Elliptic curve matrices over group ring to improve elliptic curve–discrete logarithm cryptosystems

An elliptic curve matrix (ECM) is created randomly based on an elliptic curve group to modify the elliptic curve-discrete logarithm (EC-DL) cryptosystems, which are elliptic Diffie-Hellman key exchange (DHKE) and elliptic ElGamal public key cryptosystem (EEPKC), and to increase the security level in comparison with the original EC-DL schemes. In proposed schemes, the keys and ciphertext are computed using the ECMs. The security of trust schemes depended on the difficulty of solving the elliptic curve discrete logarithm problem (ECM-DLP). New experimental results on proposed schemes are discussed. The ECM-DL schemes consider new insights for more secure communications.