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Two-party elliptic curve digital signature algorithm supporting key refreshing

An elliptic curve and key technology, applied in the field of cryptography, can solve problems such as key shares cannot be refreshed

Active Publication Date: 2020-06-02
FUDAN UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

However, the problem with this method is that the attacker can use the attack method to obtain one of the key shares first, and then use other methods to crack the other key share.
The biggest problem with this method is that the key share cannot be refreshed

Method used

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  • Two-party elliptic curve digital signature algorithm supporting key refreshing
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  • Two-party elliptic curve digital signature algorithm supporting key refreshing

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Embodiment Construction

[0065] The specific implementation of the present invention is mainly divided into two parts: the code is written using the Golang programming language, and the elliptic curve digital signature algorithm is implemented as a library, which can be directly embedded in the application for use.

[0066] Algorithm module:

[0067] The algorithm module is mainly responsible for the implementation of the two-party elliptic curve signature algorithm, and the three interfaces of key generation, signature, and key refresh can be implemented according to specific programming languages.

[0068] External service module:

[0069] The external service module refers to packaging the algorithm, and only opens three interfaces to users: the three functions of KeyGen(), Sign() and Refresh().

[0070] Appendix 1, Two-Party Key Generation Process

[0071]

[0072] Appendix 2 Two-Party Signature Process

[0073]

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Abstract

The invention belongs to the technical field of passwords, and particularly relates to a two-party elliptic curve signature algorithm supporting key refreshing. According to the algorithm, a functionof supporting key refreshing is added in a bipartite elliptic curve signature algorithm. In the secret key generation process of the two-party elliptic curve signature algorithm, two participants respectively generate a secret key share, a main secret key is composed of two secret key shares x1 and x2, and the main secret key x does not appear in the secret key generation and signature stage; theformula is as follows: x = x1 * x2mod q; the key refreshing process is participated by two parties, the key refreshing results are that the key shares x1 and x2 are changed into the key shares x '1 and x' 2, and the main key x is ensured to be unchanged; P1 and P2 are set as two parties, random numbers f1 and f2 are correspondingly generated, and finally respective calculation is performed to obtain x '1 and x' 2 through information communication of an interaction process; and after refreshing, x = x '1 * x' 2 = (x1 * f) * (x2 * f-1) mod q = x1 * x2 modq. The method provided by the invention provides high security for an elliptic curve signature algorithm.

Description

technical field [0001] The invention belongs to the technical field of encryption, and in particular relates to a two-party elliptic curve digital signature algorithm. Background technique [0002] In 1985, Miller and Koblitz proposed a public key cryptosystem based on elliptic curves, and the discrete logarithm problem (Elliptic Curve Discrete Logarithm Problem) based on elliptic curves was proved to be difficult to solve. Compared with RSA and ElGamal cryptosystems, the signature algorithm based on Elliptic Curve Cryptography (ECC) requires less key length to ensure the same security strength, making Elliptic Curve Cryptography more and more popular. ECDSA became a NIST standard in 2013. [0003] The signing process of ECDSA is as follows: [0004] 1. Use the agreed hash function to find the hash value z=HASH(m) for the original message, [0005] 2. Randomly select an integer value k∈[1,n-1], n is the order of the raw member, [0006] 3. Calculate the point (x 1 ,y 1...

Claims

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Application Information

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IPC IPC(8): H04L9/32H04L9/30H04L9/08
CPCH04L9/0891H04L9/3066H04L9/3252
Inventor 阚海斌张如意刘百祥李鸣吴小川
Owner FUDAN UNIV
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