Binary GH Sequences for Multiparty Communication

This paper investigates cross correlation properties of sequences derived from GH sequences modulo p, where p is a prime number and presents comparison with cross correlation properties of pseudo noise sequences. For GH sequences modulo prime, a binary random sequence B(n) is constructed, based on whether the period is p-1 (or a divisor) or 2p+2 (or a divisor). We show that B(n) sequences have much less peak cross correlation compared to PN sequence fragments obtained from the same generator. Potential applications of these sequences to cryptography are sketched.Comment: 7 pages, 6 figure

New Classes of Random Sequences for Coding and Cryptography Applications

Cryptography is required for securing data in a digital or analog medium and there exists a variety of protocols to encode the data and decrypt them without third party interference. Random numbers must be used to generate keys so that they cannot be guessed easily. This thesis investigates new classes of random numbers, including Gopala-Hemachandra (GH) and Narayana sequences, which are variants of the well-known Fibonacci sequences. Various mathematical properties of GH and Narayana sequences modulo prime have been found including their periods. Considering GH sequences modulo prime p, the periods are shown to be either (p-1) (or a divisor) or (2p+2) (or a divisor) while the Narayana sequence for prime modulo have either p2+p+1 (or a divisor) or p2-1 (or a divisor) as their periods. New results on the use of the Narayana sequence as a universal code have been obtained.It is shown that the autocorrelation and cross correlation properties of GH and Narayana sequences justify their use as random sequences. The signal to noise ratio values are calculated based on the use of delayed sequences to carry different sets of data in wireless applications. The thesis shows that GH and Narayana sequences are suitable for many encoding and decoding applications including key generation and securing transmission of data.Electrical Engineerin