Design Of New Commitment Schemes And Their Applications

In this thesis, we give a general method and design non-interactive non-malleable commitment schemes based on functions with special properties(q-one way group homomorphism). The scheme is proven secure. Our scheme needs less communication and is more general than most existing schemes. Furthermore, our scheme can be instantiated as concrete schemes based on number-theoretic assumptions.Next we consider the adversarial model in the internet environment. We analyze properties that commitment schemes should have especially in the bare public key model and give a formal definition. Under this definition, we design a concurrent equivocal commitment scheme and give a security proof. Our scheme is based on one-way function families. As one-way function families are the least necessary conditions in all modern cryptography primitive such as encryption, signature, key-exchange, zero-knowledge and so on, the assumption of our scheme is the weakest compared with that of the existing corresponding protocols. But our scheme need one more interaction and this would be the problem our future work focus on.As commitment schemes are basic tools of many cryptographic primitives, our two schemes can be widely used especially in internet environment.