Homomorphic cryptosystems based on subgroup membership problems

Authors:
Kristian Gjøsteen
Affiliations:
Department of Telematics, Norwegian University of Science and Technology, Trondheim, Norway
Venue:
Mycrypt'05 Proceedings of the 1st international conference on Progress in Cryptology in Malaysia
Year:
2005

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Abstract

We define an abstract subgroup membership problem, and derive a number of general results for subgroup membership problems. We define an homomorphic public key cryptosystem based essentially on a subgroup membership problem, and show that this abstract construction gives a uniform description of many famous cryptosystems, such as ElGamal, Goldwasser-Micali and Paillier. We show that the abstract theory gives new insights into older results, and allows us to derive new results.