Abstract: “Public key cryptography is extensively used for encryption, signing contracts and secure exchanges over the unreliable network. The findings of Shor in 1994, of a powerful algorithm which was based on quantum mechanics for computing discrete logarithms and factoring large integers sabotaged the security presumptions upon which the currently used public key cryptographic protocols are based, like ElGamal, RSA and ECC. However, few cryptosystems, known as post quantum cryptosystems, while not currently in wide use are considered to be resistant to such attacks. In this paper, a quantum version of ElGamal Cryptosystem is proposed whose security relies on the commutative rotation transformations and measurements in computational basis of qubits. An understanding of the new scheme over the quantum channels is provided. The proposed cryptosystem allows the party to send messages in the form of qubits over a quantum channel. Also the proposed protocol provides an opportunity for two parties t”

Keywords: Quantum, elgamal, shor, post quantum, commutative rotation, qubits, cryptosystem.