Method for realizing secret sharing on non-Euclidean ring by using general coefficient discovery algorithm

Abstract

The invention discloses a method for realizing secret sharing on a non-Euclidean ring by using a general coefficient discovery (GCF) algorithm, and provides two GCF algorithms of augmented matrix transformation and a quotient domain to support a Chinese remainder theorem algorithm on the non-Euclidean ring so as to construct a corresponding secret sharing scheme. In the secret sharing scheme basedon the non-Euclidean ring, the modular polynomials of any two coprime can be easily generated, the problem of information leakage does not exist, the non-Euclidean ring method has extremely high efficiency, the efficiency of the secret distribution stage can be remarkably improved by improving the efficiency of generating the coprime modulus, and then the effect of the secret sharing scheme is improved. Besides, the non-Euclidean ring can be an infinite ring, and the length of the secret polynomial coefficient is uncertain, so that the secret sharing scheme on the non-Euclidean ring can theoretically ensure that the probability of secret recovery of the non-authorized set tends to 0, and the confidentiality of the scheme is ensured.

Description

technical field [0001] The invention relates to network and information security, in particular to a method for realizing a secret sharing scheme on a non-Euclidean ring by using a generalized coefficient finding algorithm (Generalized Coefficient Finding--GCF). Background technique [0002] 1. Euclidean algorithm and extended Euclidean algorithm [0003] The Euclidean algorithm, also known as the rolling and dividing method, is mainly used to solve the greatest common divisor of two positive integers. The greatest common divisor of positive integers a and b can be expressed as gcd(a,b). We can understand gcd(a,b) as the smallest positive linear combination of a and b. If we want to get the values ​​of integers u and v in the equation au+bv=gcd(a,b), we will use extended Eu Several algorithm (Extended Euclidean Algorithm-EEA). Among them, the time complexity of the Euclidean algorithm and the extended Euclidean algorithm are both O(logb), b<a, and thus have high efficie...

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Problems solved by technology

It is more difficult to generate large numbers, and it is more difficult to select a pairwise prime modulus, and the length of each participant's sub-secret is greater than the length of the secret, so the scheme cannot achieve ideal secret sharing

However, in the CRT-based secret sharing scheme on F[x], no deterministic algorithm has been found to generate any set of modulo polynomials that are mutually prime

[0057] However, the current CRT-based secret sharing schemes are all implemented for Euclidean rings (such as integer ring Z or polynomial ring F[x] with coefficients on the field), but cannot be implemented on non-Euclidean rings

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