Abstract
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.
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Gjøsteen, K. (2005). Symmetric Subgroup Membership Problems. In: Vaudenay, S. (eds) Public Key Cryptography - PKC 2005. PKC 2005. Lecture Notes in Computer Science, vol 3386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30580-4_8
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DOI: https://doi.org/10.1007/978-3-540-30580-4_8
Publisher Name: Springer, Berlin, Heidelberg
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