GM/T Translated English of Chinese Standard: GM/T CRYPTOGRAPHY INDUSTRY STANDARD

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1 Translated English of Chinese Standard: GM/T Buy True-PDF Auto-delivery. GM CRYPTOGRAPHY INDUSTRY STANDARD OF THE PEOPLE S REPUBLIC OF CHINA ICS L 80 File No.: GM/T Public key cryptographic algorithm SM2 based on elliptic curves - Part 5: Parameter definition SM2 椭圆曲线公钥密码算法第 5 部分 : 参数定义 GM/T How to BUY & immediately GET a full-copy of this standard? Search --> Add to Cart --> Checkout (3-steps); 3. No action is required - Full-copy of this standard will be automatically & immediately delivered to your address in 0~60 minutes. 4. Support: Sales@ChineseStandard.net. Wayne, Sales manager Issued on: March 21, 2012 Implemented on: March 21, 2012 Issued by: State Cryptography Administration Buy True-PDF Auto-delivery. Page 1 of 16

2 Table of Contents Foreword Scope 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 C.1 General requirements C.2 SM2 message encryption and decryption of elliptic curves Buy True-PDF Auto-delivery. Page 2 of 16

3 Foreword GM/T 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 This Part was drafted in accordance with the rules given in GB/T 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. Buy True-PDF Auto-delivery. Page 3 of 16

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

4 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: Buy True-PDF Auto-delivery. Page 4 of 16

5 Annex A (Informative) Example of digital signature and verification A.1 General requirements This Annex adopts the cryptographic hash function given in GM/T SM3 cryptographic hash algorithm, the input of which is a message bit string less than 2 64 in length, and the output of which is a 256-bit hash value, denoted as. 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 A.2 SM2 elliptic curve digital signature Elliptic curve equation: EXAMPLE: 256 Prime p: Coefficient a: Coefficient b: Base point,, the order of which is denoted as n. Coordinate : Coordinate : Order n: Message to be signed M: message digest The ASCII code of M is expressed in 6D Private key : Public key, : Buy True-PDF Auto-delivery. Page 5 of 16

--> Buy True-PDF --> Auto-delivered in 0~10 minutes. GM/T Translated English of Chinese Standard: GM/T0044.

--> Buy True-PDF --> Auto-delivered in 0~10 minutes. GM/T Translated English of Chinese Standard: GM/T0044. Translated English of Chinese Standard: GM/T0044.1-2016 www.chinesestandard.net Buy True-PDF Auto-delivery. Sales@ChineseStandard.net CRYPTOGRAPHY INDUSTRY STANDARD OF THE PEOPLE S REPUBLIC OF CHINA GM