BibTex RIS Kaynak Göster

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

Yıl 2019, Cilt: 8 Sayı: 3, 44 - 52, 01.09.2019

Öz

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.

Kaynakça

  • 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.
Yıl 2019, Cilt: 8 Sayı: 3, 44 - 52, 01.09.2019

Öz

Kaynakça

  • 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.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Busra Ozden Bu kişi benim

Oguz Yayla Bu kişi benim

Yayımlanma Tarihi 1 Eylül 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 8 Sayı: 3

Kaynak Göster

IEEE B. Ozden ve O. Yayla, “Cryptographic Functions and Bit-Error-Rate Analysis with Almost $p$-ary Sequences”, IJISS, c. 8, sy. 3, ss. 44–52, 2019.