Due to their simple construction, LFSRs are commonly used as building blocks in various random number generators. Nonlinear feedforward logic is incorporated in LFSRs to increase the linear complexity of the generated sequences. This work deals with Nonlinear Feedforward Generators (NLFGs) that generate sequences over arbitrary finite fields. We analyze the frequency of symbols in sequences generated by such configurations. Further, we propose a method of using nonlinear feedforward logic with word-based σ-LFSRs wherein vectors over a finite field are seen as elements of an extension field. We then briefly analyze sequences generated by an existing scheme and show that sequences generated by the proposed scheme are statistically more balanced.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Bedi, S., Pillai, N.: Cryptanalysis of the nonlinear feedforward generator. In: Rangan, C., Ding, C. (eds.) Progress in cryptology INDOCRYPT 2001, lecture notes in computer science, vol. 2247, pp 188–194. Springer, Berlin (2001). https://doi.org/10.1007/3-540-45311-318
Dawson, E., Asenstorfer, J., Gray, P.: Cryptographic properties of groth sequences. Australasian Journal of Combinatorics 1, 53–65 (1990)
Gammel, B. M., Göttfert, R.: Linear filtering of nonlinear shift-register sequences. In: Coding and Cryptography, pp. 354–370. Springer (2006)
Golomb, S. W.: Shift register sequences. Aegean Park Press, Laguna Hills (1981)
Groth, E.: Generation of binary sequences with controllable complexity. IEEE Trans. Inf. Theory 17(3), 288–296 (1971). https://doi.org/10.1109/TIT.1971.1054618
Hasan, S. U., Panario, D., Wang, Q. Helleseth, T., Jedwab, J. (eds.): Word-oriented transformation shift registers and their linear complexity, vol. 7280. Springer, Berlin (2012)
KEY, E.: An analysis of the structrue and complexity of nonlinear binary sequence generators. IEEE Trans. Inf. Theory 22(6), 732–736 (1976)
Krishnaswamy, S.: On multisequences and applications. Indian Institute of Technology Bombay, Ph.D. thesis (2012)
Krishnaswamy, S., Pillai, H. K.: On the number of linear feedback shift registers with a special structure. IEEE Trans. Inf. Theory 58(3), 1783–1790 (2012). https://doi.org/10.1109/TIT.2011.2174332
Lidl, R., Niederreiter, H.: Finite fields, Encyclopedia of mathematics and its applications, vol. 20. Cambridge University Press, Cambridge (1997)
Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of applied cryptography. Discrete mathematics and its applications. CRC Press (1996)
Niederreiter, H.: The multiple-recursive matrix method for pseudorandom number generation. Finite Fields Appl. 1(1), 3–30 (1995)
Paar, C., Pelzl, J.: Understanding cryptography: A textbook for students and practitioners. Springer, Berlin (2009)
Peterson, W., Weldon, E.: Error-correcting codes. MIT Press (1972)
Pickholtz, R., Schilling, D., Milstein, L.: Theory of spread-spectrum communications–a tutorial. IEEE Trans. Comm. 30(5), 855–884 (1982). https://doi.org/10.1109/TCOM.1982.1095533
Roy, S., Krishnaswamy, S., Goyal, P.: On nonlinear feedforward logic for σ-lfsrs. In: 22nd international symposium on mathematical theory of networks and systems (MTNS 2016), pp 366-372. Minneapolis, MN, USA (2016)
Teo, S. G.: Analysis of nonlinear sequences and streamciphers. Queensland University of Technology, Ph.D. thesis (2013)
Zeng, G., Han, W., He, K.: High efficiency feedback shift register: σ-lfsr. IACR Eprint archive (2007)
The authors are grateful to Prof. Harish K. Pillai, Department of Electrical Engineering, Indian Institute of Technology Bombay, without whom this work would never have been possible.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Roy, S., Krishnaswamy, S. On the frequency of symbols in sequences generated by nonlinear Feedforward generators. Cryptogr. Commun. 12, 115–126 (2020). https://doi.org/10.1007/s12095-019-00379-1
- Pesudorandom number generator (PRNG)
- Linear feedback shift register (LFSR)
- Nonlinear feedforward generator (NLFG)
- Balanced distribution
- Linear complexity
Mathematics Subject Classification (2010)