Cryptology ePrint Archive: Report 2010/458

Key Agreement Protocols Using Multivariate Equations on Non-commutative Ring

Masahiro Yagisawa

Abstract: In this paper we propose two KAP(key agreement protocols) using multivariate equations. As the enciphering functions we select the multivariate functions of high degree on non-commutative ring H over finite field Fq. Two enciphering functions are slightly different from the enciphering function previously proposed by the present author. In proposed systems we can adopt not only the quaternion ring but also the non-associative octonion ring as the basic ring. Common keys are generated by using the enciphering functions. Proposed systems are immune from the Gröbner bases attacks because obtaining parameters of the enciphering functions to be secret keys arrives at solving the multivariate algebraic equations, that is, one of NP complete problems .Our protocols are also thought to be immune from the differential attacks because of the equations of high degree. We can construct our system on the some non-commutative rings, for example quaternion ring, matrix ring or octonion ring.

Category / Keywords: public-key cryptography / key agreement protocol, multivariate equations, Gröbner bases, NP complete problems, non-commutative ring

Date: received 24 Aug 2010, last revised 22 Nov 2010

Contact author: tfktyagi2 at c3-net ne jp

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Note: I corrected the numbers of the paragraph in subsection4.3 .

Version: 20101122:140727 (All versions of this report)

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