Contribution to privacy-preserving cryptographic techniques

Digital signatures are fundamental cryptographic primitives. They are useful as a stand-alone application and building blocks of complex cryptographic systems. Accumulators are another useful cryptographic primitive which provide a way to combine a set of values into one short value. They are useful in improving efficiency of cryptographic systems. In particular, these two primitives are key components in privacy-preserving cryptographic systems. In this thesis, we study the use of digital signatures and accumulators in cryptographic applications. We design digital signature schemes and accumulators with different features that are suitable for a wide range of applications. We are interested in privacy-preserving cryptographic applications including anonymous electronic cash systems, anonymous authentication schemes and anonymous credential systems. We construct three different digital signature schemes, each with distinctive features. We also propose two novel constructions of accumulators. Based on our signature schemes and accumulators, we design two compact electronic cash schemes and a divisible electronic cash scheme. All our schemes are truly anonymous, meaning that privacy of the users is well-protected. We also explore other applications of our newly proposed signatures and accumulators. Specifically, we give a construction of k-times anonymous authentication schemes and attribute-based anonymous credential systems. During the course of the development of the thesis, we generalise existing techniques of zero-knowledge proof-of-knowledge protocol of double-discrete logarithms into zero-knowledge proof-of-knowledge protocol of representation of a committed value. Our protocol is compatible with existing zero-knowledge proof-of-knowledge protocols that demonstrate relationship amongst discrete logarithms. We believe that this protocol, together with the newly introduced primitives, are of independent interest.