A public key Cryptography based on the m-injectivity of $Z_{p q}$ over itself
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Abstract
In this paper, we present a new public key scheme which is based on factoring, RSA encryption, proposed by Rivest-Shamir-Adleman(1978) [5]and discrete logarithm problem(DLP) [6], proposed by Diffie and Hellman[15], particularly, known as the Computational Diffie-Hellman Problem (CDH)[17]. The idea of DLP was mainly applied to groups, Finite fields and Elliptic Curves but in this paper, we are going to apply it to a particular ring $Z_{p q}$, where $p$ and $q$ are two large primes. The encryption and decryption processes of the proposed scheme uses the Elgamal encryption scheme related to DLP. Also, the proposed system benefits from the fact that this ring is $\mathrm{m}$-injective over itself i.e, the existence of many R-monomorphisms from this ring to itself, which are subjected to certain conditions.
Keywords:
m-injective, R-monomorphisms,, Public Key Cryptography, RSA Cryptosystem, Discrete Logarithm Problem, Computational Diffie-Hellman ProblemMathematics Subject Classification:
Mathematics- Pages: 130-135
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
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