Several Secret Sharing Schemes Based On Chinese Remainder Theorem

Secret sharing is an important subject in modern cryptography,and is one of significant methods to ensure information security.Secret sharing has been a hot topic of information security.The basic idea of secret sharing is that the secret is divided into different shares and different shares are sent to different participants,in which the participants of authorized set can recover the secret correctly,while participants of the unauthorized set can't obtain any information about the secret.Researchers utilize different mathematical tools to construct secret sharing,and also consider the requirements of verification,correctness and security.This thesis focuses on three Chinese Remainder Theorem(CRT)based secret sharing schemes: a secret redistribution scheme based on Chinese Remainder Theorem,a verifiable secret sharing scheme based on Chinese Remainder Theorem,and a weighted secret sharing scheme with special access structure based on general Chinese Remainder Theorem.Our main contributions are as follows.1)We propose a secret redistribution scheme based on Chinese Remainder Theorem.Our scheme is an extension of CRT-based secret sharing scheme in secret redistribution.The participants of qualified set are regarded as new dealers who redistribute their shares to all new participants.The linear property of CRT is used to design the secret redistribution and secret reconstruction.New participants are different from previous ones in our scheme.The authorized participants can reconstruct the secret correctly,and the proposed scheme is secure.2)We present a verifiable secret sharing scheme based on Chinese Remainder Theorem.The secret distribution and reconstruction are designed based on CRT.In distribution phase,the participants can check the validity of share from some public values,and this is an efficient way to verify the dishonest behavior of the dealer.Our scheme enjoys the good properties of less public values and lower computation through comparing with some related works.Furthermore,we also claim that our scheme is correct and secure.3)We design a weighted secret sharing scheme with special access structure based on generalized Chinese Remainder Theorem.There are two authorized sets of participants in our scheme,and all of them in these two set are required to work together to reconstruct the final secret.We implement the verifiable secret sharing schemes using generalized CRT and participant weights for all participants in first authorized set,and while we design the verifiable secret sharing schemes using interpolation polynomials and Feldman's verification scheme for all participants in second authorized set.At last,the final secret is obtained by adding the reconstructed secrets from these two sets.Compared with the related work,our scheme have the properties of shorter share,lower computational complexity,special access structure and verifiability.