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SM9 digital signature collaborative generation method and system by means of intermediate parameters

A technology of digital signature and intermediate parameters, applied in the field of information security

Active Publication Date: 2019-10-01
WUHAN UNIV OF TECH
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

Although the probability of this situation is extremely small, it is still possible, especially when ri is difficult to achieve a truly random selection

Method used

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Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0118] In this embodiment, there are two devices labeled No. 1 and No. 2. The No. 1 device stores the integer secret c in the interval [1, n-1] 1 , the No. 2 device saves the integer secret c in the interval [1,n-1] 2 , where n is the group G in the SM9 cryptographic algorithm 1 , G 2 , G T The order (is a prime number);

[0119] (initialization phase) precomputed with:

[0120] P A =[c -1 ]d A , where d A Identify the private key for the user's SM9, c -1 is the modulo n multiplicative inverse of c, c=(c 1 c 2 ) mod n is an integer secret that is not kept by both devices;

[0121] P U =[u]d A , where u is an integer secret in the interval [1,n-1] that neither device holds;

[0122] u and c -1 Not necessarily different from each other (the two are different or the same);

[0123] g U =g ^ u, wherein ^ is exponentiation (exponentiation is carried out to the element in front of ^, and the number of times of exponentiation is behind ^), g=e (P 1 ,P pub ), P 1 f...

Embodiment 2

[0143] The difference between embodiment 2 and embodiment 1 is that c 1 It is non-secret, its value is 1 or other integers in [1,n-1] (other integers selected subjectively or randomly in [1,n-1]), P A The non-disclosure is kept as a secret by No. 1 device (of course if P U =P A , then P U is also not disclosed, and is kept as a secret by device No. 1), and P B ≠P A , other unchanged.

Embodiment 3

[0145] In this embodiment, there are m devices respectively labeled No. 1, No. 2, ..., to No. m devices, m≥2, and the device No. i stores an integer secret c in the interval [1, n-1] i , i=1,...,m, where n is the group G in the SM9 cryptographic algorithm 1 , G 2 , G T The order (is a prime number);

[0146] (initialization phase) precomputed with:

[0147] P A =[c -1 ]d A , where d A Identify the private key for the user's SM9, c -1 is the modulo n multiplicative inverse of c, c=(c 1 c 2 …c m )modn is an integer secret that m devices do not save;

[0148] P U =[u]d A , where u is an integer secret in the interval [1,n-1] that is not saved by m devices;

[0149] u and c -1 Not necessarily different from each other (the two are different or the same);

[0150] g U =g ^ u, wherein ^ is exponentiation (exponentiation is carried out to the element in front of ^, and the number of times of exponentiation is behind ^), g=e (P 1 ,P pub ), P 1 for G 1 generator in...

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Abstract

An SM9 digital signature generation method comprises the following steps that: devices labeled from first to mth are respectively provided with integer secret ci in [1,n-1], n is the order of the SM9group, i is equal to 1,...,m, and m is greater than or equal to 2; PA=[(c1c2...Cm)<-1>]dA, PU is equal to [u]dA, dA is a private key of a user, and u is an integer secret in [1,n-1]; wherein PB is a non-zero element in the group G1; during message signing, w=gU^(r1r2...rm), h=H2(M||w,n) and T=[r1r2...rm]PU+[-F(z1,...,zm)]PB, V=[F(z1,..., zm)]PB+[-h<c1c2...cm]PA, F(z1,z2,...,zm) and z1a2a3...am+z2a3...am+...+zm(mod n) are congruent, and S is equal to T+V; and (h,S) is the digital signature of the dA to the message M.

Description

technical field [0001] The invention belongs to the technical field of information security, in particular to a SM9 digital signature collaborative generation method and system by means of intermediate parameters. Background technique [0002] SM9 is an identification cryptographic algorithm based on bilinear mapping (pairing operation) promulgated by the State Cryptography Administration, where the bilinear mapping (pairing operation) is: [0003] e:G 1 ×G 2 →G T , where G 1 , G 2 is the additive cyclic group, G T is a multiplicative cyclic group, G 1 , G 2 , G T The order of is a prime number n (Note: In the SM9 specification, G 1 , G 2 , G T The order used is a capital letter N, and this patent application uses a lowercase n), that is, if P, Q, and R are respectively G 1 , G 2 element in , then e(P,Q) is G T elements in , and: [0004] e(P+R,Q)=e(P,Q)e(R,Q), [0005] e(P,Q+R)=e(P,Q)e(P,R), [0006] e(aP,bQ)=e(P,Q) ab . [0007] Based on the SM9 cryptogr...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H04L9/32
CPCH04L9/3236H04L9/3247
Inventor 龙毅宏
Owner WUHAN UNIV OF TECH