1 Abstract— In symmetric key cryptography the sender as well as the receiver possess a common key. Asymmetric key cryptography involves generation of two distinct keys which are used for encryption and decryption correspondingly. The sender converts the original message to cipher text using the public key while the receiver can decipher this using his private key. This is also called Public Key Cryptography. For every public key there can exist only one private key that can decipher the encrypted text. Security of RSA Algorithm can be compromised using mathematical attack, by guessing the factors of a large number. It may also be compromised if one can guess the private key. In accordance with the mathematical attack, we propose a secure algorithm in this paper. In this algorithm, we try to eliminate the distribution of n which is the large number whose factors if found compromises the RSA algorithm. We also present a comparative analysis of the proposed algorithm with the RSA algorithm. Index Terms— RSA, Security, Encryption, Complexity, Public key, Private key I. INTRODUCTION The asymmetric key cryptosystem [1], [2] involves the use of two distinct but related keys namely, the public key and the private key. Plaintext is converted to cipher text using the public key. This process is known as encryption which is performed by the sender. On the other hand, deciphering of the cipher text is performed by making use of the private key. This process is known as decryption and is performed by the receiver. Only the receiver possesses the knowledge of the private key. In order to maintain the confidentiality of the private key, the public key is disclosed to the public. The public key is used for authentication to ensure that the message is coming from the intended sender. Public key cryptosystem also ensures confidentiality. Only the receiver’s private key can decipher the cipher text originating from the sender. Communication of messages can be done in a secure manner since knowledge of the public key is not sufficient to decrypt the cipher text. Due to the above advantages, in our proposed algorithm we follow the asymmetric key cryptography technique. In this scheme, there is a mathematical relation between the two keys. Owing to this fact, it is likely that the system may be compromised if someone discovers the relation between the keys and successfully derives the private key. In RSA [3], [4] both the keys comprise of the large number ‘n’, which can be factored into 'p' and 'q'. The public key is known to all. It is easy to derive the private key if someone can guess the factors of 'n' [5], [6] . To prevent this from happening, in our algorithm we try to eliminate the distribution of 'n' in both the keys. Instead, we apply a mathematical transformation over 'n' to get a replacement for 'n' using which one cannot trace back to the factors of 'n' that are 'p' and 'q'. This improves the security of the RSA algorithm [7] by a greater extent. II. RSA CRYPTOSYSTEM RSA is an asymmetric key cryptosystem relies on the assumption that it is difficult to find the factors of large integers. It involves distribution of public and private key to sender and receiver to encrypt and decrypt the message respectively. RSA is a three step process that involves Key generation, Message encryption and message decryption. The algorithm is as follows: A. Key generation i. Generate two distinct random prime numbers p and q. ii. Calculate n = p x q. Its length is the key length which is usually expressed in bits. iii. Calculate φ(n) = (p - 1) x (q - 1) where φ is the Euler's totient function. iv. Calculate e based on the following conditions:  1 < e < φ(n)  GCD(e, φ(n)) = 1 i.e., e and φ(n) are co- prime.  e must have a short bit-length and small Hamming weight [2] . v. Find d which satisfies the relation (e x d) Mod (n) = 1 Now, the Public Key comprises e and n i.e., (e, n). The Private Key comprises of d and n i.e., (d, n). B. Message Encryption The sender uses the following method to encipher the message M:  Cipher text C = M e Mod (n) where C is the cypher text generated after encryption. C. Message Decryption The receiver uses the following method to decipher the cipher text C:  The original message M = C d Mod(n). An Algorithm to Enhance Security in RSA Rohit Minni, Kaushal Sultania, Saurabh Mishra, Prof Durai Raj Vincent PM, VIT University IEEE - 31661 4th ICCCNT 2013 July 4-6, 2013, Tiruchengode, India