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. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Gjøsteen, K. (2005). Homomorphic cryptosystems based on subgroup membership problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3715 LNCS, pp. 314–327). Springer Verlag. https://doi.org/10.1007/11554868_22
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