GM/T 0044: Evolution and historical versions
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Basic data | Standard ID | GM/T 0044-2016 (GM/T0044-2016) | | Description (Translated English) | See GM/T 0044.1-2016...GM/T 0044.5-2016 (SM9 identification cryptographic algorithm) | | Sector / Industry | Chinese Industry Standard (Recommended) | | Classification of Chinese Standard | L80 | | Date of Issue | 2016-03-28 | | Date of Implementation | 2016-03-28 | | Regulation (derived from) | Announcement of the State Password Bureau (No.30) | | Issuing agency(ies) | State Administration of Cryptography | GM/T 0044.1-2016: Identity-based cryptographic algorithms SM9 - Part 1: General---This is a DRAFT version for illustration, not a final translation. Full copy of true-PDF in English version (including equations, symbols, images, flow-chart, tables, and figures etc.) will be manually/carefully translated upon your order.
Identity-based cryptographic algorithms SM9-Part 1.General
ICS 35.040
L80
Record number. 55618-2016
People's Republic of China Password Industry Standard
SM9 identification password algorithm
Part 1.General
Part 1.General
Released on.2016-03-28
2016-03-28 Implementation
Issued by the National Cryptography Administration
Table of contents
Foreword Ⅰ
Introduction Ⅱ
1 Scope 1
2 Terms and definitions 1
3 Symbols and abbreviations 1
4 Finite fields and elliptic curves 2
4.1 Finite Field 2
4.2 Elliptic curve on a finite field 3
4.3 Elliptic Curve Group 4
4.4 Calculation of multiple points on elliptic curve 4
4.5 Verification of points on elliptic curve subgroups 4
4.6 Discrete logarithm problem 5
5 Bilinear pairing and safety curve 5
5.1 Bilinear pairing 5
5.2 Security 5
5.3 Embedding times and safety curve 6
6 Data types and conversion 6
6.1 Data Type 6
6.2 Data type conversion 6
7 System parameters and their verification 10
7.1 System parameters 10
7.2 Verification of system parameters 10
Appendix A (informative appendix) Background knowledge about elliptic curves 12
Appendix B (informative appendix) Calculation of bilinear pairs on elliptic curves 19
Appendix C (informative appendix) Number theory algorithm 26
References 32
Foreword
GM/T 0044 "SM9 Identification Password Algorithm" is divided into 5 parts.
---Part 1.General Provisions;
---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 1 of GM/T 0044.
This section was drafted in accordance with the rules given in GB/T 1.1-2009.
Please note that certain contents of this document may involve patents. The issuing agency of this document is not responsible for identifying these patents.
This part is proposed and managed by the Cryptographic Industry Standardization Technical Committee.
Drafting organizations of this section. National Information Security Engineering Technology Research Center, Shenzhen Aolian Information Security Technology Co., Ltd., Wuhan University, Shanghai
Hai Jiaotong University, Institute of Information Engineering, Chinese Academy of Sciences, Northern Institute of Information Technology.
The main drafters of this section. Chen Xiao, Cheng Chaohui, Ye Dingfeng, Hu Lei, Chen Jianhua, Lu Beike, Ji Qingguang, 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 cryptography system,
The user's private key is calculated by the Key Generation Center (KGC) based on the master key and the user ID, and the user's public key is uniquely confirmed by the user ID
Therefore, users do not need to guarantee the authenticity of their public keys through a third party. Compared with certificate-based public key cryptography, identification cryptography
The key management link in can be appropriately simplified.
In.1999, K. Ohgishi, R. Sakai, and M. Kasahara proposed in Japan to use elliptic curve pairing to construct logo-based
Key sharing scheme; In.2001, D. Boneh and M. Franklin, as well as R. Sakai, K. Ohgishi and M. Kasahara, etc. independently proposed
An elliptic curve pair is used to construct an identification public key encryption algorithm. These efforts have led to new developments in identification codes, and a number of
The identification cryptographic algorithms implemented by wire pairs include digital signature algorithms, key exchange protocols, key encapsulation mechanisms, and public key encryption algorithms.
The elliptic curve pair has a bilinear property. It establishes a connection between the cyclic subgroup of the elliptic curve and the multiplicative cyclic subgroup of the extended domain, and constructs
It has become bilinear DH, bilinear inverse DH, decision bilinear inverse DH, τ-bilinear inverse DH and τ-Gap-bilinear inverse DH, etc.
When the elliptic curve discrete logarithm problem and the extended domain discrete logarithm problem are equally difficult to solve, the elliptic curve pair can be used to construct safety and real
Now the identification password with both efficiency.
This part describes the necessary basic mathematical knowledge and related cryptographic techniques to help achieve the cryptographic requirements specified in other parts of this standard
mechanism.
SM9 identification password algorithm
Part 1.General
1 Scope
This part of GM/T 0044 describes the necessary basic mathematical knowledge and related cryptographic techniques to help realize other aspects of GM/T 0044.
The password mechanism stipulated by his various parts.
This section applies to the realization, application and detection of identification passwords in commercial cryptographic algorithms.
This section specifies the use of an elliptic curve on Fp (prime number p >2191).
2 Terms and definitions
The following terms and definitions apply to this document.
2.1
Identity
Information that can uniquely determine the identity of an entity. The identification should consist of information that the entity cannot deny, such as the entity’s identifiable name, electronic
Email, ID number, phone number, etc.
2.2
Master key
The key at the top of the hierarchy of identification cryptographic keys, including the master private key and the master public key. The master public key is public, and the master private key is owned by KGC
Keep it secret. KGC uses the master private key and the user's identity to generate the user's private key. In the identification password, the master private key is generally
The machine number generator is generated, and the master public key is generated by the master private key combined with system parameters.
In this section, the master key of the signature system is different from the master key of the encryption system. The digital signature algorithm belongs to the signature system, and its master key is
Signature master key, key exchange protocol, key encapsulation mechanism and public key encryption algorithm belong to the encryption system, and its master key is the encryption master key.
2.3
Key generation center; KGC
In the SM9 identification password, the trusted organization responsible for selecting system parameters, generating the master key and generating the user's private key.
3 Symbols and abbreviations
The following symbols and abbreviations apply to this document.
cf. The cofactor of the elliptic curve order relative to N.
cid. Curve identifier represented by one byte to distinguish the type of curve used.
DLP. Discrete logarithm problem on finite fields.
deg(f). The degree of polynomial f(x).
d1, d2.two factors of k.
E. An elliptic curve defined on a finite field.
ECDLP. Discrete logarithm problem of elliptic curve.
E(Fq). The set of all rational points (including the infinity point O) of the elliptic curve E on the finite field Fq.
E(Fq)[r]. The set of r-twist points on E(Fq) (ie, the r-th order twist subgroup on the curve E(Fq)).
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