Paper 2014/568

New Classes of Public Key Cryptosystems over $F_2^8$ Constructed Based on Reed-Solomon Codes, K(XVII)SE(1)PKC and K(XVII)$\mathrm{\Sigma }\mathrm{\Pi }$PKC

Masao KASAHARA

Abstract

In this paper, we present new classes of public key cryptosystem over $F_2^8$ based on Reed-Solomon codes, referred to as K(XVII)SE(1)PKC and K(XVII)$\mathrm{\Sigma }\mathrm{\Pi }$PKC, a subclass of K(XVII)SE(1)PKC. We show that K(XVII)SE(1)PKC over $F_2^8$ can be secure against the various attacks. We also present K(XVII)$\mathrm{\Sigma }\mathrm{\Pi }$PKC over $F_2^8$, a subclass of K(XVII)SE(1)PKC. We show that any assertion of successfull attack on K(XVII)SE(1)PKC including K(XVII)$\mathrm{\Sigma }\mathrm{\Pi }$PKC whose parameters are properly chosen is a coding theoretical contradiction. We thus conclude that K(XVII)SE(1)PKC and K(XVII)$$PKC would be secure against the various attacks including LLL attack. The schemes presented in this paper would yield brand-new techniques in the field of code-based PKC.