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On-Line Error Detection and Off-Line Test Design in Polynomial Basis Multiplier over GF(2m) Using Irreducible Trinomials

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Business, Economics, Financial Sciences, and Management

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 143))

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Abstract

The concurrent error detection capability can give countermeasure to recent developed fault-based cryptanalysis. The design-for-testability is one of evaluated indexes to detect the faulty element of VLSI chips for manufacturability and maintainability issues. Thus, design of multipliers in GF(2m) with both concurrent error detection and design-for-testability is an important issue for elliptic curve cryptosystem. In this study, a novel self-checking alternating logic (SCAL) multiplier in GF(2m) is presented for achieving both on-line test and off-line test purposes. The proposed polynomial basis multiplier using irreducible trinomials requires only about 33% extra space complexity of existing multipliers. As our best knowledge, the proposed polynomial basis multiplier is the first polynomial basis multiplier which can provide both on-line error detection and off-line test capabilities.

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References

  1. Macwilliams, F.J., Sloane, N.J.A.: The theory of error-correcting codes. North-Holland, Amsterdam (1977)

    MATH  Google Scholar 

  2. Lidl, R., Niederreiter, H.: Introduction to finite fields and their applications. Cambridge University Press, NewYork (1994)

    MATH  Google Scholar 

  3. Blahut, R.E.: Fast algorithms for digital signal processing. Addison-Wesley, Reading (1985)

    MATH  Google Scholar 

  4. Reed, I.S., Truong, T.K.: The use of finite fields to compute convolutions. IEEE Trans. Inf. Theory IT-21(2), 208–213 (1975)

    Article  MathSciNet  Google Scholar 

  5. Biham, E., Shamir, A.: Differential fault analysis of secret key cryptosystems. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 513–525. Springer, Heidelberg (1997)

    Google Scholar 

  6. Boneh, D., DeMillo, R.A., Lipton, R.J.: On the importance of checking cryptographic protocols for faults. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 37–51. Springer, Heidelberg (1997)

    Google Scholar 

  7. Kelsey, J., Schneier, B., Wagner, D., Hall, C.: Side channel cryptanalysis of product ciphers. In: Quisquater, J.-J., Deswarte, Y., Meadows, C., Gollmann, D. (eds.) ESORICS 1998. LNCS, vol. 1485, pp. 97–110. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  8. Fenn, S., Gossel, M., Benaissa, M., Taylor, D.: On-line error detection for bit-serial multipliers in GF(2m). Journal of Electronic Testing: Theory and Applications 13, 29–40 (1998)

    Article  Google Scholar 

  9. Bayat-Sarmadi, S., Hasan, M.A.: On concurrent detection of errors in polynomial basis multiplication. IEEE Trans. VLSI systems 15(4), 413–426 (2007)

    Article  Google Scholar 

  10. Chiou, C.W.: Concurrent error detection in array multipliers for GF(2m) fields. IEE Electronics Letters 38(14), 688–689 (2002)

    Article  Google Scholar 

  11. Lee, C.Y., Chiou, C.W., Lin, J.M.: Concurrent Error Detection in a Polynomial Basis Multiplier over GF(2m). Journal of Electronic Testing: Theory and Applications 22(2), 143–150 (2006)

    Article  Google Scholar 

  12. Chiou, C.W., Lee, C.Y., Deng, A.W., Lin, J.M.: Concurrent Error Detection In Montgomery Multiplication Over GF(2m). IEICE Trans. on Fundamentals of Electronics, Communications and Computer Science E89-A(2), 566–574 (2006)

    Article  Google Scholar 

  13. Yamamoto, H., Watanabe, T., Urano, Y.: Alternating logic and its application to fault detection. In: Proc. 1970 IEEE International Computing Group Conference, Washington, D.C., pp. 220–228 (June 1970)

    Google Scholar 

  14. Reynolds, D.A., Metze, G.: Fault detection capabilities of alternating logic. IEEE Trans. Computers 12(c-27), 1093–1098 (1978)

    Article  MathSciNet  Google Scholar 

  15. Woodard, S.E.: Design of digital systems using self-checking alternating logic. Ph.D. Thesis, University of Illinois at Urbana-Champaign, U.S.A (1977)

    Google Scholar 

  16. Siavash, B.-S., Hasan, M.A.: Concurrent Error Detection in Finite-Field Arithmetic Operations Using Pipelined and Systolic Architectures. IEEE Transactions on computers, 58(11) (November 2009)

    Google Scholar 

  17. Baker, R.J.: CMOS-circuit, design, layout, and simulation, 2nd edn. IEEE Press (2004)

    Google Scholar 

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Correspondence to Chi Hsiang Chang .

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Chang, C.H., Tuan, CC., Huang, WT., Chiou, C.W. (2012). On-Line Error Detection and Off-Line Test Design in Polynomial Basis Multiplier over GF(2m) Using Irreducible Trinomials. In: Zhu, M. (eds) Business, Economics, Financial Sciences, and Management. Advances in Intelligent and Soft Computing, vol 143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27966-9_104

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  • DOI: https://doi.org/10.1007/978-3-642-27966-9_104

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27965-2

  • Online ISBN: 978-3-642-27966-9

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