Homomorphic Commitment Schemes Based on Bilinear Groups

Commitment scheme is one of the fundamental and useful cryptographic primitives; it has found applications to a wide range of security mechanisms: digital signature schemes, electronic payment systems, zero-knowledge protocols, secure multiparty function evaluation protocols, and so on. Therefore, commitment has received extensive study in the literature. From the perspective of design approach, many of the known and efficient constructions of commitment schemes fall into the paradigm of q-one-way group homomorphism. Though effective and fairly general, q-one-wayness is a strong requirement so that when one tries to instantiate it, the choices of algebraic structures turn out to be limited; hence, it is an important topic to find alternative to the construction of commitment schemes of various properties. In this paper, using bilinear groups of composite order, a perfect hiding trapdoor commitment scheme is constructed for the first time, which is provably computational binding under the subgroup decision assumption. A dual construction of unconditional binding commitment scheme is also presented, which is proven to be computational hiding under the same intractability assumption. These proposals thus give alternative approach to constructing commitment schemes. Moreover, due to the bilinear maps associated with the bilinear groups, the proposed commitment schemes demonstrate unique multiplicative homomorphic property.