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GB/T 32918.5-2017 PDF English

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GB/T 32918.5-2017: Information security technology - Public key cryptographic algorithm SM2 based on elliptic curves - Part 5: Parameter definition
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GB/T 32918.5-2017: Information security technology - Public key cryptographic algorithm SM2 based on elliptic curves - Part 5: Parameter definition


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GB NATIONAL STANDARD OF THE PEOPLE’S REPUBLIC OF CHINA ICS 35.040 L 80 Information security technology - Public key cryptographic algorithm SM2 based on elliptic curves - Part 5. Parameter definition Issued on: MAY 12, 2017 Implemented on: DECEMBER 1, 2017 Issued by. General Administration of Quality Supervision, Inspection and Quarantine of the PRC; Standardization Administration of the PRC.

Table of Contents

Foreword ... 3 Introduction ... 4 1 Scope ... 6 2 Normative references ... 6 3 Symbols ... 6 4 Parameter definition ... 7 Appendix A (Informative) Example of digital signature and verification ... 8 Appendix B (Informative) Example of key exchange and verification ... 10 Appendix C (Informative) Example of message encryption and decryption ... 14 References ... 16

Introduction

In 1985, N.Koblitz and V.Miller independently proposed the application of elliptic curves to public key cryptosystems. The nature of the curve on which the elliptic curve’s public key cryptography is based is as follows. - The elliptic curve on the finite field forms a finite exchange group under the point addition operation, its order is similar to the base field size; - Similar to the power operation in the finite field multiplication group, the elliptic curve’s multiple-point-multiplication operation constitutes a one-way function. In the multiple-point-multiplication operation, the multiple-point-multiplication and the base point are known, the problem of solving the multiplication is called the elliptic curve’s discrete logarithm problem. For the discrete logarithm problem of general elliptic curves, there is only a solution method for exponential computational complexity. Compared with the large number decomposition problem and the discrete logarithm problem on the finite field, the elliptic curve’s discrete logarithm problem is much more difficult to solve. Therefore, under the same level of security, the elliptic curve cryptography is much smaller than the key size required for other public key cryptographies. SM2 is an elliptic curve’s cryptographic algorithm standard which is developed and proposed by the National Cryptography Authority. The main objectives of GB/T 32918 are as follows. - GB/T 32918.1 defines and describes the related concepts and mathematical basics of the SM2 elliptic curve cryptographic algorithm, and outlines the relationship between this part and other parts. - GB/T 32918.2 describes a signature algorithm based on elliptic curve, that is, the SM2 signature algorithm. - GB/T 32918.3 describes a key exchange protocol based on elliptic curve, that is, the SM2 key exchange protocol. - GB/T 32918.4 describes a public key encryption algorithm based on elliptic curve, that is, the SM2 encryption algorithm, which uses the SM3 cryptographic hash algorithm as defined in GB/T 32905-2016. - GB/T 32918.5 gives the elliptic curve parameters used by the SM2 Information security technology - Public key cryptographic algorithm SM2 based on elliptic curves - Part 5. Parameter definition

1 Scope

This Part of GB/T 32918 specifies the curve parameters of public key cryptographic algorithm SM2 based on elliptic curves. This Part applies to digital signature and verification (SEE Appendix A), key exchange and verification (SEE Appendix B), and example of message encryption and decryption (SEE Appendix C).

2 Normative references

The following documents are indispensable for the application of this document. For the dated references, only the versions with the dates indicated are applicable to this document. For the undated references, the latest version (including all the amendments) are applicable to this document. GB/T 32905-2016 Information security techniques - SM3 cryptographic hash algorithm GB/T 32918.1-2016 Information security technology - Public key cryptographic algorithm SM2 based on elliptic curves - Part 1. General GB/T 32918.2-2016 Information security technology - Public key cryptographic algorithm SM2 based on elliptic curves - Part 2. Digital signature algorithm GB/T 32918.3-2016 Information security technology - Public key cryptographic algorithm SM2 based on elliptic curves - Part 3. Key exchange protocol GB/T 32918.4-2016 Information security technology - Public key cryptographic algorithm SM2 based on elliptic curves - Part 4. Public key encryption algorithm

3 Symbols

Appendix A

(Informative) Example of digital signature and verification A.1 Overview This appendix selects the cryptographic hash algorithm given in GB/T 32905- 2016. The input is a message bit string of length less than 264. The output is a hash value of 256 bits in length, which is recorded as H256(). This appendix uses the digital signature algorithm specified in GB/T 32918.2- 2016 to calculate the corresponding values in each step. In this appendix, all numbers, expressed in hexadecimal form, are high on the left and low on the right. In this appendix, the message uses the code in GB/T 1988. Assume that the GB/T 1988 code of IDA is. 31323334 35363738 31323334 35363738. ENTLA=0080. A.2 Digital signature SM2 based on elliptic curves Elliptic curve equation is. y2=x3+ax+b Example 1. Fp-256 Base point G= (xG, yG). Its order is recorded as n. Prime number p Factor a Factor b Coordinate xG Coordinate yG Order n Message M to be signed The hexadecimal representation of the GB/T 1988 code of M Private key dA Public key Coordinate xA Coordinate yA Hash value

Appendix B

(Informative) Example of key exchange and verification B.1 General requirements This appendix selects the cryptographic hash algorithm given in GB/T 32905- 2016. The input is a message bit string of length less than 264. The output is a hash value of 256 bits in length, which is recorded as H256(). This appendix uses the key exchange protocol specified in GB/T 32918.3-2016 to calculate the corresponding values in each step. In this appendix, all numbers, expressed in hexadecimal form, are high on the left and low on the right. Assume that the GB/T 1988 code of IDA is. 31323334 35363738 31323334 35363738. ENTLA=0080. Assume that the GB/T 1988 code of IDB is. 31323334 35363738 31323334 35363738. ENTLB=0080. B.2 Key exchange protocol SM2 based on elliptic curves Elliptic curve equation is. y2=x3+ax+b Example 1. Fp-256 Cofactor h. 1 Base point G= (xG, yG). Its order is recorded as n. Prime number p Factor a Factor b Coordinate xG Coordinate yG Order n User A’s private key dA User A’s public key Coordinate xA ......

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