Studies On UC Secure Multiparty Computation And Its Applications

Secure multi-party computation (MPC) can be defined as the problem of n players tocompute an agreed function of their inputs in a secure way, where security means guaranteeingthe correctness of the output as well as the privacy of the players'inputs, even when someplayers cheat. Concretely, we assume we have inputs x1,...,xn, where player i knows xi, andwe want to compute f(x1,...,xn) = (y1,...,yn) such that player i is guaranteed to learn yi,but can get nothing more than that.Secure Multiparty Computation protocol is an important area in cryptography. It's thebasis of many distributed cryptographic protocols such as threshold cryptosystems, electronicvoting and electronic auction, etc. In fact, almost all protocols in distributed environmentcan be viewed as a special case of secure multiparty computation. It is based on manybasic cryptographic protocols ( e.g. homomorphic encryption and zero-knowledge proof )andsome basic protocols in distributed computation ( e.g. oblivious transfer and broadcastprotocol ). Although Secure Multiparty Computation protocol is relatively more complexthan other cryptographic protocols, it has drawn many researchers and institutes's attentionin these years. We believe that the field of multiparty computations is today where publickey cryptography was ten years ago, namely an extremely powerful tool and rich theorywhose real life usage is at this time only beginning but will become in the future an integralpart of our computing reality.Some interesting topics in the currently researching of Secure Multiparty Computationare listed below.1. How to define Secure Multiparty Computation?2. To improve the e?ciency of general Secure Multiparty Compuation protocols. ManySecure Multiparty Computation protocols have large communication and computationcosts, which is not practical for real life.3. Developing new special protocol for special purpose.4. Researching in the applications of Secure Multiparty Computation, like ThresholdCryptosystem and Private Information Retrieval, etc. To sum up, the works and innovations of this thesis could be summarized as follows:We research the general secure multiparty computation and the definition of securemultiparty computation. We study a new paradigm (UC security) to design protocols,and presents some ideas for UC security.This thesis presents a non-committing encryption scheme based on quadratic residue.It is a solution to adaptive security of multiparty computation with non-erasing par-ties in the cryptographic model. The scheme is more e?cient than all previous non-committing encryption schemes. Furthermore, we give security proofs.We put forward a solution to secure threshold RSA cryptosystems in the adaptiveadversary model. Most protocols in the current literature for threshold cryptosystemswere secure only against static adversary, especially for threshold RSA which is harderto be distributed than discrete logarithm schemes due to the unknown order of RSAexponents. In this paper, we point out that Canetti's solution to RSA is not secure.Then we propose a simple e?cient adaptive secure RSA signature. And the proofs ofadaptive secure simulation is given.We present a new identity based signcryption scheme with public verifiability usingpairings over elliptic curves, and give a security proof about the original scheme in therandom oracle model. Furthermore, most studies about threshold signcryption in thecurrent literature do not take into account multi-sender system models and deal withmulti-sender threshold signcryption. Here, this thesis focuses on a multi-sender(t,n)identity based threshold sighcryption. Finally, through protocol emulation, we provethe scheme of threshold setting is secure as the original scheme. We conclude thatthe new original scheme is secure and more e?cient than Libert and Quisquater's one,and the threshold scheme is more e?cient than traditional signature-and-encryptionthreshold schemes.This thesis proposes a new simple e?cient electronic auction scheme based on quadraticresidue. Our scheme satisfies the basic security requirements for a sealed-bid auctionsystem.