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SM9 digital signature collaborative generation method and system with product r parameter

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

Active Publication Date: 2021-01-08
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

[0104] This embodiment concerns two devices designated No. 1 and No. 2, respectively.

[0105] During the initialization phase, knowing d A The device randomly selects an integer c and an integer b in [1,n-1], and calculates P A =[c -1 ]d A , P B =[b]d A , g B =g^(bc); c is kept as a secret by No. 1 device, P A It is kept as a secret by the No. 2 device; b, d A Destroy;P B and g B Used by the device that needs to be used.

[0106] here to know d A The device is one of the No. 1 and No. 2 devices, or a device other than the two devices (such as an identification private key generation system, other key service systems).

[0107] When it is necessary to use the user's SM9 identification private key d A When performing a digital signature on the message M, the two devices generate a digital signature on the message M according to the scheme 1 of the aforementioned SM9 digital signature collaborative generation method.

Embodiment 2

[0109] This embodiment concerns two devices designated No. 1 and No. 2, respectively.

[0110] During the initialization phase, knowing d A The device randomly selects an integer c and an integer b in [1,n-1], and calculates P A =[c -1 ]d A , P B =[b]d A , g B = g^b; P A It is kept as a secret by No. 1 device, c is kept as a secret by No. 2 device; b, d A Destroy;P B and g B Used by the device that needs to be used.

[0111] here to know d A The device is one of the No. 1 and No. 2 devices, or a device other than the two devices (such as an identification private key generation system, other key service systems).

[0112] When it is necessary to use the user's SM9 identification private key d A When digitally signing the message M, the two devices generate a digital signature for the message M according to the second scheme of the aforementioned SM9 digital signature collaborative generation method.

Embodiment 3

[0114] This embodiment concerns two devices designated No. 1 and No. 2, respectively.

[0115] During the initialization phase, knowing d A The device randomly selects an integer c and an integer b in [1,n-1], and calculates P B =[c -1 b]d A , g B =g^b;

[0116] After that, randomly select two integers c in [1,n-1] 1 、c 2 and (c 1 +c 2 )mod n≠0, then calculate d A1 =[c 1 (c 1 +c 2 ) -1 ]d A , d A2 =[c 2 (c 1 +c 2 ) -1 ]d A , where (c 1 +c 2 ) -1 is (c 1 +c 2 ) modulo n multiplicative inverse;

[0117] or, know d A The device randomly selects an integer t in [2,n-1], and then calculates d A1 =[t]d A , d A2 = d A -d A1 ;

[0118] or, know d A The device randomly selects an integer t in [1,n-1], and then calculates d A1 =[t]P 1 , d A2 = d A -d A1 , where P 1 is the group G in the SM9 bilinear map 1 generator of ; if d A2 is zero, then reselect t and recalculate d A1 、d A2 , until d A2 not zero;

[0119] calculated d A1 、d A2 After th...

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PUM

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Abstract

The invention relates to an SM9 digital signature generation method, which comprises the following steps: a device 1 having an integer secret c in [1, n-1], and n being an order of an SM9 group; the device 2 having a secret PA = [c-1] dA, and dA being a user private key; calculating pB = [b] dA, gB = g^(bc) in advance, b being an integer secret in [1, n-1] which is unknown to the two devices, andg = e (P1, Ppub); when the message M needs to be signed by dA, the two devices calculating w = gB ^ (r1r2), and r1 and r2 being integers randomly selected from [1, n-1] by the devices 1 and 2; calculating h = H2 (M | | w, n); the device 1 calculating S1 = [r1] PB; the device 2 calculating S2 = [r2] S1 + [-h] PA; and the device 1 calculating S = [c] S2, then verifying the validity of (h, S) by using the user identifier and the message M, and if the validity is valid, the (h, S) being a digital signature for the message M.

Description

technical field [0001] The invention belongs to the technical field of information security, in particular to an SM9 digital signature collaborative generation method and system with a product r parameter. 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 cryptographic al...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): H04L9/32H04L9/08
CPCH04L9/0861H04L9/3247
Inventor 龙毅宏
Owner WUHAN UNIV OF TECH