Cryptographic Functions and Bit-Error-Rate Analysis with Almost $p$-ary Sequences

Year 2019, Volume: 8 Issue: 3, 44 - 52, 01.09.2019

Busra Ozden Oguz Yayla

Abstract

Sequences are used for achieving non-linearity in a cryptosystem, and they are important in Code Division Multiple Access CDMA to ensure a proper communication. In this study, we show a method for obtaining cryptographic functions from p-ary sequences with s consecutive zero-symbols of type γ1, γ2 . In fact, most of the cases we obtain functions with the highest non-linearity, i.e. generalized bent functions. In CDMA, instead of distributing time and frequency sources to users, each user is given a unique sequence to transmit data at the same frequency and time. In this study, we examined the bit-error-rate BER performance of p-ary sequences with s consecutive zero-symbols of type γ1, γ2 on CDMA.

Keywords

nearly perfect sequences, cryptographic functions, generalized bent function, CDMA, bit-error-rate

References

• P. V. Kumar, R. A. Scholtz, and L. R. Welch. ”Generalized bent functions and their properties.” Journal of Combinatorial Theory, Series A 40.1 (1985): 90-107.
• S. Kurt, and O. Yayla. ”Near Butson-Hadamard Matrices and Nonlinear Boolean Functions.” International Conference on Number-Theoretic Methods in Cryptology. Springer, Cham, 2017.
• B. ¨Ozden, and O. Yayla. ”Almost p-ary Sequences.” arXiv preprint arXiv:1807.11412 (2018).
• D. Jungnickel, and A. Pott. Perfect and Almost Perfect Se- quences. Discrete Applied Mathematics 95 (1999): 331-359.
• K.-U Schmidt. Quaternary Constant-Amplitude Codes for Mul- ticode CDMA. IEEE Transactions on Information Theory 55 (2007): 1824-1832.
• C.-L I, and R. D. Gitlin, Multi-code CDMA wireless per- sonal communications networks, Proc. IEEE ICC’95, Vol. 2, pp10601064, June 1995.
• J. Hollon, M. Rangaswamy, and P. Setlur. ”New families of optimal high-energy ternary sequences having good correlation properties.” Journal of Algebraic Combinatorics (2018): 1-38.
• S. W. Golomb, and G. Gong. Signal design for good correlation: for wireless communication, cryptography, and radar. Cambridge University Press, 2005.
• T. Helleseth, and P. V. Kumar, Sequences with low correlation, in: Vera S. Pless and W. Cary Huffman, eds., Handbook in Coding Theory, volume II, chapter 21, pp. 1765-1853, Elsevier Science B.V., Amsterdam, 1998.
• H. Y. Liu, and K. Q. Feng. ”New results on nonexistence of perfect p-ary sequences and almost p-ary sequences.” Acta Mathematica Sinica, English Series 32.1 (2016): 2-10.