GM/T 0044.22016 (GM/T0044.22016, GMT 0044.22016, GMT0044.22016)
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Identitybased cryptographic algorithms SM9  Part 2: Digital signature algorithm
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GM/T 0044.22016

Standards related to: GM/T 0044.22016
Standard ID  GM/T 0044.22016 (GM/T0044.22016)  Description (Translated English)  Identitybased cryptographic algorithms SM9  Part 2: Digital signature algorithm  Sector / Industry  Chinese Industry Standard (Recommended)  Classification of Chinese Standard  L80  Word Count Estimation  11,190  Date of Issue  20160328  Date of Implementation  20160328  Regulation (derived from)  Industry Standard Record Announcement 2016 No.10 (No.202) 
GM/T 0044.22016
GM
CRYPTOGRAPHY INDUSTRY STANDARD
OF THE PEOPLE’S REPUBLIC OF CHINA
ICS 35.040
L 80
File No.. 556142016
Identitybased cryptographic algorithms
SM9  Part 2. Digital signature algorithm
ISSUED ON. MARCH 28, 2016
IMPLEMENTED ON. MARCH 28, 2016
Issued by. State Cryptography Administration
Table of Contents
Foreword ... 3
Introduction .. 4
1 Scope .. 5
2 Normative references ... 5
3 Terms and definitions ... 5
4 Symbols ... 6
5 Algorithm parameters and auxiliary functions ... 8
5.1 General ... 8
5.2 System parameter group ... 8
5.3 Generation of system signature master key and user signature key ... 9
5.4 Auxiliary functions ... 9
6 Digital signature generation algorithm and flow .. 11
6.1 Digital signature generation algorithm ... 11
6.2 Digital signature generation algorithm flow ... 12
7 Digital signature verification algorithm and flow .. 13
7.1 Digital signature verification algorithm ... 13
7.2 Digital signature verification algorithm flow ... 13
Foreword
GM/T 0044 “Identitybased 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 2 of GM/T 0044.
This Part was drafted in accordance with the rules given in GB/T 1.12009.
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 organizations of this Part. National Information Security
Engineering Center, Shenzhen Olym Information Security Technology Co., Ltd.,
Wuhan University, Shanghai Jiao Tong University, Institute of Information
Engineering of Chinese Academy of Sciences, North Institute of Information
Technology.
Main drafters of this Part. Chen Xiao, Cheng Zhaohui, Ye Dingfeng, Hu Lei,
Chen Jianhua, Lu Beike, Ji Qinguang, Cao Zhenfu, Yuan Wengong, Liu Ping,
Ma Ning, Yuan Feng, Li Zengxin, Wang Xuejin, Yang Hengliang, Zhang Qingpo,
Ma Yanli, Pu Yusan, Tang Ying, Sun Yisheng, An Xuan.
Introduction
A. Shamir proposed the concept of IdentityBased Cryptography in 1984. In the
identitybased cryptographic system, the user’s private key is calculated by the
key generation center (KGC) based on the master key and the user identity.
The user's public key is uniquely identified by the user identity so that the user
does not need to guarantee the authenticity of his public key through a third
party. Compared with certificatebased public key cryptographic system, the
key management in the identitybased cryptographic system may be properly
simplified.
In 1999, K. Ohgishi, R. Sakai and M. Kasahara proposed in Japan an identity
based key sharing scheme constructed using elliptic curve pairing. In 2001, D.
Boneh and M. Franklin, as well as R. Sakai, K. Ohgishi and M. Kasahara, et al.
independently proposed the identitybased public key encryption algorithm
constructed using elliptic curve pairing. These efforts led to a new development
of identitybased cryptography. A number of identitybased cryptographic
algorithms implemented using elliptic curve pairing have emerged, such as
digital signature algorithm, key exchange protocol, key encapsulation
mechanism and public key encryption algorithm.
Elliptic curve pairing has the property of bilinearity. It establishes a relationship
between cyclic subgroups of elliptic curve and multiplicative cyclic subgroups
of extended field, and forms difficult problems such as bilinear DH, bilinear
inverse DH, deterministic bilinear inverse DH, τbilinear inverse DH and τGap
bilinear inverse DH. When elliptic curve discrete logarithm problem and
extended field discrete logarithm problem are equally difficult to solve, it may
use elliptical curve pairing to construct identitybased cryptography with both
safety and efficiency.
