Abstract
In this paper, we propose a new method for fault tolerant computation over GF(2k) for use in public key cryptosystems. In particular, we are concerned with the active side channel attacks, i.e., fault attacks. We define a larger ring in which new computation is performed with encoded elements while arithmetic structure is preserved. Computation is decomposed into parallel, mutually independent, identical channels, so that fault effects do not spread to the other channels. By assuming certain fault models, our proposed model provides protection against their error propagation. Also, we provide an analysis of the error detection and correction capabilities of our proposed model.
This is a preview of subscription content, log in via an institution to check access.
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
Bao, F., Deng, R.H., Han, Y., Jeng, A.B., Narasimhalu, A.D., Ngair, T-H.: Breaking Public Key Cryptosystems on Tamper Resistant Devices in the Presence of Transient Faults. In: Christianson, B., Lomas, M. (eds.) Security Protocols. LNCS, vol. 1361, pp. 115–124. Springer, Heidelberg (1998)
Beckmann, P.E., Musicus, B.R.: Fast Fault-Tolerant Digital Convolution Using a Polynomial Residue Number System. IEEE Trans. Signal Processing 41(7), 2300–2313 (1993)
Boneh, D., DeMilo, R.A., Lipton, R.J.: On the Importance of Eliminating Errors in Cryotographic Computations. J. Cryptology 14, 101–119 (2001)
Gathen, J., Gerhard, J.: Modern Computer Algebra. Cambridge University Press, UK (1999)
Gaubatz, G., Sunar, B.: Robust Finite Field Arithmetic for Fault-Tolerant Public-Key Cryptography. In: 2005 Workshop on Fault Diagnosis and Tolerance in Cryptography, Edinburgh, Scotland (2005)
Imbert, L., Dimitrov, L.S., Jullien, G.A.: Fault-Tolerant Computation Over Replicated Finite Rings. IEEE Trans. Circuits Systems-I: Fundamental Theory and Applications 50(7), 858–864 (2003)
Kocher, P.C., Jaffe, J., Jun, B.: Differential Power Analysis. In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)
Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications. Cambridge University Press, London (1986)
Otto, M.: Fault Attacks and Countermeasures. PhD Thesis (2004)
Reed, I.S., Solomon, G.: Polynomial Codes over Certain Finite Fields. J. Society for Industrial and Applied Mathematics 8(2), 300–304 (1960)
Reyhani-Masoleh, A., Hasan, M.A.: Towards Fault-Tolerant Cryptographic Computations over Finite Fields. ACM Trans. Embedded Computing Systems 3(3), 593–613 (2004)
Welch, L., Berlekamp, E.R.: Error Corrections for Algebraic Block Codes. U.S. Patent 4 633 470 (1983)
Wicker, S.B., Bhargava, V.K.: Reed-Solomon Codes and Their Applications. IEEE Press, New York (1994)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Medoš, S., Boztaş, S. (2007). Fault-Tolerant Finite Field Computation in the Public Key Cryptosystems. In: Boztaş, S., Lu, HF.(. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2007. Lecture Notes in Computer Science, vol 4851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77224-8_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-77224-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77223-1
Online ISBN: 978-3-540-77224-8
eBook Packages: Computer ScienceComputer Science (R0)