Analysis of an Enhanced Dual RSA Algorithm Using Pell’s Equation to Hide Public Key Exponent and a Fake Modulus to Avoid Factorization Attack

Abstract

Public key cryptography generates two distinct keys: one for encryption and another separate but related key for decryption. There exists only one private key for every public key to decipher the message. A variant of RSA, called the Dual RSA, has two different key pairs having separate private and public key exponents. Security of the RSA is compromised using mathematical attacks, by the factorization of ‘n’. This paper proposed an enhanced approach to Dual RSA with the help of Pell’s equation and a fake modulus key. The algorithm eliminates the distribution of ‘n’, whose factors compromise the RSA algorithm. Also, the solutions to Pell’s equation are shared instead of the public key components. A comparative analysis is carried out with respect to RSA, Dual RSA and the proposed algorithm based on the complexity of each step of the algorithm. It is observed that the proposed system provides more security to the public key exponents and the system modulus ‘n’, than RSA and Dual RSA.