Skip to main content
SpringerLink
Log in

Practical construction of ring LFSRs and ring FCSRs with low diffusion delay for hardware cryptographic applications

  • Published:
Cryptography and Communications Aims and scope Submit manuscript

Abstract

Linear Feedback Shift Registers (LFSRs) and Feedback with Carry Shift Registers (FCSRs) are two pseudo-random generators which are widely used in many cryptographic applications. The Ring representation of them has been proposed using a matrix approach. In this paper, we show how to construct Ring LFSRs and Ring FCSRs with low diffusion delay (close to the expected value \(\sqrt {n}\)) when considering other hardware cryptographic criteria.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Arnault, F., Berger, T.P.: F-FCSR: design of a new class of stream ciphers. In: Gilbert, H., Handschuh, H. (eds.) FSE. Lecture Notes in Computer Science, vol. 3557, pp. 83–97. Springer, New York (2005)

  2. Arnault, F., Berger, T.P., Benjamin, P.: A Matrix Approach for FCSR Automata. Cryptogr. Commun. 3(2), 109–139 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Arnault, F., Berger, T.P., Lauradoux, C.: Update on F-FCSR Stream Cipher. ECRYPT-Network of Excellence in Cryptology (Call for stream Cipher Primitives-Phase 2 2006) (2006). [http://www.ecrypt.eu.org/stream/]

  4. Arnault, F., Berger, T.P., Lauradoux, C., Minier, M., Pousse, B.: A new approach for FCSRs. In: M.J.J. Jr., Rijmen, V., Safavi-Naini, R. (eds.) Selected Areas in Cryptography. Lecture Notes in Computer Science, vol. 5867, pp 433–448. Springer, New York (2009)

  5. Arnault, F., Berger, T.P., Minier, M., Pousse, B.: Revisiting LFSRs for cryptographic applications. IEEE Trans. Inf. Theory 57(12), 8095–8113 (2011)

    Article  MathSciNet  Google Scholar 

  6. Berger, T.P., Minier, M., Pousse, B.: Software oriented stream ciphers based upon FCSRs in diversified mode. In: Roy, B.K., Sendrier, N. (eds.) INDOCRYPT. Lecture Notes in Computer Science, vol. 5922, pp 119–135. Springer, New York (2009)

  7. Flajolet, P., Odlyzko, A.M.: Random mapping statistics. Advances in cryptologyEUROCRYPT’89, pp 329–354. Springer, Berlin (1990)

    MATH  Google Scholar 

  8. Goresky, M., Klapper, A.: Arithmetic crosscorrelations of feedback with carry shift register sequences. IEEE Trans. Inf. Theory 43(4), 1342–1345 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Goresky, M., Klapper, A.: Fibonacci and Galois representations of feedback-with-carry shift registers. IEEE Trans. Inf. Theory 48(11), 2826–2836 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hell, M., Johansson, T.: Breaking the F-FCSR-H Stream Cipher in Real Time. In: Pieprzyk, J. (ed.) ASIACRYPT. Lecture Notes in Computer Science, vol. 5350, pp 557–569. Springer, New York (2008)

  11. Imase, M., Itoh, M.: Design to minimize diameter on building-block network. IEEE Trans. Comput. 100(6), 439–442 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  12. Imase, M., Itoh, M.: A design for directed graphs with minimum diameter. IEEE Trans. Comput. 32(8), 782–784 (1983)

    Article  MATH  Google Scholar 

  13. Klapper, A., Goresky, M.: 2-adic shift registers. In: Anderson, R.J. (ed.) FSE. Lecture Notes in Computer Science, vol. 809, pp 174–178. Springer, New York (1993)

  14. Klapper, A., Goresky, M.: Large Period Nearly deBruijn FCSR Sequences. Advances in Cryptology-EUROCRYPT’95, pp 263–273. Springer, Berlin (1995)

    MATH  Google Scholar 

  15. Lin, Z., Ke, L., Lin, D., Gao, J.: On the LFSRization of a Class of FCSR Automata. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 98(1), 434–440 (2015)

    Article  Google Scholar 

  16. Lin, Z., Pei, D., Lin, D.: Construction of Transition Matrices for Binary FCSRs. Tech. Rep. 2015/1181. Available: http://eprint.iacr.org/

  17. Mruglaski, G., Rajski, J., Tyszer, J.: Ring generators-new devices for embedded test applications. Computer-Aided Design of Integrated Circuits and Systems. IEEE Trans. Comput.-Aided Design 23(9), 1306–1320 (2004)

    Article  Google Scholar 

  18. Tian, T., Qi, W.F.: Linearity properties of binary FCSR sequences. Des. Codes Cryptography 52, 249–262 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wang, H., Stankovski, P., Johansson, T.: A generalized birthday approach for efficiently finding linear relations in l-sequences. Des. Codes Cryptography 74(1), 41–57 (2015)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100195, China

    Zhiqiang Lin & Dongdai Lin

  2. College of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Dingyi Pei

Authors
  1. Zhiqiang Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dongdai Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dingyi Pei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhiqiang Lin.

Additional information

This work is supported by a National Key Basic Research Project of China (2011CB302400), National Natural Science Foundations of China (11371106), National Science Foundation of China (61379139) and the “Strategic Priority Research Program” of the Chinese Academy of Sciences (XDA06010701).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, Z., Lin, D. & Pei, D. Practical construction of ring LFSRs and ring FCSRs with low diffusion delay for hardware cryptographic applications. Cryptogr. Commun. 9, 431–443 (2017). https://doi.org/10.1007/s12095-016-0183-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12095-016-0183-8

Keywords

Mathematics Subject Classification (2010)

Search

Navigation