A Public-Key Cryptosystem Using Cyclotomic Matrices
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Confidentiality and Integrity are two paramount objectives of asymmetric key cryptography. Where two non-identical but mathematically related keys -- a public key and a private key effectuate the secure transmission of messages. Moreover, the private key is non-shareable and the public key has to be shared. The messages could be secured if the amount of computation rises to very high value. In this work we propose a public key cryptosystem using the cyclotomic numbers, where cyclotomic numbers are certain pair of solutions (a,b)_e of order e over a finite field F_q with characteristic p. The strategy employs cyclotomic matrices of order 2l^2, whose entries are cyclotomic numbers of order 2l^2, l be prime. The public key is generated by choosing a particular generator γ^' of F_p^*. Secret key (private key) is accomplished by discrete logarithm problem (DLP) over a finite field F_p.
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