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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Macwilliams, F.J., Sloane, N.J.A.: The theory of error-correcting codes. North-Holland, Amsterdam (1977)
Lidl, R., Niederreiter, H.: Introduction to finite fields and their applications. Cambridge University Press, NewYork (1994)
Blahut, R.E.: Fast algorithms for digital signal processing. Addison-Wesley, Reading (1985)
Reed, I.S., Truong, T.K.: The use of finite fields to compute convolutions. IEEE Trans. Inf. Theory IT-21(2), 208–213 (1975)
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)
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)
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)
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)
Bayat-Sarmadi, S., Hasan, M.A.: On concurrent detection of errors in polynomial basis multiplication. IEEE Trans. VLSI systems 15(4), 413–426 (2007)
Chiou, C.W.: Concurrent error detection in array multipliers for GF(2m) fields. IEE Electronics Letters 38(14), 688–689 (2002)
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)
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)
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)
Reynolds, D.A., Metze, G.: Fault detection capabilities of alternating logic. IEEE Trans. Computers 12(c-27), 1093–1098 (1978)
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)
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)
Baker, R.J.: CMOS-circuit, design, layout, and simulation, 2nd edn. IEEE Press (2004)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag GmbH Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: EngineeringEngineering (R0)