An Algebraic-geometric Publicly Verifiable Multi-secret Sharing Scheme

Secret sharing was rst proposed independently by Shamir and Blakley in 1979. In most known schemes both the dealer and the players are supposed to be honest. However, in real world it is conceivable that some of them might attempt to cheat. To achieve security against cheating players or dealer, the concept of verifiable secret sharing (VSS) was introduced in 1985 by Chor, Goldwasser, Micali and Awerbuch. In CRYPTO 2006, Chen and Cramer pro-posed the-first secret sharing scheme based on algebraic geometry.In this thesis, we construct a new publicly verifiable multi-secret threshold scheme using algebraic curves with many rational points. The authentication is performed by employing the modi-fied Weil pairing on elliptic curves to prevent possible cheating of both dealers and participants. The security of our scheme is based on the difficulty to solve the elliptic curve discrete logarithm problem. Comparing with the schemes based on discrete logarithm prob-lem, for the same level of security, our scheme employs a much smaller elliptic curve group with a relative smaller key length which reduces the storage and transmission requirements.