GM/T 0044.5-2016 English PDF (GMT0044.5-2016)

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GM/T 0044.5-2016: Identity-based cryptographic algorithms SM9 -- Part 5: Parameter definition
GM/T 0044.5-2016
GM
CRYPTOGRAPHY INDUSTRY STANDARD
OF THE PEOPLE’S REPUBLIC OF CHINA
ICS 35.040
L 80
File No.. 55617-2016
Identity-based cryptographic algorithms SM9 -
Part 5. Parameter definition
ISSUED ON. MARCH 28, 2016
IMPLEMENTED ON. MARCH 28, 2016
Issued by. State Cryptography Administration
Table of Contents
Foreword ... 3
1 Scope .. 4
2 Normative references ... 4
3 Parameter definitions ... 4
Annex A (informative) Example of digital signature algorithm ... 8
Annex B (informative) Example of key exchange protocol ... 15
Annex C (informative) Example of key capsulation mechanism ... 30
Annex D (informative) Example of public key encryption algorithm ... 36
Foreword
GM/T 0044 “Identity-based cryptographic algorithms SM9” consists of five parts.
- Part 1. General;
- Part 2. Digital signature algorithm;
- Part 3. Key exchange protocol;
- Part 4. Key encapsulation mechanism and public key encryption algorithm;
- Part 5. Parameter definition.
This Part is Part 5 of GM/T 0044.
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.
This Part was proposed by and shall be under the jurisdiction of Code Industry
Standardization Technical Committee.
Main drafting organization of this Part. National Information Security
Engineering Center.
Main drafters of this Part. Chen Xiao, Ma Ning, Zhang Qingpo, Yuan Wengong,
Liu Ping, Li Zengxin, Wang Xuejin, Yang Hengliang, Xiong Ronghua, Ma Yanli,
Pu Yusan, Tang Ying, Sun Yisheng, An Xuan.
Identity-based cryptographic algorithms SM9 -
Part 5. Parameter definition
1 Scope
This Part of GM/T 0044 specifies the curve parameters of SM9 identity-based
cryptographic algorithm, and gives the example of digital signature algorithm,
key exchange protocol, key encapsulation mechanism and public key
encryption algorithm.
This Part is applicable to the verification of the correctness of each step in the
implementation of SM9 algorithm.
2 Normative references
The following referenced documents are indispensable for the application of
this document. For dated references, only the dated edition cited applies. For
undated references, the latest edition of the referenced document (including all
amendments) applies.
GM/T 0004-2012 SM3 cryptographic hash algorithm
GM/T 0002-2012 SM4 block cipher algorithm
GM/T 0044.1-2016 Identity-based cryptographic algorithms SM9 - Part 1.
General
GM/T 0044.2-2016 Identity-based cryptographic algorithms SM9 - Part 2.
Digital signature algorithm
GM/T 0044.3-2016 Identity-based cryptographic algorithms SM9 - Part 3.
Key exchange protocol
GM/T 0044.4-2016 Identity-based cryptographic algorithms SM9 - Part 4.
Key encapsulation mechanism and public key encryption algorithm
3 Parameter definitions
3.1 System parameters
This Part uses the 256-bit BN curve.
Annex A
(informative)
Example of digital signature algorithm
A.1 General requirements
This annex selects the cryptographic hash function given in GM/T 0004-2012.
The input is a message bit string with less than 264 in length. The output is a
hash value with 256 bits in length, denoted as H256 ( ).
In this annex, for all numbers in hexadecimal, the high bit is on the left and the
low bit is on the right.
In this annex, the message is ASCII encoded.
A.2 Digital signature and verification
Elliptic curve equation. y2 = x3 + b.
Base field characteristics q.
Equation parameter b. 05
Groups G1 and G2’s order N.
Cofactor cf. 1
Number of embeddings k. 12
Twisted curve parameter β. √െ2
Group G1’s generator P1 = (xP1, yP1).
coordinate xP1.
coordinate yP1.
Annex D
(informative)
Example of public key encryption algorithm
D.1 General requirements
This annex selects the cryptographic hash function given in GM/T 0004-2012.
The input is a message bit string with less than 264 in length. The output is a
hash value with 256 bits in length, denoted as H256 ( ).
This annex selects the block cipher function given in GM/T 0002-2012 as the
block cipher algorithm used for encryption. In this example, the block length is
128 bits, the filling method follows PKCS#5, and the work mode is ECB.
In this annex, for all numbers in hexadecimal, the high bit is on the left and the
low bit is on the right.
In this annex, the plaintext is ASCII encoded.
D.2 Public key encryption and decryption
Elliptic curve equation. y2 = x3 + b.
Base field characteristics q.
Equation parameter b. 05
Groups G1 and G2’s order N.
Cofactor cf. 1
Number of embeddings k. 12
Twisted curve parameter β. √െ2
Group G1’s generator P1 = (xP1, yP1).
coordinate xP1.