## Cryptology ePrint Archive: Report 2014/711

New Class of Multivariate Public Key Cryptosystem, K(XI)RSE(2)PKC, Constructed based on Reed-Solomon Code Along with K(X)RSE(2)PKC over $\mathbb{F}_2$

Masao KASAHARA

Abstract: Extensive studies have been made of the public key cryptosystems based on multivariate polynomials (Multi-variate PKC, MPKC) over $\mathbb{F}_2$ and $\mathbb{F}_2^m$. However most of the proposed MPKC are proved not secure. In this paper, we propose a new class of MPKC based on Reed-Solomon code, referred to as K(XI)RSE(2)PKC. In Appendix, we present another class of MPKC referred to as K(X)RSE(2)PKC over $\mathbb{F}_2$. Both K(X)RSE(2)PKC and K(XI)RSE(2)PKC yield the coding rate of 1.0. We show that the proposed schemes can be sufficiently secure against various attacks, including Gr\"obner basis attack.

Category / Keywords: public-key cryptography / Public-key cryptosystem, Gr\"obner basis attack, Multivariate PKC, Code-based PKC

Original Publication (with major differences): oral presentation