ISO/IEC 15946-1:2016
Information technology — Security techniques — Cryptographic techniques based on elliptic curves — Part 1: General
ISO/IEC 15946-1:2016 describes the mathematical background and general techniques necessary for implementing the elliptic curve cryptography mechanisms defined in ISO/IEC 15946‑5, ISO/IEC 9796‑3, ISO/IEC 11770‑3, ISO/IEC 14888‑3, ISO/IEC 18033‑2 and other ISO/IEC standards.
ISO/IEC 15946-1:2016 does not specify the implementation of the techniques it defines. For example, it does not specify the basis representation to be used when the elliptic curve is defined over a finite field of characteristic two. Thus, interoperability of products complying with ISO/IEC 15946-1:2016 will not be guaranteed.
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Foreword
Introduction
1 Scope
2 Normative references
3 Terms and definitions
4 Symbols
5 Conventions for fields
5.1 Finite prime fields F(p)
5.2 Finite fields F(pm)
6 Conventions for elliptic curves
6.1 Definitions of elliptic curves
6.1.1 Elliptic curves over F(pm)
6.1.2 Elliptic curves over F(2m)
6.1.3 Elliptic curves over F(3m)
6.2 Group law on elliptic curves
6.3 Generation of elliptic curves
6.4 Cryptographic bilinear map
7 Conversion functions
7.1 Octet string/bit string conversion: OS2BSP and BS2OSP
7.2 Bit string/integer conversion: BS2IP and I2BSP
7.3 Octet string/string conversion: OS2IP and I2OSP
7.4 Finite field element/integer conversion: FE2IPF
7.5 Octet string/finite field element conversion: OS2FEPF and FE2OSPF
7.6 Elliptic curve point/octet string conversion: EC2OSPE and OS2ECPE
7.6.1 Compressed elliptic curve points
7.6.2 Point decompression algorithms
7.6.3 Conversion functions
7.7 Integer/elliptic curve conversion: I2ECP
8 Elliptic curve domain parameters and public key
8.1 Elliptic curve domain parameters over F(q)
8.2 Elliptic curve key generation
Annex A (informative) Background information on finite fields
Annex B (informative) Background information on elliptic curves
Annex C (informative) Background information on elliptic curve cryptosystems
Annex D (informative) Summary of coordinate systems
Bibliography
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Foreword
Introduction
1 Scope
2 Normative references
3 Terms and definitions
4 Symbols
5 Conventions for fields
5.1 Finite prime fields F(p)
5.2 Finite fields F(pm)
6 Conventions for elliptic curves
6.1 Definitions of elliptic curves
6.1.1 Elliptic curves over F(pm)
6.1.2 Elliptic curves over F(2m)
6.1.3 Elliptic curves over F(3m)
6.2 Group law on elliptic curves
6.3 Generation of elliptic curves
6.4 Cryptographic bilinear map
7 Conversion functions
7.1 Octet string/bit string conversion: OS2BSP and BS2OSP
7.2 Bit string/integer conversion: BS2IP and I2BSP
7.3 Octet string/string conversion: OS2IP and I2OSP
7.4 Finite field element/integer conversion: FE2IPF
7.5 Octet string/finite field element conversion: OS2FEPF and FE2OSPF
7.6 Elliptic curve point/octet string conversion: EC2OSPE and OS2ECPE
7.6.1 Compressed elliptic curve points
7.6.2 Point decompression algorithms
7.6.3 Conversion functions
7.7 Integer/elliptic curve conversion: I2ECP
8 Elliptic curve domain parameters and public key
8.1 Elliptic curve domain parameters over F(q)
8.2 Elliptic curve key generation
Annex A (informative) Background information on finite fields
Annex B (informative) Background information on elliptic curves
Annex C (informative) Background information on elliptic curve cryptosystems
Annex D (informative) Summary of coordinate systems
Bibliography