ﻤﺘﺘﺎﻟﻴﺎﺕ ﺨﺼﺎﺌﺹ ﻨﻤﺫﺠﺔABSTRACT: Based on an analytical study of the theory of m-sequences, a tool is developed to facilitate practicing engineers to either generate m-sequence for its application, or to test applied msequence, or both. The developed test-kit simulates all the properties of m-sequences including number of 1s and 0s, the run lengths, pulse periods as well as autocorrelation properties. This simplified tool is developed using MATLAB-SIMULINK with required codes as well as desired blocks. The model is cost-effective and the output files of the generated SIMULINK models can be utilized in any software program or simulation procedures.
KEYWORDS: LFSR, M-Sequence, PN Codes, Stream Cipher, Run Length
IntroductionT he m-sequences are of great importance in many fields of engineering and sciences. Cryptography is the most prominent of these applications. One important way of generating such sequences is via Linear Feedback Shift Registers (LFSRs).In cryptography, m-sequences are used in two ways; one for designing simple forms of encrypting systems and, the other for selecting cryptographic keys (Pless, 1977;Konheim, 1981;Meyer and Matyas, 1982; Barker, 1984;Siegenthaler, 1985;Rueppel, 1986 and1991;Davis et. al, 1994;Schneier, 1996; Diffie and Hellman,1996;Golic, 1998 and2000;and Ahmad et. al, 2001). Apart from the use of m-sequences as stream ciphers, in crypto-security, they have also found a wide range of applications including error control, coding and spread spectrum communications (Shannon, 1963;Neumann, 1963;Massey, 1969;Newbridge Microsystems, 1992;Glaise, 1997). Table1 below shows a few of such practical applications of m-sequences. The table also depicts the used lengths of the m-sequences and the sizes of the corresponding LFSRs which generate them. Besides these, there are numerous other applications of m-sequences as briefly summarized below:147