As e-commerce applications and the underlying public key infrastructure have become more popular over time, many digital mechanisms emulating traditional business activities have been developed and deployed. To build a full-fledged secure digital world, secure implementations of more commercial activity primitives are required. In this paper, we present a secure proxy signature scheme and its threshold version based on the homomorphic Paillier cryptosystem, which can be used in many e-commerce applications such as e-voting, e-bidding/auction, and privacy-preserving data mining. These two schemes are existentially unforgeable against chosen-message attacks and chosen-warrant attacks in the random oracle model. Although it is based on factoring, the threshold Paillier proxy scheme operates without requiring any trusted dealer or combiner. Thus, these two schemes are practical for integration in modularized secure multi-party protocols.

关键词： Paillier proxy signature,  Threshold scheme,  Secure multi-party protocols,  Cryptographic primitives