GM/T 0003.5-2012 PDF in English
GM/T 0003.5-2012 (GM/T0003.5-2012, GMT 0003.5-2012, GMT0003.5-2012)
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Public key cryptographic algorithm SM2 based on elliptic curves - Part 5: Parameter definition
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GM/T 0003.5-2012: PDF in English (GMT 0003.5-2012) GM/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.
......
Source: Above contents are excerpted from the PDF -- translated/reviewed by: www.chinesestandard.net / Wayne Zheng et al.
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