Design a New Cryptosystem Based on Michael O. Rabin Cryptosystem

Abstract

Cryptography is the art of protecting information by transforming encryption into an unreadable format called ciphertext. Only those who possess a secret key can decipher the message into plaintext. Either single or more cryptographic primitives are often used to develop a more complex algorithm which is called a cryptosystem. Michael O. Rabin Cryptosystem can generate the same ciphertext from different plaintext as well as multiple plaintexts from a single cyphertext. There are several techniques to reveal original plaintext, but none of them can separate similar cyphertext against each plaintext generated from modular reduction arithmetic. Another problem is a forgery attack on the Rabin encryption algorithm and private key derivation. To solve those issues, a new cryptosystem has been designed which can efficiently separate similar ciphertext against each plaintext by removing all of the problems of the Rabin cryptosystem identified in problem statements. The proposed cryptosystem comprises five algorithms: Key generation, Encryption, Decryption, Signature generation, and Signature verification algorithm. To authenticate the messages, the encryption algorithm has been designed. The proposed cryptosystem construction is based on quadratic residue, quadratic quotient, floor function, absolute value counting, Diffie-Hellman key exchange protocol, the concept of Michael O. Rabin signature algorithm, and probability theorem. The advantage of the proposed crypto intensive technique is intended receiver gets only one plain value distinguishing the ciphertext against the plaintext by verifying the signature of the sender. Another advantage is that the sender generates a signature using encrypted text and the intended receiver can retrieve plaintext from the signature through a signature verification system. The proposed crypto technique requires less time complexity and is probably secure against a man-in-the-middle attack, chosen-plaintext, cyphertext attack, and modular squaring attack. The newly designed techniques use a random padding system including additional quotient and residuum. In terms of signature, the Rabin signature is pair but the proposed cryptosystem uses a 4-tuple signature system.