Cryptography: a Mathematical Approach P. M. Durai Raj Vincent 1* , Syed Amber Iqbal 2 , Karan Bhagat 2 and Kamal Kant Kushwaha 2 1 Assistant Professor (Senior), SITE, VIT University; pmvincent@vit.ac.in 2 III B.Tech(IT), SITE, VIT University; syedamber91@yahoo.com, karan.bhagat2010@vit.ac.in, kushwaha.kamalkant@yahoo.com Abstract Networking is a way of connecting geographically distributed devices so as to communicate and share resources such as printers, files etc. Nowadays, Networking is extensively used in banking sector, e–commerce, social networking sites, news groups, sharing of software, sharing of valuable information among others and so many more. The unauthorized access to these networks is restrained by the administrator who apply and use various provisions and policies which is termed as network securities. Network security refers to any activity designed to protect network. Network security is an extremely valuable and procreative amenity. A threat exists whenever the security is perceived to get breached and vulnerability likely to be exploited. To enhance and strengthen a safeguard mechanism in protecting information multiple layers of security are implemented in our algorithm instead of adopting a single layer which at times may fall through. Keywords: Transposition, Randomization, Quadratic Encryption, Hash Code, Cryptography. *Corresponding author: P. M. Durai Raj Vincent (pmvincent@vit.ac.in) 1. Introduction To maintain the integrity of network security there are certain encryption and decryption algorithms that are fol- lowed and cryptography is used as explained [1, 2]. For successful transmission of a message we have to ensure that the secrecy of message is maintained. For this purpose a key is generated which is used to create cipher texts that is being sent to the destination [3, 1]. e key is symmetric so that the sender and the receiver will use the same key [4]. To increase the complexity of the encryption algorithm multiple layers of security are used in algorithm. Sender will verify the received message in order to check for any alteration using the hash function [5]. e algorithm is built on five modules and it is practically impossible to break it [6]. 1.1 Key Generation Primarily an odd number is used to generate the Pythagorean triplets [7]. A Pythagorean triplet is selected and a set of mathematical operations are performed and a key is generated [8]. We obtain a sum of the Pythagorean Triplet which is then sent to the destination. 1.2 Key Finder e Pythagorean triplet can be re–derived from the sum which is obtained from the sender [9]. 1.3 Cryptographic Algorithm e generated key is used in the encryption algorithm which comprises of three layers: Transposition [10], Randomization and Quadratic Encryption sequentially. Decryp-tion process involves obtaining the original mes- sage back using Quadratic Decryption, De–randomization and Transposition sequentially. To ensure authentication, digital signature is used [11]. 1.4 Hash Code Generation Conversion of the message to its equivalent hash code is done using a hash function [12]. Hash Code is generated for each message. 1.5 Hash Code Verification Integrity of the message is preserved by comparing received hash code and generated hash code [12]. If both the received and generated hash code is equal then the message is unaltered. Indian Journal of Science and Technology, Vol 6(12), 5607–5611, December 2013