Secret Sharing and Application of Secret Sharing in Proxy Signature
|Keywords||Information Security Cryptography Secret sharing Digital signature|
The secret sharing is an important part of the cryptography protocol.In 1979,Shamir and Blakley first developed the concepts of the (t , n )threshold secret sharing (SS) scheme.Proxy signatures are signature schemes in which an original signer delegates her signing capability to a proxy signer, and then the proxy signer creates a proxy signature on behalf of the original signer. When a receiver verifies a proxy signature, he can verify both the signature itself and original signer’s agreement together.we choose the secret sharing and proxy signature as our priority research areas. The main contributions of this paper are as follows:1. A new verifiable multi-secret sharing scheme based on the discrete logarithm. To overcome the drawbacks of YCH scheme, we proposed a verifiable threshold secret sharing scheme based on the discrete logarithm. The new scheme has the following properties: (1) the scheme can resist to the cheating, no matter to the dealer or to the participants; (2) the scheme does not need a security channel, this property ensure that our scheme can be used in the system (eg. Current network disk) where security channel is not existed; (3) we just need construct a Lagrange interpolation polynomials to recover several secrets synchronously, this improvement solves the drawbacks of YCH scheme.2. A novel exchangeable secret sharing scheme. To solve the problem that sub-secret can be distributed on the open channel, we design a new secret sharing scheme based on the exchangeability of modular exponentiation function. The security of this scheme is based on the intractability discrete logarithm problem. When recovering the secret, the system does not need all the participants being on line At the same time, the sub-secret does not need security channel to distribute.3. A proxy signature scheme with forward secrecy property. Aiming at the flaws in WCF scheme, an improved forward secure proxy signature scheme was proposed. The new scheme proposed an evolution on proxy signer’s key, under the strong RSA assumption and Diffie-Hellman problem, the new scheme was truly forward secure. A forward-secure proxy multi-signature scheme was proposed on the basis of the forward-security and proxy multi-signature schemes. The new scheme satisfies securities of general proxy multi-signature schemes and forward-security.