Rapid Hardware Design for Cryptographic Modules with Filtering Structures over Small Finite Fields

  • Nusa ZidaricEmail author
  • Mark Aagaard
  • Guang Gong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11321)


This paper presents a design automation toolkit for hardware implementations of linear and non-linear feedback shift registers (FSRs). The toolkit is implemented in the GAP computer algebra system and generates both executable GAP code and VHDL for synthesizable hardware. To design an FSR, the user needs only to provide a template and instantiate a few parameters. The primary objects are LFSRs; NLFSRs; and arbitrary combinational functions, which are modelled as FILFUNs, for “filtering functions”. Conventional feedback functions are modelled as univariate or multivariate polynomials. More complex functions can be modelled as FILFUNs. The paper demonstrates the capabilities of the toolkit using the WG-7 and WG-8 keystream generators and the Grain v1 stream cipher. Less than 30 lines of GAP code are required to generate a complete datapath in VHDL.


Feedback shift registers Filtering generators Rapid hardware design Stream ciphers GAP VHDL 


  1. 1.
    Robshaw, M.: New Stream Cipher Designs - The eSTREAM Project. Springer, Heidelberg (2008). Scholar
  2. 2.
    Wu, H.: ACORN: A Lightweight Authenticated Cipher (v1).
  3. 3.
    CAESAR: Competition for Authenticated Encryption.
  4. 4.
    ETSI/SAGE Specification version 1.1: Specification of the 3GPP Confidentiality and Integrity Algorithms UEA2 & UIA2. Document 2: SNOW 3G SpecificationGoogle Scholar
  5. 5.
    ETSI/SAGE Specification Version 1.6: Specification of the 3GPP Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3. Document 2: ZUC SpecificationGoogle Scholar
  6. 6.
    The GAP Group: GAP - Groups, Algorithms, and Programming, Version 4.8.8 (2017).
  7. 7.
    Lidl, R., Niederreiter, H.: Finite fields. In: Encyclopedia of Mathematics and its Applications, vol. 20, Cambridge University Press, Cambridge (1997)Google Scholar
  8. 8.
    Golomb, S.W., Gong, G.: Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar. Cambridge University Press, Cambridge (2005)CrossRefGoogle Scholar
  9. 9.
    Chen, L., Gong, G.: Communication System Security. CRC Press, Boca Raton (2012)CrossRefGoogle Scholar
  10. 10.
  11. 11.
  12. 12.
    Symbolic Linear Feedback Shift Registers.
  13. 13.
  14. 14.
    Coussy, P., Gajski, D.D., Meredith, M., Takach, A.: An introduction to high-level synthesis. IEEE Design Test Comput. 26(4), 8–17 (2009). Scholar
  15. 15.
    Mandal, K., Gong, G.: Generating good span n sequences using orthogonal functions in nonlinear feedback shift registers. In: Koç, Ç.K. (ed.) Open Problems in Mathematics and Computational Science, pp. 127–162. Springer, Cham (2014). Scholar
  16. 16.
    Gong, G., Aagaard, M., Fan, X.: Resilience to distinguishing attacks on WG-7 cipher and their generalizations. Cryptogr. Commun. 5(4), 277–289 (2013)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Yang G., Fan X., Aagaard M., Gong G.: Design space exploration of the lightweight stream cipher WG-8 for FPGAs and ASICs. In: WESS 2013, Article No. 8. ACM, New York (2013).
  18. 18.
    Hell, M., Johansson, T., Meier, W.: Grain - a stream cipher for constrained environments. Int. J. Wirel. Mob. Comput. 2(1), 86–93 (2007). Scholar
  19. 19.
    Hell, M., Johansson, T., Maximov, A., Meier, W.: The grain family of stream ciphers. In: Robshaw, M., Billet, O. (eds.) New Stream Cipher Designs. LNCS, vol. 4986, pp. 179–190. Springer, Heidelberg (2008). Scholar
  20. 20.
    Hwang, D., Chaney, M., Karanam, S., Ton, N., Gaj, K.: Comparison of FPGA-targeted hardware implementations of eSTREAM stream cipher candidates. SASC 2008, 151–162 (2008)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.University of WaterlooWaterlooCanada

Personalised recommendations