Abstract
A theoretical framework for the design of—in the sense of IND-CCA—provably secure public key cryptosystems taking non-abelian groups as a base is given. Our construction is inspired by Cramer and Shoup’s general framework for developing secure encryption schemes from certain language membership problems; thus all our proofs are in the standard model, without any idealization assumptions. The skeleton we present is conceived as a guiding tool towards the construction of secure concrete schemes from finite non-abelian groups (although it is possible to use it also in conjunction with finite abelian groups).
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Vasco, M.I.G., Martínez, C., Steinwandt, R., Villar, J.L. (2005). A New Cramer-Shoup Like Methodology for Group Based Provably Secure Encryption Schemes. In: Kilian, J. (eds) Theory of Cryptography. TCC 2005. Lecture Notes in Computer Science, vol 3378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30576-7_27
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