Generation of maximum length non-binary key sequence and its application for stream cipher based on residue number system

Abstract

A cipher system in which the data is sequence of binary digits from data source and secrete key is also a random sequence of binary digits is called Stream cipher system. The stream cipher system which uses only binary information and key to get binary cipher text is known as binary stream cipher system. In this the encryption algorithm is bit by bit XOR operations of plain text bit and corresponding key sequence bit respectively. This concept further generalized to a non binary cipher system defined over any finite field GF (p), where p is prime integer. Again generalizing further it can also be defined a stream cipher system over the a ring Zm, arithmetic operations are carried out over modulo m, where m is suitable large composite integers and the ring is a set which satisfies closure, associative, distributive and commutative properties on addition and multiplication operation.The effectiveness of the non binary stream cipher system is based on different parameters mainly on encryption/decryption algorithm, key generation and its parameters. This paper concentrates on generating non binary key sequence of maximum length. This generated key is used for the application of Residue Number System (RNS) based stream cipher system. The properties like, uniformity, independence and maximum length for the key sequence is tested and verified. Also security issues of cipher systems using these key sequences for an image are tested and evaluated for its strength.