Construction Of Secret Sharing Based On Polynomials And Its Extended Application Research

Secret Sharing(SS)is an essential technology in cryptography.This thesis focuses on the research of SS schemes based on the Chinese Remainder Theorem(CRT).The existing SS schemes based on CRT have the following two problems:(1)The construc-tion of the scheme is complicated,and it is difficult for the dealer to choose the modulus;(2)The information rate of the scheme is low,thus the cost of sharing a secret is a little high.Based on the(t,n)SS scheme proposed by Ning,we research the unsolved prob-lems in Ning's scheme.We propose two SS schemes and uses practical applications as the background to expand the schemes in this thesis.The main contributions are as follows:(1)An ideal SS scheme based on coprime polynomials is proposed.In this scheme,the dealer can directly generate coprime modular polynomials,which can improve the efficiency and practicability of SS.The complexity of generating n coprime modular polynomials is reduced from O(nd3logdlogp)to O(n)in this scheme.This scheme is an ideal SS scheme,the com-biner of this scheme cannot obtain any additional information related to the secret when he obtains less than t shares.And the length of the secret is equal to the length of the share,which means that this scheme has the highest information rate among the SS schemes.(2)This thesis combines the actual application scenarios and applies the ideal SS scheme based on coprime polynomialS,which is effective for the SS problem of the hierarchical access structure and the virtual KGC(Key Generation Center)construction problem in the large-scale Internet of Things scenario.(3)A common factor-based(t,n)SS scheme is proposed,which can resist eaves-dropping attacks and tampering attacks to a certain extent.This scheme is based on a coprime polynomial,sharing a common factor among all the participants in the SS scheme.This common factor can add the following func-tions to the SS scheme:(1)In the reconstruction phase,the common factor can provide a verification function after receiving the share,and the shareholder can verify whether the received message is correct by comparing the received message with the public in-formation.(2)This common factor can be used to construct a security channel between shareholders and the combiner to ensure that the share will not be tampered with by the attacker during the transmission process.Therefore,the scheme can resist eavesdrop-ping attacks and tampering attacks by Outsiders,and improves the security of the SS scheme without greatly reducing the efficiency.