Key Exchange and Encryption Schemes Based on Non-commutative Skew Polynomials

Delphine Boucher (1) , Philippe Gaborit (2) , Willi Geiselmann (3) , Olivier Ruatta (2) , Félix Ulmer (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 DMI
3 TH - Universität Karlsruhe

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.

Mots clés: cryptography

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Delphine Boucher, Philippe Gaborit, Willi Geiselmann, Olivier Ruatta, Félix Ulmer. Key Exchange and Encryption Schemes Based on Non-commutative Skew Polynomials. Nicolas Sendrier. Post-Quantum Cryptography: Proceedings of the Third International Workshop (PQCrypto 2010) Darmstadt, Germany, May 25-28, 2010, Springer, pp.126-141, 2010, Lecture Notes in Computer Science, vol. 6061, 978-3-642-12928-5. ⟨10.1007/978-3-642-12929-2_10⟩. ⟨hal-00684800⟩