Research On Threshold Signature Schemes And Their Applications

With the development of the computer and the communication net,the information age began. It has brought out more and more convenience of the workand life of people, people can transmit quickly, inquire timely and communicateinteractively the information. However, the development of technique or attack alsobrought out the situation that the information may be wiretapped, distorted, or deleted indeliver of process, and information security is suffered to threaten seriously. It has led toa lot of unnecessary troubles for the work and life of people. So the digital signature isused as a kind of technique having function of the new integrity authentication,identification, non-repudiation and encryption.Secret sharing and threshold cryptography have played an important role in thearea of cryptography and information security. Since the concept of the secret sharingand group signature was proposed, many researchers have been studying the problem,some secure and efficient signature schemes have been presented. The applications ofthe secret sharing in fields such as threshold cryptography, key escrow, securemulti-party computation, electronic commerce, and electronic voting etc. have been putinto act.In this paper, a further research on the threshold signature schemes has donewhich aiming at the effectiveness of the schemes primarily. The main contributions areas follows:1. Double secret sharing is studied for the first time. A signature scheme isproposed. The feature is that any~t or more group members coming from all kinds oforganizations can cooperate to generate a valid group signature, a valid group signaturecannot be conspired to forge when one or more organizations don't agree to do so. Thenew scheme has the same security and more efficient performance when compared withthe relevant schemes.2. An improved signature scheme is proposed which based on discrete logarithmand the Wang. et. al signature scheme. No information of the former participants needschanging when a new participant joins.3. By means of the intractability of discrete logarithm in finite field, quadratic residue on some special conditions and Asmuth-Bloom threshold scheme, a forwardsecure threshold signature scheme with periodic renewing is presented. In our scheme,an adversary could not forge signature pertaining to the past even if she/he has gottenthe current signature key, that is, previous generated signature remain still valid.4. Based on practical problems, we present a proxy threshold signature scheme anda threshold signature scheme with proxy signers. The two schemes need littlercomputation in recovering secret and can increase or delete shares easily. When theoriginal signer is unable to perform his duties because of health or other reasons, proxysigner can perform the right standing for the original signer. Proxy signature has beenwidely applied in the network environment and a variety of proxy signature schemeshave been designed to satisfy the need of people. Threshold signature and proxysignature have been combined to produce the proxy threshold signature. Therefore, theresearch on proxy threshold signature system is very important.