Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, , 45 - 68, 30.04.2021
https://doi.org/10.30931/jetas.778792

Öz

Kaynakça

  • [1] Schneier, B., “Applied Cryptography-Protocols, Algorithms and Source Code in C”, John Wiley & Sounds, Inc, New York, Second Edition, (1996).
  • [2] Menezes, A.J., Oorschot, P.C.V., Vanstone, S. A., “ Handbook of applied cryptography” by CRC Press LLC (1997).
  • [3] George, M., Alfke, P., “Linear feedback shift registers in virtex devices (application note)”_http://www.xilinx.com/bvdocs/appnotes/xapp210.pdf.
  • [4] Goresky, M., Klapper, A., “Fibonacci and galois representations of feedback withcarry shift registers”, IEEE Transactions on Information Theory 48(11) (2002 : 2826-2836.
  • [5] Stackoverflow. “Galois VS Fibonacci LFSR, more computer-friendly but what else?”, novembre 2011, .[https://stackoverflow.com/questions/ 5781458/galois-vs-fibonacci].
  • [6] S. W. Golomb, Shift Register Sequences, Aegean Park Press, Laguna Hills, CA, 1982 (consulté le 21 mars 2018).
  • [7] Nyathi, J., Delgado-Frias, J.G., Lowe, J., “A high-performance, hybrid wave--pipelined linear feedback shift register with skew tolerant clocks” 46th IEEE Midwest Symposium on Circuits and Systems, Cairo, Egypt, In Press, Dec. (2003).
  • [8] Mioc, M.A., Stratulat, M., “Study of software implementation for linear feedback shift register based on 8th degree irreducible polynomials”, International Journal Of Computers 8 (2014) : 46-55.
  • [9] Devaney, L, “A First course in chaotic dynamical systems”, Westview Press Studies in Nonlinearity (1992).
  • [10] Gleick, J., “Chaos: Making a new science”, Albin Michel edition (1987).
  • [11] Knuth, D.E., “The Art of Computer Programming", Addison-Wesley (1998).
  • [12] Berbain, C., “Analysis and design of stream algorithm - in French language - » PhD thesis, University Paris 7. Diderot, (2007).
  • [13] Chen, G., Mao, Y., Chui, C. K., (2004), “A symmetric image encryption scheme based on 3D chaotic cat maps”, Chaos, Solitons and Fractals 21 (2004) : 749-761.
  • [14] Noura, H., “Conception et simulation des générateurs, crypto-systèmes et fonctions de hachage basés chaos performants”, Thèse de Docteur de l’Université de Nantes, (2012).
  • [15] Li, S., Mou, X., Cai, Y., Ji, Z., Zhang, J., “On the security of a chaotic encryption scheme: problems with computerized chaos in finite computing precision”, Computer Physics Communications 153 (1) (2003) : 52-58.

Lengthening the Period of a Linear Feedback Shift Register

Yıl 2021, , 45 - 68, 30.04.2021
https://doi.org/10.30931/jetas.778792

Öz

A linear feedback shift register (LFSR) is the basic element of the pseudo-random generators used to generate a sequence of pseudo-random values for a stream cipher. It consists of several cells; each cell is a flip-flop and a feedback function. The feedback function is a linear polynomial function; this function has a degree equal to the number of cells in the register. The basic elements of the register are connected to each other in two different ways, either in Fibonacci mode or in Galois mode.

In the best case, the length of an LFSR is equal to two to the power of the number of cells of this register minus one, which is very low for cryptographic applications. To increase this length, one must look for primitive polynomials of great degree or to use adequate methods to lengthen LFSR with a reduced number of cells and, this is the objective of this work. Our method of lengthening of period of a LFSR is based on the logistics map.

