Abstract
Security-aware embedded devices which are likely to operate in hostile environments need protection against physical attacks. For the RSA public-key algorithm, protected versions of the Montgomery powering ladder have gained popularity as countermeasures for such attacks.
In this paper, we present a general fault attack against RSA implementations which use the Montgomery powering ladder. In a first step, we discuss under which realistic fault assumptions our observation can be used to attack basic implementations. In a second step, we extend our attack to a scenario, where the message is blinded at the beginning of the exponentiation algorithm. To the best of our knowledge this is the first fault attack on a blinded Montgomery powering ladder.
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
Boneh, D., DeMillo, R.A., Lipton, R.J.: On the Importance of Checking Cryptographic Protocols for Faults (Extended Abstract). In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 37–51. Springer, Heidelberg (1997)
Boreale, M.: Attacking right-to-left modular exponentiation with timely random faults. In: Breveglieri, L., Koren, I., Naccache, D., Seifert, J.-P. (eds.) FDTC 2006. LNCS, vol. 4236, pp. 24–35. Springer, Heidelberg (2006)
Schmidt, J.M., Herbst, C.: A Practical Fault Attack on Square and Multiply. In: Breveglieri, L., Gueron, S., Koren, I., Naccache, D., Seifert, J.P. (eds.) Proceedings of Fifth International Workshop on Fault Diagnosis and Tolerance in Cryptography, FDTC 2008, August 10, pp. 53–58. IEEE Computer Society, Washington DC, USA (2008)
Kocher, P.C.: Timing attacks on implementations of diffie-hellman, RSA, DSS, and other systems. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 104–113. Springer, Heidelberg (1996)
Kocher, P.C., Jaffe, J., Jun, B.: Differential power analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)
Schmidt, J.M., Medwed, M.: A Fault Attack on ECDSA. In: Naccache, D., Oswald, E. (eds.) Procceedings of Sixth International Workshop on Fault Diagnosis and Tolerance in Cryptography, FDTC 2009, Lausanne, Switzerland, September 6, pp. 93–99. IEEE-CS Press, Los Alamitos (2009)
Park, J., Bae, K., Moon, S., Choi, D., Kang, Y., Ha, J.: A New Fault Cryptanalysis on Montgomery Ladder Exponentiation Algorithm. In: Proceedings of the 2nd International Conference on Interaction Sciences: Information Technology, Culture and Human. ACM International Conference Proceeding Series, vol. 403, pp. 896–899. ACM Press, New York (2009)
Fumaroli, G., Vigilant, D.: Blinded fault resistant exponentiation. In: Breveglieri, L., Koren, I., Naccache, D., Seifert, J.P. (eds.) FDTC 2006. LNCS, vol. 4236, pp. 62–70. Springer, Heidelberg (2006)
Joye, M., Yen, S.M.: The Montgomery Powering Ladder. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 291–302. Springer, Heidelberg (2003)
Menezes, A.J., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. Series on Discrete Mathematics and its Applications. CRC Press, Boca Raton (1997), http://www.cacr.math.uwaterloo.ca/hac/ , ISBN 0-8493-8523-7
Yen, S.M., Joye, M.: Checking Before Output May Not Be Enough Against Fault-Based Cryptanalysis. In: IEEE Transactions on Computers, vol. 49, pp. 967–970. IEEE Computer Society, Los Alamitos (2000)
Skorobogatov, S.P., Anderson, R.J.: Optical Fault Induction Attacks. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 2–12. Springer, Heidelberg (2003)
Bar-El, H., Choukri, H., Naccache, D., Tunstall, M., Whelan, C.: The Sorcerer’s Apprentice Guide to Fault Attacks. Cryptology ePrint Archive Report 2004/100 (2004), http://eprint.iacr.org/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schmidt, JM., Medwed, M. (2011). Fault Attacks on the Montgomery Powering Ladder. In: Rhee, KH., Nyang, D. (eds) Information Security and Cryptology - ICISC 2010. ICISC 2010. Lecture Notes in Computer Science, vol 6829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24209-0_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-24209-0_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24208-3
Online ISBN: 978-3-642-24209-0
eBook Packages: Computer ScienceComputer Science (R0)