Institute of Advanced Engineering and Science International Journal of Information & Network Security (IJINS) Vol.4, No.1, February 2015, pp. 11~13 ISSN: 2089-3299  11 Journal homepage: http://iaesjournal.com/online/index.php/ IJINS w w w . i a e s j o u r n a l . c o m Rabin Cryptosystem and Its Extension Nisheeth Saxena*, Dr.Rajeev Pourush** * Assistant Professor – CSE Department - FET MUST ** Assistant Professor – ECE Department – FET MUST Article Info ABSTRACT Article history: Received Dec 12 th , 2014 Revised Jan 20 th , 2015 Accepted Feb 26 th , 2015 The Rabin cryptosystem is an asymmetric cryptographic algorithm. Its security is based on the problem of integer factorization [4]. Rabin cryptosystem has the advantage that the problem on which its security depends is proved to be as hard as factorization [5]. Its minor disadvantage is that each output of the Rabin algorithm is generated by any of four possible inputs. If each output is a cipher text, extra complexity is required on decryption to identify which of the four possible inputs was the true plaintext. The process was published in January 1979 by Michael O. Rabin [2]. The Rabin cryptosystem was the first asymmetric cryptosystem where recovering the entire plaintext from the cipher text could be proven to be as hard as integer factorization. Keyword: Rabin cryptosystem, cipher text, integer factorization Copyright @ 2015 Insitute of Advanced Engineeering and Science. All rights reserved. Corresponding Author: Nisheeth Saxena, Assistant Professor – CSE Department - FET MUST, Email: nisheethsaxena.fet@mitsuniversity.ac.in, rajeevpourush.fet@modyuniversity.ac.in 1. INTRODUCTION The Rabin cryptosystem is a variation of the RSA cryptosystem. Rabin cryptosystem is based on the concept of quadratic congruences while RSA cryptosystem is based on exponentiation congruences [4].In Rabin cryptosystem value of e and d are fixed and are equal to 2 and ½ respectively. In RSA cryptosystem 1<e< ∅ (n) and e is coprime to ∅(n) , whereas d is inverse of e modulo ∅(n) i.e.    ∅[4].The equations for encryption and decryption can be written as :              The public key in the Rabin Cryptosystem is given by  , where  and  are very large prime numbers and the 2-tuple (   forms the private key. Everyone can encrypt the a message using  but only intended recipient (Bob )can decrypt the message using   .Bob needs to keep    untill the end of the decryption process, he can’t discard them after the key generation procedure is over. The two primes selected for key generation can be congruent to    as well as    . The decryption process is easier when    are of the form       4). The decryption process is much more difficult when we take    of the form       4). The Rabin cryptosystem is implemented only for the primes of the form       4). We will extend Rabin cryptosystem for the class of integers which are congruent to 5   which can be considered as a subset of the set of primes belonging to the set   . Algorithm Rabin_Key_Generation { // Choose two large prime numbers    of the form    i.e. both are congruent to         ; Public_Key =   Private_Key =   Send(Public_Key , Private_Key) ;