Protected Fair Secret Sharing Based Bivariate Asymmetric Polynomials in Satellite Network

Abstract

Verifiable secret sharing mainly solves the cheating behavior between malicious participants and the ground control center in the satellite network. The verification stage can verify the effectiveness of secret shares issued by the ground control center to each participant and verify the effectiveness of secret shares shown by participants. We use a lot of difficult assumptions based on mathematical problems in the verification stage, such as solving the difficult problem of the discrete logarithm, large integer prime factorization, and so on. Compared with other verifiable secret sharing schemes designed for difficult problems under the same security, the verifiable secret sharing scheme based on the Elliptic Curve Cryptography (ECC) system has the advantages of less computational overhead and shorter key. At present, the binary polynomial is a single secret scheme and cannot provide effective verification. Therefore, based on a Protected Verifiable Synchronous Multi Secret Sharing (PVS-MSS) scheme, this paper is designed based on bivariate asymmetric polynomials. The advanced verifiable attribute is introduced into the Protected Secret Sharing (PSS) scheme. This paper extends the protected synchronous multi-secret sharing scheme based on bivariate polynomial design. The ECC system constructs the security channel between the ground control center and participants and constructs the verification algorithm. Through the verification algorithm, any participant can verify the consistency and effectiveness of the secret shadow and secret share received from other participants or presented by the secret distribution center. Therefore, no additional key agreement protocol is required; participants do not need to negotiate the session key for encryption; the secret share polynomial can generate the session key between participants and speed up the secret reconstruction process. The verification stage has lower computational complexity than the verifiable scheme constructed by Rivest Shamir Adleman (RSA) and other encryption methods. Chinese Remainder Theorem (CRT) is used to update the secret shadow. The secret shadow does not need to be updated with the change of the scheme shared secret, and the public value update efficiency is higher. Reduce the complexity of sharing secret updates in a synchronous multi-secret sharing scheme.