In this paper, we first present a new class of code based public key cryptosystem(PKC) based on Reed-Solomon code over extension field of less than m=9, 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 binary cyclic code.
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 Grobner bases attack due to a non-linear structure introduced when constructing the ciphertexts.
Namely, thanks to a 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 sort of linear transformation attacks such as Grobner bases attack, although the degree of any multivariate polynomial used for public key is 1.
A new scheme presented in this paper that transforms message variables in order to realize a non-linear transformation, K(II)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 of m=8, extensively used in the present day storage systems
or the various digital transmission systems.
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