This Part describes the identitybased digital signature algorithm implemented
using elliptic curve pairing.
Identitybased cryptographic algorithms
SM9  Part 2. Digital signature algorithm
1 Scope
This Part of GM/T 0044 specifies the identitybased digital signature algorithm
implemented using elliptic curve pairing, including digital signature generation
algorithm and verification algorithm, and gives digital signature and verification
algorithm and their corresponding flows.
This Part is applicable for recipients to verify the integrity of date and the identity
of date sender through the signer’s identity, and for third parties to determine
the authenticity of the signature and the signed data.
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 00042012 SM3 cryptographic hash algorithm
GM/T 0044.12016 Identitybased cryptographic algorithms SM9  Part 1.
General
3 Terms and definitions
For the purpose of this document, the following terms and definitions apply.
3.1
message
A bit string of any finite length.
3.2
signed message
A set of data elements consisting of a message and a digitally signed portion of
< P>. looping group generated by element P.
[u]P. u times element P in addition group G1, G2.
ڿݔۀ. ceiling function, the minimum integer not less than x. For example, ڿ7ۀ =
7, ڿ8.3ۀ = 9.
ہݔۂ. floor function, the maximum integer not greater than x. For example, ہ7ۂ =
7, ہ8.3ۂ = 8.
x II y. concatenation of x and y; x and y are bit strings or byte strings.
[x, y]. a set of integers not less than x and not more than y.
β. twist curve parameter.
5 Algorithm parameters and auxiliary functions
5.1 General
This Part specifies an identitybased digital signature algorithm implemented
using elliptic curve pairing. The signer of this algorithm holds an identity and a
corresponding signature private key, which is generated by the key generation
center through the combination of signature master private key and signer's
identity. The signer generates a digital signature of the data with its own
signature private key, and the verifier verifies the reliability of the signature with
the signer's identity.
Before the signature generation and verification process, the message to be
signed M and the message to be verified M’ are compressed by cryptographic
hash function.
5.2 System parameter group
The system parameter group consists of curve identifier cid; parameters of
elliptic curve base field Fq; parameters a and b of elliptic curve equation;
parameter β of twist curve (if the lower 4 bits of cid are 2); prime factor N of
curve order and remaining factor cf relative to N; number of embedding times
of curve E (Fq) relative to N; generator P1 of N order cyclic subgroup G1 of E
(Fqd1) (d1 divides k); generator P2 of N order cyclic subgroup G2 of E (Fqd2) (d2
divides k); identifier eid of bilinear pairing e; homomorphism map ψ of (options)
G2 to G1.
The range of the bilinear pairing e is N order multiplicative cyclic group GT.
For a detailed description of system parameters and their verification, see
7 Digital signature verification algorithm and flow
7.1 Digital signature verification algorithm
In order to verify the received message M' and its digital signature (h', S'), the
user B as the verifier shall implement the following calculation steps.
B1. According to the details given in 6.2.3 of GM/T 0044.12016, convert the
data type of h' into integer, and verify whether h' ∈ [1, N  1] is true, if not,
the verification fails;
B2. According to the details given in 6.2.9 of GM/T 0044.12016, convert the
data type of S' into point on the elliptic curve; according to the detail given
in 4.5 of GM/T 0044.12016, verify whether S' ∈ G1 is true, if not, the
verification fails;
B3. Calculate element g = e (P1, Ppubs) in group GT;
B4. Calculate element t = gh' in group GT;
B5. Calculate integer h1 = H1 (IDA II hid, N);
B6. Calculate element P = [h1] P2 + Ppubs in group G2;
B7. Calculate element u = e (S', P) in group GT;
B8. Calculate element w' = u • t in group GT; and convert the data type of w'
into the bit string according to the details given in 6.2.6 and 6.2.5 of GM/T
0044.12016;
B9. Calculate the integer h2 = H2 (M' II w', N), verify if h2 = h' is true, if yes, pass
the verification; otherwise, the verification fails.
7.2 Digital si...
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