Symmetric Subgroup Membership Problems

  • Kristian Gjøsteen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3386)


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.


public key encryption hybrid encryption standard model subgroup membership problem 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Kristian Gjøsteen
    • 1
  1. 1.Department of Matematical SciencesNorwegian University of Science and TechnologyTrondheimNorway

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