d . 71
E.3 The Weil pairing . 72
E.4 The Tate pairing . 72
E.5 The reduced Tate pairing . 73
Annex F (informative) Numerical examples . 74
F.1 General . 74
F.2 DSA mechanism . 74
F.2.1 Example 1: 2048-bit Prime P, SHA-224 . 74
F.2.1.1 General . 74
F.2.1.2 Parameters . 74
F.2.1.3 Signature key and verification key . 75
F.2.1.4 Per message data . 75
F.2.1.5 Signature . 75
F.2.1.6 Verification . 75
F.2.2 Example 2: 3072-bit Prime P, SHA-256 . 75
F.2.2.1 General . 75
F.2.2.2 Parameters . 76
F.2.2.3 Signature key and verification key . 77
F.2.2.4 Per message data . 78
F.2.2.5 Signature . 78
F.2.2.6 Verification . 78
F.3 KCDSA mechanism . 78
F.3.1 Example 1: 2048-bit Prime P, 224-bit Prime Q, SHA-224 . 78
F.3.1.1 General . 78
F.3.1.2 Parameters . 78
F.3.1.3 Signature key and verification key . 79
F.3.1.4 Per message data . 80
F.3.1.5 Signature . 80
F.3.1.6 Verification . 80
F.3.2 Example 2: 3072-bit Prime P, 256-bit Prime Q, SHA-256 . 80
F.3.2.1 General . 80
F.3.2.2 Parameters . 80
F.3.2.3 Signature key and verification key . 81
F.3.2.4 Per message data . 82
F.3.2.5 Signature . 82
© ISO/IEC 2015 – All rights reserved iii
ISO/IEC 14888-3:2017(E)
Deleted: 2016
F.3.2.6 Verification . 83
F.3.3 Example 3: 2048-bit Prime P, 224-bit Prime Q, SHA-256 . 83
F.3.3.1 General . 83
F.3.3.2 Parameters . 83
F.3.3.3 Signature key and verification key . 84
F.3.3.4 Per message data . 84
F.3.3.5 Signature . 84
F.3.3.6 Verification .
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