Kaynakça

  • [1] Schneier, B., “Applied Cryptography-Protocols, Algorithms and Source Code in C”, John Wiley & Sounds, Inc, New York, Second Edition, (1996).
  • [2] Menezes, A.J., Oorschot, P.C.V., Vanstone, S. A., “ Handbook of applied cryptography” by CRC Press LLC (1997).
  • [3] George, M., Alfke, P., “Linear feedback shift registers in virtex devices (application note)”_http://www.xilinx.com/bvdocs/appnotes/xapp210.pdf.
  • [4] Goresky, M., Klapper, A., “Fibonacci and galois representations of feedback withcarry shift registers”, IEEE Transactions on Information Theory 48(11) (2002 : 2826-2836.
  • [5] Stackoverflow. “Galois VS Fibonacci LFSR, more computer-friendly but what else?”, novembre 2011, .[https://stackoverflow.com/questions/ 5781458/galois-vs-fibonacci].
  • [6] S. W. Golomb, Shift Register Sequences, Aegean Park Press, Laguna Hills, CA, 1982 (consulté le 21 mars 2018).
  • [7] Nyathi, J., Delgado-Frias, J.G., Lowe, J., “A high-performance, hybrid wave--pipelined linear feedback shift register with skew tolerant clocks” 46th IEEE Midwest Symposium on Circuits and Systems, Cairo, Egypt, In Press, Dec. (2003).
  • [8] Mioc, M.A., Stratulat, M., “Study of software implementation for linear feedback shift register based on 8th degree irreducible polynomials”, International Journal Of Computers 8 (2014) : 46-55.
  • [9] Devaney, L, “A First course in chaotic dynamical systems”, Westview Press Studies in Nonlinearity (1992).
  • [10] Gleick, J., “Chaos: Making a new science”, Albin Michel edition (1987).
  • [11] Knuth, D.E., “The Art of Computer Programming", Addison-Wesley (1998).
  • [12] Berbain, C., “Analysis and design of stream algorithm - in French language - » PhD thesis, University Paris 7. Diderot, (2007).
  • [13] Chen, G., Mao, Y., Chui, C. K., (2004), “A symmetric image encryption scheme based on 3D chaotic cat maps”, Chaos, Solitons and Fractals 21 (2004) : 749-761.
  • [14] Noura, H., “Conception et simulation des générateurs, crypto-systèmes et fonctions de hachage basés chaos performants”, Thèse de Docteur de l’Université de Nantes, (2012).
  • [15] Li, S., Mou, X., Cai, Y., Ji, Z., Zhang, J., “On the security of a chaotic encryption scheme: problems with computerized chaos in finite computing precision”, Computer Physics Communications 153 (1) (2003) : 52-58.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Mohammed Naım Bu kişi benim

Hana Alı-pacha Bu kişi benim

Adda Ali-pacha

Naima Hadj-saıd Bu kişi benim

Yayımlanma Tarihi 30 Nisan 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Naım, M., Alı-pacha, H., Ali-pacha, A., Hadj-saıd, N. (2021). Lengthening the Period of a Linear Feedback Shift Register. Journal of Engineering Technology and Applied Sciences, 6(1), 45-68. https://doi.org/10.30931/jetas.778792
AMA Naım M, Alı-pacha H, Ali-pacha A, Hadj-saıd N. Lengthening the Period of a Linear Feedback Shift Register. JETAS. Nisan 2021;6(1):45-68. doi:10.30931/jetas.778792
Chicago Naım, Mohammed, Hana Alı-pacha, Adda Ali-pacha, ve Naima Hadj-saıd. “Lengthening the Period of a Linear Feedback Shift Register”. Journal of Engineering Technology and Applied Sciences 6, sy. 1 (Nisan 2021): 45-68. https://doi.org/10.30931/jetas.778792.
EndNote Naım M, Alı-pacha H, Ali-pacha A, Hadj-saıd N (01 Nisan 2021) Lengthening the Period of a Linear Feedback Shift Register. Journal of Engineering Technology and Applied Sciences 6 1 45–68.
IEEE M. Naım, H. Alı-pacha, A. Ali-pacha, ve N. Hadj-saıd, “Lengthening the Period of a Linear Feedback Shift Register”, JETAS, c. 6, sy. 1, ss. 45–68, 2021, doi: 10.30931/jetas.778792.
ISNAD Naım, Mohammed vd. “Lengthening the Period of a Linear Feedback Shift Register”. Journal of Engineering Technology and Applied Sciences 6/1 (Nisan 2021), 45-68. https://doi.org/10.30931/jetas.778792.
JAMA Naım M, Alı-pacha H, Ali-pacha A, Hadj-saıd N. Lengthening the Period of a Linear Feedback Shift Register. JETAS. 2021;6:45–68.
MLA Naım, Mohammed vd. “Lengthening the Period of a Linear Feedback Shift Register”. Journal of Engineering Technology and Applied Sciences, c. 6, sy. 1, 2021, ss. 45-68, doi:10.30931/jetas.778792.
Vancouver Naım M, Alı-pacha H, Ali-pacha A, Hadj-saıd N. Lengthening the Period of a Linear Feedback Shift Register. JETAS. 2021;6(1):45-68.