ANSI X9.63 (2011) (R2017) - Key Agreement and Key Transport Using Elliptic Curve Cryptography

Cover......Page 1
Foreword......Page 3
X9 Member Organization Representative......Page 4
X9F Member Organization Representative......Page 5
X9F1 Member Organization Representative......Page 8
ToC......Page 9
List of Figures......Page 13
List of Tables......Page 14
2.1 Definitions and Abbreviations......Page 15
2.2 Symbols and Notation......Page 25
2.3 Normative References......Page 28
3.1 General......Page 29
3.2 The Schemes in This Standard......Page 30
3.4 Annexes......Page 31
4.3.1 Integer-to-Octet-String Conversion......Page 33
5.1.1 Primitives for Elliptic Curve Domain Parameter Generation and Validation over F_p......Page 34
5.3 Challenge Generation Primitive......Page 35
5.4.1 Standard Diffie-Hellman Primitive......Page 36
5.5 MQV Primitive......Page 37
5.6.1 Associate Value Function (AVF)......Page 38
5.6.2 Cryptographic Hash Functions......Page 39
5.6.3 Key Derivation Function (KDF)......Page 40
5.7 Mac Schemes......Page 41
5.7.1 Tagging Transformation......Page 42
5.8 Asymmetric Encryption Scheme......Page 43
5.8.1 Encryption Transformation......Page 44
5.8.2 Decryption Transformation......Page 45
5.9 Signature Scheme......Page 46
5.9.2 Verifying Transformation......Page 47
6 Key Agreement Schemes......Page 48
6.1 Ephemeral Unified Model Scheme......Page 50
6.2 1-Pass Diffie-Hellman Scheme......Page 52
6.2.1 Initiator Transformation......Page 53
6.2.2 Responder Transformation......Page 54
6.3 Static Unified Model Scheme......Page 55
6.4 Combined Unified Model With Key Confirmation Scheme......Page 56
6.5 1-Pass Unified Model Scheme......Page 57
6.5.1 Initiator Transformation......Page 58
6.5.2 Responder Transformation......Page 59
6.6 Full Unified Model Scheme......Page 60
6.7 Full Unified Model With Key Confirmation Scheme......Page 62
6.8 Station - to -Station Scheme......Page 63
6.8.1 Initiator Transformation......Page 64
6.8.2 Responder Transformation......Page 66
6.9 1-Pass MQV Scheme......Page 69
6.9.1 Initiator Transformation......Page 70
6.10 Full MQV Scheme......Page 71
6.11 Full MQV With Key Confirmation Scheme......Page 73
7.2 3-Pass Transport Scheme......Page 74
Annex A (Normative) Normative Number-Theoretic Algorithms......Page 75
Annex B (Informative) Mathematical Background......Page 76
Annex C (Informative) Tables of Trinomials, Pentanomials, and Gaussian Normal Bases......Page 77
Annex D (Informative) Informative Number-Theoretic Algorithms......Page 78
Annex E (Informative) Complex Multiplication (CM) Elliptic Curve Generation Method......Page 79
F.4.1 the ECDLP and Key Establishment Schemes......Page 80
F.4.2 Security Attributes and Key Establishment Schemes......Page 81
F.4.3 Security Attributes of the Schemes in this Standard......Page 82
F.4.4 Appropriate Key Lengths......Page 84
G.1 Examples of Data Conversion Methods......Page 88
G.4 Sample Elliptic Curves Over the Field F_{2^M}......Page 91
G.4.1 2 Examples with m = 193......Page 92
G.4.2 2 Examples with m = 233......Page 93
G.4.3 Example with m = 239......Page 95
G.4.4 2 Examples with m = 283......Page 96
G.4.5 2 Examples with m = 409......Page 97
G.4.6 2 Examples with m = 571......Page 99
G.5.1 2 Examples with a 192-bit Prime......Page 101
G.5.2 2 Examples with a 224-bit Prime......Page 102
G.5.3 2 Examples with a 256-bit Prime......Page 104
G.5.4 An Example with a 384-bit Prime......Page 106
G.5.5 An Example with a 521-bit Prime......Page 107
H.1 Syntax for Finite Field Identification......Page 109
H.3 Syntax for Elliptic Curve Domain Parameters......Page 112
H.4 Syntax for Public Keys......Page 113
H.5 Scheme Syntax......Page 117
H.5.1 Ephemeral Unified Model Scheme......Page 118
H.5.4 Combined Unified Model with Key Confirmation Scheme......Page 119
H.5.6 Full Unified Model Scheme......Page 120
H.5.8 Station-to-Station Scheme......Page 121
H.5.12 1-Pass Key Transport Scheme......Page 122
H.6 Key Derivation Syntax......Page 123
H.7 ASN.1 Module......Page 125
I.2.1 Combined Unified Model with Key Confirmation......Page 132
I.2.2 Full Unified Model with Key Confirmation Scheme......Page 138
I.2.3 Full MQV with Key Confirmation Scheme......Page 143
I.3 Legacy Key Transport Schemes......Page 148
I.3.1 1-Pass Transport Scheme......Page 149
I.3.2 3-Pass Transport Scheme......Page 152
Annex J (Informative) Bibliography......Page 158