Symmetric Subgroup Membership Problems

Abstract. We define and discuss symmetric subgroup membership problems and their properties, including a relation to the Decision DiffieHellman 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. Key words: public key encryption, hybrid encryption, standard model, subgroup membership problem.

• Type: Conference
• Year: 2005
• Where: PKC
• Authors: Kristian Gjøsteen
• Keywords: Cryptography, PKC 2005, Standard Model, Subgroup Membership Problem, Symmetric Subgroup Membership