Abstract
The single-shot collision attack on RSA proposed by Hanley et al. is studied focusing on the difference between two operands of multipliers. There are two consequences. Firstly, designing order of operands can be a cost-effective countermeasure.We show a concrete example in which operand order determines success and failure of the attack. Secondly, countermeasures can be ineffective if the asymmetric leakage is considered. In addition to the main results, the attack by Hanley et al. is extended using the signal-processing technique of the big mac attack. An experimental result to successfully analyze an FPGA implementation of RSA with the multiply-always method is also presented.
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
Notes
- 1.
Clavier et al. proposed another single-shot extension [15]. The purpose of the attack is to distinguish multiplication and squaring. There is a practical result on a software implementation.
- 2.
The method can be thought as a missing variant with “regular algorithm + unknown message” in the categorization by Bauer et al. [10].
- 3.
Note that Walter and Samyde noticed that leakage from the Booth recoding is not the one by the Hamming-weight model [13]. However, the difference between operands was not discussed.
- 4.
Hanley et al. considered more general cases considering a collision between input and output. However, the input-output collision was very weak in our setup.
References
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)
Mangard, S., Oswald, E., Popp, T.: Power Analysis Attacks: Revealing the Secrets of Smart Cards. Springer-Verlag, New York (2007)
Coron, J.-S.: Resistance against differential power analysis for elliptic curve cryptosystems. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, p. 292. Springer, Heidelberg (1999)
Amiel, F., Feix, B., Tunstall, M., Whelan, C., Marnane, W.P.: Distinguishing multiplications from squaring operations. In: Avanzi, R.M., Keliher, L., Sica, F. (eds.) SAC 2008. LNCS, vol. 5381, pp. 346–360. Springer, Heidelberg (2009)
Homma, N., Miyamoto, A., Aoki, T., Satoh, A., Shamir, A.: Collision-based power analysis of modular exponentiation using chosen-message pairs. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 15–29. Springer, Heidelberg (2008)
Heyszl, J., Ibing, A., Mangard, S., De Santis, F., Sigl, G.: Clustering algorithms for non-profiled single-execution attacks on exponentiations. In: Francillon, A., Rohatgi, P. (eds.) CARDIS 2013. LNCS, vol. 8419, pp. 79–93. Springer, Heidelberg (2014)
Perin, G., Imbert, L., Torres, L., Maurine, P.: Attacking randomized exponentiations using unsupervised learning. In: Prouff, E. (ed.) COSADE 2014. LNCS, vol. 8622, pp. 144–160. Springer, Heidelberg (2014)
Hanley, N., Kim, H.,Tunstall, M.: Exploiting collisions in addition chain-based exponentiation algorithms using a single trace. Cryptography ePrint Archive: Report 2012/485. http://eprint.iacr.org/2012/485
Clavier, C., Feix, B., Gagnerot, G., Roussellet, M., Verneuil, V.: Horizontal correlation analysis on exponentiation. In: Soriano, M., Qing, S., López, J. (eds.) ICICS 2010. LNCS, vol. 6476, pp. 46–61. Springer, Heidelberg (2010)
Bauer, A., Jaulmes, E., Prouff, E., Wild, J.: Horizontal and vertical side-channel attacks against secure RSA implementations. In: Dawson, E. (ed.) CT-RSA 2013. LNCS, vol. 7779, pp. 1–17. Springer, Heidelberg (2013)
Bajard, J.-C., Imbert, L., Liardet, P.-Y., Teglia, Y.: Leak resistant arithmetic. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 62–75. Springer, Heidelberg (2004)
Walter, C.D.: Sliding windows succumbs to Big Mac attack. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, p. 286. Springer, Heidelberg (2001)
Walter, C.D.,Samyde, D.: Data Dependent Power Use in Multipliers. In: 17thIEEE Symposium on Computer Arithmetic (ARITH 2005)
Witteman, M.F., van Woudenberg, J.G.J., Menarini, F.: Defeating RSA multiply-always and message blinding countermeasures. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 77–88. Springer, Heidelberg (2011)
Clavier, C., Feix, B., Gagnerot, G., Giraud, C., Roussellet, M., Verneuil, V.: ROSETTA for single trace analysis. In: Galbraith, S., Nandi, M. (eds.) INDOCRYPT 2012. LNCS, vol. 7668, pp. 140–155. Springer, Heidelberg (2012)
Koç, C.K., Acar, T., Kaliski Jr, B.S.: Analyzing and comparing montgomery multiplication algorithms. Micro, IEEE 16(3), 26–33 (1996)
Koren, I.: Computer Arithmetic Algorithms, 2nd edn. A K Peters, CRC Press, Boston, Boca Raton (2001)
Sugawara, T., Suzuki, D., Saeki, M., Shiozaki, M., