Private Information Retrieval Based on the Subgroup Membership Problem
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
A Public Key Cryptosystem Based on the Subgroup Membership Problem
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Concrete chosen-ciphertext secure encryption from subgroup membership problems
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SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
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Designs, Codes and Cryptography
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We define and discuss symmetric subgroup membershipproblems and their properties, including a relation to the Decision Diffie-Hellman problem. We modify the Cramer-Shoup framework, so that we can derive a chosen ciphertext secure cryptosystem in the standard model from symmetric subgroup membership problems. We also discuss how chosen ciphertext secure hybrid cryptosystems based on a symmetric subgroup membership can be constructed in the standard model, giving a very efficient cryptosystem whose security relies solely on the symmetric subgroup membership problem.