Verifiable Secret Sharing Scheme

With the rapid development of computer communication technology and the diversification of information transmission methods,information security issues have become increasingly prominent.Secret sharing is one of the important means to enhance information security and improve data confidentiality.The secret sharing scheme is divided into two steps.The first step is secret distribution.The secret is divided into a plurality of shares containing secret information,which are held by members participating in the secret sharing,and the member cannot obtain the secret without other member shares.The second step is secret reconstruction.When the number of members participating in the recovery reaches the threshold,the secret of the custody can be obtained through a specific process.The verifiable secret sharing scheme can improve the security of the scheme in the presence of a distributor.It can verify the information in the reconstruction phase and guarantee the security of the secret during the verification process.Through studying many secret sharing schemes in the past to learn how these schemes can achieve share verification.Through continuous improvement schemes,a secret sharing scheme with low computational complexity and verifiable design is designed.Based on the binary symmetric polynomials,two schemes are designed,one is a scheme that can identify cheater,and one is a scheme without a trusted center that can verify the correctness of the share.The constructed secret sharing schemes use the symmetry of symmetric polynomials to verify the shares,reducing the secret shares and the information capacity used to verify the shares.By using the nature of the binary symmetric polynomial,each pair of participants can exchange a set of verification shares that are not related to the secret,effectively resisting the external attacker steals secret information.This paper focuses on the areas of verifiability,no trusted centers,and reduced capacity for share information.Using the verification information published in the secret distribution and secret reconstruction phases,participants can verify the share of other participants and the reconstructed secret information.This improves program security and prevent secret disclosure.