Abstract
At ACISP 2004, Giraud and Knudsen presented the first fault analysis of DSA, ECDSA, XTR-DSA, Schnorr and ElGamal signatures schemes that considered faults affecting one byte. They showed that 2304 faulty signatures would be expected to reduce the number of possible keys to 240, allowing a 160-bit private key to be recovered. In this paper we show that Giraud and Knudsen’s fault attack is much more efficient than originally claimed. We prove that 34.3% less faulty signatures are required to recover a private key using the same fault model. We also show that their original way of expressing the fault model under a system of equations can be improved. A more precise expression allows us to obtain another improvement of up to 47.1%, depending on the values of the key byte affected.
Chapter PDF
Similar content being viewed by others
References
Bao, F., Deng, R., Han, Y., Jeng, A., Narasimhalu, A.D., Ngair, T.-H.: Breaking Public Key Cryptosystems an Tamper Resistance Devices in the Presence of Transient Fault. In: Christianson, B., Lomas, M. (eds.) Security Protocols 1997. LNCS, vol. 1361, pp. 115–124. Springer, Heidelberg (1998)
Bar-El, H., Choukri, H., Naccache, D., Tunstall, M., Whelan, C.: The Sorcerer’s Apprentice Guide to Fault Attacks. IEEE 94(2), 370–382 (2006)
Bellcore. New Threat Model Breaks Crypto Codes. Press Release (September 1996)
Biham, E., Shamir, A.: Differential Fault Analysis of Secret Key Cryptosystem. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 513–525. Springer, Heidelberg (1997)
Boneh, D., DeMillo, R., Lipton, R.: On the Importance of Checking Cryptographic Protocols for Faults. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 37–51. Springer, Heidelberg (1997)
Dottax, E.: Fault Attacks on NESSIE Signature and Identification Schemes. Technical report, NESSIE (October 2002)
ElGamal, T.: A Public-Key Cryptosystems and a Signature Scheme based on Discret Logarithms. IEEE Transaction on Information Theory 31(4), 172–469 (1985)
FIPS PUB 186-3. Digital Signature Standard. National Institute of Standards and Technology, Draft (March 2006)
Giraud, C., Knudsen, E.: Fault Attacks on Signature Schemes. In: Wang, H., Pieprzyk, J., Varadharajan, V. (eds.) ACISP 2004. LNCS, vol. 3108, pp. 478–491. Springer, Heidelberg (2004)
Giraud, C., Thiebeauld, H.: A Survey on Fault Attacks. In: Quisquater, J.-J., Paradinas, P., Deswarte, Y., Kalam, A.E. (eds.) Smart Card Research and Advanced Applications VI – CARDIS 2004, pp. 159–176. Kluwer Academic Publishers, Dordrecht (2004)
Joye, M., Lenstra, A., Quisquater, J.-J.: Chinese Remaindering Based Cryptosystems in the Presence of Faults. Journal of Cryptology 12(4), 241–245 (1999)
Joye, M., Quisquater, J.-J., Bao, F., Deng, R.: RSA-type Signatures in the Presence of Transient Faults. In: Darnell, M.J. (ed.) Cryptography and Coding 1997. LNCS, vol. 1355, pp. 155–160. Springer, Heidelberg (1997)
Lenstra, A.: Memo on RSA Signature Generation in the Presence of Faults. Manuscript (1996)
Lenstra, A., Verheul, E.: An Overview of the XTR Public Key System. In: Alster, K., Urbanowicz, J., Williams, H. (eds.) Public Key Cryptography and Computational Number Theory, de Gruyter, pp. 151–180 (2000)
Naccache, D., Nguyen, P., Tunstall, M., Whelan, C.: Experimenting with Faults, Lattices and the DSA. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 16–28. Springer, Heidelberg (2005)
Saha, D., Mukhopadhyay, D., RoyChowdhury, D.: A Diagonal Fault Attack on the Advanced Encryption Standard. Cryptology ePrint Archive, Report 2009/581 (2009), http://eprint.iacr.org/
Schnorr, C.: Efficient Identification and Signatures for Smart Cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, Heidelberg (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Giraud, C., Knudsen, E.W., Tunstall, M. (2010). Improved Fault Analysis of Signature Schemes. In: Gollmann, D., Lanet, JL., Iguchi-Cartigny, J. (eds) Smart Card Research and Advanced Application. CARDIS 2010. Lecture Notes in Computer Science, vol 6035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12510-2_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-12510-2_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12509-6
Online ISBN: 978-3-642-12510-2
eBook Packages: Computer ScienceComputer Science (R0)