Key exchange and encryption schemes based on non-commutative skew polynomials

Authors:
Delphine Boucher;Philippe Gaborit;Willi Geiselmann;Olivier Ruatta;Felix Ulmer
Affiliations:
Université de Rennes 1, IRMAR, CNRS, UMR 6625, Université européenne de Bretagne;Université de Limoges, CNRS, XLIM-DMI, Limoges Cedex, France;Karlsruhe Institut of Technology (KIT), Karsruhe, Germany;Université de Limoges, CNRS, XLIM-DMI, Limoges Cedex, France;Université de Rennes 1, IRMAR, CNRS, UMR 6625, Université européenne de Bretagne
Venue:
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
Year:
2010

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Abstract

In this paper we introduce a new key exchange algorithm (Diffie-Hellman like) based on so called (non-commutative) skew polynomials. The algorithm performs only polynomial multiplications in a special small field and is very efficient. The security of the scheme can be interpretated in terms of solving binary quadratic equations or exhaustive search of a set obtained through linear equations. We give an evaluation of the security in terms of precise experimental heuristics and usual bounds based on Groebner basis solvers. We also derive an El Gamal like encryption protocol. We propose parameters which give 3600 bits exchanged for the key exchange protocol and a size of key of 3600 bits for the encryption protocol, with a complexity of roughly 223 binary operations for performing each protocol. Overall this new approach based on skew polynomials, seems very promising, as a good tradeoff between size of keys and efficiency.