A secure threshold Paillier proxy signature scheme

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-fledgedsecure digital world,secure implementations of more commercial activity primitives are required. In this paper,we present asecure proxy signature scheme and its threshold version based on the homomorphic Paillier cryptosystem,which can be used inmany e-commerce applications such as e-voting,e-bidding/auction,and privacy-preserving data mining. These two schemes areexistentially unforgeable against chosen-message attacks and chosen-warrant attacks in the random oracle model. Although it isbased on factoring,the threshold Paillier proxy scheme operates without requiring any trusted dealer or combiner. Thus,these twoschemes are practical for integration in modularized secure multi-party protocols.