International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 18 July 2015

Masao KASAHARA
ePrint Report ePrint Report
In this paper, we first present a new class of code based public key cryptosystem(PKC) based on Reed-Solomon code over $\\mathbb{F}_{2^m}$, referred to as K(XVI)SE(1)PKC.

We then present a new class of quadratic multivariate PKC, K(XVI)SE(2)PKC, based on cyclic code over $\\mathbb{F}_2$.

We show that both K(XVI)SE(1)PKC and K(XVI)SE(2)PKC can be secure against the various linear transformation attacks such as Gr\\\"obner bases attack due to a non-linear structure introduced to the ciphertexts.

Namely, thanks to the non-linear transformation introduced in the construction of K(XVI)SE(1)PKC and K(XVI)SE(2)PKC the ciphertexts can be made very secure against the various sorts of linear transformation attacks such as Gr\\\"obner bases attack, although the degree of the multivariate polynomial is all degree 1.

A new scheme presented in this paper that transforms message variables in order to realize non-linear transformations, K(I)TS, would yield a brand-new technique in the field of both code based PKC and multivariate PKC, for much improving the security.

We shall show that the K(XVI)SE(1)PKC can be effectively constructed based on the Reed-Solomon code over $\\mathbb{F}_{2^8}$, extensively used in the present day storage systems

or the various digital transmission systems.

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