Skip to product information
1 of 7

PayPal, credit cards. Download editable-PDF and invoice in 1 second!

GM/T 0044.2-2016 English PDF (GMT0044.2-2016)

GM/T 0044.2-2016 English PDF (GMT0044.2-2016)

Regular price $145.00 USD
Regular price Sale price $145.00 USD
Sale Sold out
Shipping calculated at checkout.
Quotation: In 1-minute, 24-hr self-service. Click here GM/T 0044.2-2016 to get it for Purchase Approval, Bank TT...

GM/T 0044.2-2016: Identity-based cryptographic algorithms SM9 - Part 2: Digital signature algorithm

This Part of GM/T 0044 specifies the identity-based 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.
GM/T 0044.2-2016
GM
CRYPTOGRAPHY INDUSTRY STANDARD
OF THE PEOPLE REPUBLIC OF CHINA
ICS 35.040
L 80
File No.. 55614-2016
Identity-based 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 ?€?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 2 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 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 Identity-Based Cryptography in 1984. In the identity-based 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 certificate-based public key cryptographic system, the key management in the identity-based 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 identity-based public key encryption algorithm constructed using elliptic curve pairing. These efforts led to a new development of identity-based cryptography. A number of identity-based 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 bi-linearity. 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, ??-bilinear inverse DH and ??-Gap- 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 identity-based cryptography with both safety and efficiency.
This Part describes the identity-based digital signature algorithm implemented using elliptic curve pairing.
Identity-based cryptographic algorithms
SM9 - Part 2. Digital signature algorithm
1 Scope
This Part of GM/T 0044 specifies the identity-based 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 0004-2012 SM3 cryptographic hash algorithm
GM/T 0044.1-2016 Identity-based 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.
?????€. ceiling function, the minimum integer not less than x. For example, ??7?€ = 7, ??8.3?€ = 9.
??????. floor function, the maximum integer not greater than x. For example, ??7?? = 7, ??8.3?? = 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.
??. twist curve parameter.
5 Algorithm parameters and auxiliary functions
5.1 General
This Part specifies an identity-based 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 ?? 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 ?? 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 0044.1-2016, 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 0044.1-2016, convert the data type of S' into point on the elliptic curve; according to the detail given in 4.5 of GM/T 0044.1-2016, verify whether S' ??? G1 is true, if not, the verification fails;
B3. Calculate element g = e (P1, Ppub-s) 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 + Ppub-s 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 0044.1-2016;
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...

View full details