Key exchange protocols over noncommutative rings. The case of

Abstract

In this paper we introduce some key exchange protocols over noncommutative rings. These protocols use some polynomials with coefficients in the centre of the ring as part of the private keys. We give some examples over the ring , where p is a prime number. We also give a security analysis of the proposed protocols and conclude that the only possible attack is by brute force.

Keywords:

• key exchange protocol
• noncommutative ring
• centre of a ring
• polynomial
• public key cryptography

2000 AMS Subject Classifications:

• 16L30
• 94A60

Acknowledgements

The authors are very grateful to the anonymous reviewers for their comments and suggestions which have led to significant improvements.

The work of the first author was partially supported by Spanish grant MTM2011-24858 of the Ministerio de Economía y Competitividad of the Gobierno de España.