Research On Secret Sharing Scheme Based On Bivariate Polynomial

Since the introduction of secret sharing,it has always been an important research direction of applied cryptography.Secret sharing can prevent authority cheating due to the singlepoint concentration of rights of secret managers,and the distributed management of secrets can effectively improve the security of important data and the robustness of the system.Secret sharing is not only an important solution for key management,but also provides theoretical support for secure multi-party computing and multi-party threshold signatures.It also has important applications in image and audio secret sharing.In recent years,in order to make secret sharing suitable for different application scenarios and improve the efficiency and security of sharing,secret sharing schemes based on various theories have emerged one after another.Among them,in order to reduce the complexity of additional key agreement between participants in the actual application of the secret sharing scheme,a protected secret sharing scheme based on a binary polynomial design has proposed.The protected feature means that the secret share polynomial obtained by the participants in the scheme can not only generate the secret share used to reconstruct the real shared secret,but also generate the session key between the two participants.It is used to ensure the security of information interaction between participants in the process of secret reconstruction.However,there are not many researches on protected secret sharing schemes,and the existing schemes have limitations and security problems.Therefore,according to different application scenarios and security requirements,this paper designs three secret sharing schemes based on binary polynomials on the premise of satisfying the protected characteristics.(1)Aiming at the limitation that the traditional secret sharing reconstruction process can only reconstruct a single secret.The shared secret set is hidden on the coefficients of the binary polynomial,and the protected synchronous multi-secret sharing scheme based on the binary asymmetric polynomial is constructed.According to the relationship between the number of shared secrets and the threshold,participants can reconstruct multiple secrets simultaneously in two different situations.Compared with the existing protected asynchronous multi-secret sharing scheme,the shared secret interval of this scheme is more flexible.(2)Aiming at the deception problem of malicious participants and secret distribution centers in the secret sharing process.Based on the scheme of SHEIKHI-GARJAN et al.,this paper introduces verifiable properties to the protected secret sharing scheme,which extends the protected synchronous multi-secret sharing scheme proposed in this paper.Using the Chinese remainder theorem to generate and update the secret shadow,reduce the complexity of updating the public value when the shared secret is updated in the synchronous multisecret sharing scheme.With elliptic curve cryptography,there is no need for a secure channel between the secret distribution center and the participants.Any participant verifies the consistency and validity of the secret shadow received from other participants or the secret share presented by the secret distribution center through the verification algorithm.(3)Aiming at the problem of deception in the process of secret reconstruction.A deception detection and recognition algorithm is introduced,combined with a bivariate symmetric polynomial to construct a protected fair secret sharing scheme.Participants reconstruct the secret according to an unknown constant round of secret reconstruction sequence,eliminate deceivers and ensure that all honest participants can complete the secret reconstruction fairly and not affected by any adversaries,and reconstruct the correct shared secret.This scheme has unconditional security,the deception detection and identification algorithm is not based on any cryptographic assumptions,and has low detection and identification overhead.Under the four standard attack models,through proof analysis,this scheme meets security and complete fairness.