Standards related to:

GM/T 0003.5-2012GM/T 0003.5-2012

GM

CRYPTOGRAPHY INDUSTRY STANDARD

OF THE PEOPLE’S REPUBLIC OF CHINA

ICS 35.040

L 80

File No.. 36830-2012

Public key cryptographic algorithm SM2 based on

elliptic curves - Part 5. Parameter definition

ISSUED ON. MARCH 21, 2012

IMPLEMENTED ON. MARCH 21, 2012

Issued by. State Cryptography Administration

Table of Contents

Foreword ... 3

1 Scope .. 4

2 Parameter definition ... 4

Annex A (Informative) Example of digital signature and verification .. 5

A.1 General requirements... 5

A.2 SM2 elliptic curve digital signature ... 5

Annex B (Informative) Example of key exchange and verification ... 8

B.1 General requirements... 8

B.2 SM2 elliptic curve key exchange protocol ... 8

Annex C (Informative) Examples of message encryption and decryption ... 14

C.1 General requirements ... 14

C.2 SM2 message encryption and decryption of elliptic curves ... 14

Foreword

GM/T 0003-2012 Public key cryptographic algorithm SM2 based on elliptic

curves is divided into 5 parts.

— Part 1. General;

— Part 2. Digital signature algorithm;

— Part 3. Key exchange protocol;

— Part 4. Public key encryption algorithm;

— Part 5. Parameter definition.

This is Part 5 of GM/T 0003-2012.

This Part was drafted in accordance with the rules given in GB/T 1.1-2009.

Attention is drawn to the possibility that some of the elements of this document

may be the subject of patent rights. The issuing authority shall not be held

responsible for identifying any or all such patent rights.

Annex A, Annex B and Annex C of this Part are informative.

This Part was proposed by and shall be under the jurisdiction of State

Cryptography Administration.

Drafting organizations of this Part. Beijing Huada Information Safety

Technology Co., Ltd, PLA Information Engineering University, Data Assurance

and Communication Security Research Center of Chinese Academy of

Sciences.

Main drafters of this Part. Chen Jianhua, Zhu Yuefei, Ye Dingfeng, Hu Lei, Pei

Dingyi, Peng Guohua, Zhang Yajuan, Zhang Zhenfeng.

Public key cryptographic algorithm SM2 based on

elliptic curves - Part 5. Parameter definition

1 Scope

This Part of GM/T 0003 specifies the curve parameters of the public key

cryptographic algorithm SM2 based on elliptic curves, and gives the examples

of digital signature and verification, key exchange and verification, message

encryption and decryption.

2 Parameter definition

SM2 adopts the elliptic curve over a 256-bit prime field.

Elliptic curve equation.

Curve parameters.

Annex A

(Informative)

Example of digital signature and verification

A.1 General requirements

This Annex adopts the cryptographic hash function given in GM/T 0004-2012

SM3 cryptographic hash algorithm, the input of which is a message bit string

less than 264 in length, and the output of which is a 256-bit hash value, denoted

as ܪଶହሺሻ.

In this Annex, for all hexadecimal digits, the high-order digits are on the left,

while the low-order digits are on the right.

In this Annex, ASCII encoding is applied to the messages.

SUPPOSE that the ASCII encoding of IDA is .

ܧܰܶܮ ൌ 0080.

A.2 SM2 elliptic curve digital signature

Elliptic curve equation. ݕଶ ൌ ݔଷ ܽݔ ܾ

EXAMPLE. ܨ െ 256

Prime p.

Coefficient a.

Coefficient b.

Base point ܩ ൌ ሺݔீ, ݕீሻ, the order of which is denoted as n.

Coordinate ݔீ.

Coordinate ݕீ.

Order n.

Message to be signed M. message digest

The ASCII code of M is expressed in 6D65737361676520646967657374

Private key ݀.

Public key ܲ ൌ ሺݔ, ݕሻ.

...