Public Key Cryptosystem Based on Circulant Matrices

Habibollah Lotfi¹ Ali A. Pouyan² Smita Bedekar³

1) PhD scholar
2) Associated Professor
3) Associated Professor

Publication : 3rd International Conference On Research Science And Technology(3rstconf.com)
Abstract :
Circulant Matrices (CM) imply an important designation in cryptography. An important aspect in public key cryptography is using CM such that given a n*n CM “C” over a field F we calculate exponent of it A=〖 C〗^rwhere r is an arbitrary integer number then A is a public key to encrypt our data. The aim of this paper is to introduce an algorithm to find such CMs which are suitable in security field. It means those CMs are not only strong against attacks in practice but also they are fast enough in computational point of view. Moreover, it proposes a new cryptosystem to public key cipher which secret key is an arbitrary integer m and a circulant matrix C with field elements and an extension of the same matrix to power of same secret key is used as a public keys. This cryptosystem is an asymmetric encryption algorithm resistant to the attack of all known plaintext.
Keywords : Circulant Matrix; Cryptosystem; Public Key; Elliptic Curves