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Method and system for collaborative generation of numbers containing secrets based on secret dynamic sharing

A dynamic sharing and secret technology, applied in the field of cryptography, can solve the problems of complex collaborative computing process, difficult calculation results, and difficult secrets.

Active Publication Date: 2020-10-02
WUHAN UNIV OF TECH
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

However, in the actual process, it is not easy to achieve the above possible or expected calculation results without revealing the secrets of the two devices
Through further analysis, it can be found that the existing technology adopts the method of static sharing (sharing) of the secret d, that is, the secret share of d shared by the two devices remains unchanged, because the secret of the secret d shared by the two devices Shares are static, making it difficult to ensure that each device's individual secrets are not leaked during the calculation process, resulting in a complex collaborative calculation process

Method used

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Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0094] This embodiment relates to secret dynamic sharing method 1 of the present invention. This embodiment includes two devices called the first device and the second device; in this embodiment, d is an integer secret that is unknown to both devices in the interval [1,n-1] and needs to be shared (shared) , n is a prime number; pre-calculated with c=E((a 1 d) mod n), where E( ) represents the encryption operation of additive homomorphic encryption using the homomorphic encryption public key of the second device, a 1 is an integer in the interval [1,n-1]; here, a 1 is the secret of the first device or is not the secret of the first device; if a 1 If it is not a secret belonging to the first device in the interval [1,n-1], then c is saved by the first device as a secret;

[0095] The two devices of this embodiment are cooperatively calculated as follows to obtain the satisfying relation d 0 (d 1 +d 2 Integer secret d of )modn=d 0 、d 1 、d 2 , where d 0 is an integer sec...

Embodiment 2

[0111] Embodiment 2 is based on Embodiment 1 and implements method 1 of collaborative generation of numbers including secrets of the present invention.

[0112] On the basis of Embodiment 1, the first device has an integer secret w randomly selected in [1,n-1] 1, or have an integer secret w computed from randomly selected integer secrets in [1,n-1] 1 ;The second device has an integer secret w randomly selected in [1,n-1] 2 , or have an integer secret w computed from randomly selected integer secrets in [1,n-1] 2 ; The two devices cooperatively generate a , containing the secret w, as follows: 1 、w 2 and the number of d u=(w 1 w 2 (z+rd))mod n, where z and r are non-secret integers in [1,n-1]:

[0113] First, the two devices calculate the integer secret d according to the secret dynamic sharing method one 0 、d 1 、d 2 ;

[0114] Afterwards, the first means calculates u 1 =((d 0 ) -1 z+rd 1 ) mod n,w 0 =(d 0 w 1 ) mod n, where (d 0 ) -1 is d 0 The modulo n mul...

Embodiment 3

[0126] The difference between this embodiment and embodiment 2 is that u=(w is calculated by the first device 0 u 2 ) mod n (of course w 0 not disclosed), and the first device does not disclose the calculated u, and at w 1 When is an integer constant, d cannot be calculated from the public data calculated by u, and the confidential data calculated by d cannot be calculated from the public data calculated by u. Therefore, in this embodiment, w 1 The value is an integer constant; here w 1 is an integer constant including w 1 is a secret integer constant or a non-secret integer constant (where the non-secret integer constant includes the case of the constant 1).

[0127] A specific application of this embodiment is to realize collaborative generation of SM9 signature private key based on secret sharing.

[0128] At this time, two private key generators, the first and second private key generators, respectively correspond to the first and second devices of the present inventi...

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Abstract

The invention provides a secret dynamic sharing-based cooperative generation method and system for a secret-containing number. Two devices dynamically calculate by utilizing homomorphic encryption toobtain d0, d1 and d2 satisfying the relationship d0 (d1 + d2) mod n = d or (d1 + d0d2) mod n = d; wherein d is an integer secret in [1, n-1], d0 is an integer secret of the first device in [1, n-1], d1 is an integer secret of the first device in [0, n-1], and d2 is an integer secret of the second device in [0, n-1]; the two devices use d0, d1 and d2 for cooperative calculation to obtain u = (w1w2(z + rd)) mod n (corresponding to d0 (d1 + d2) mod n = d) or u = (w1w2z + rd) mod n (corresponding to (d1 + d0d2) mod n = d); wherein w1 and w2 are integer secrets randomly selected by the first device and the second device in [1, n-1] or integers calculated by random integers, and r and z are non-confidential integers.

Description

technical field [0001] The invention belongs to the technical field of encryption, in particular to a secret dynamic sharing method and a method and system for synergistically generating numbers containing secrets based on the method. Background technique [0002] In the application of cryptographic technology, due to application requirements, such as the need for private key security protection, cryptographic operations based on secret sharing are often required, such as ECDSA (Elliptic Curve Digital Signature) digital signature generation based on secret sharing, SM2 ellipse based on secret sharing Curve digital signature generation, SM9 elliptic curve digital signature generation based on secret sharing, collaborative generation of SM9 identification private key based on secret sharing, etc. Below are some specific examples (of course not all). [0003] 1. Collaborative generation of ECDSA digital signature [0004] Suppose G is the base point of the elliptic curve poin...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): H04L9/08H04L9/00
CPCH04L9/008H04L9/085
Inventor 龙毅宏
Owner WUHAN UNIV OF TECH
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