International Association
for Cryptologic Research

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)$\\Sigma \\Pi$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)$\\Sigma \\Pi$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)$\\Sigma \\Pi$PKC whose parameters are properly chosen

is a coding theoretical contradiction.

We thus conclude that K(XVII)SE(1)PKC and K(XVII)$\\Sigma \\Pi$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.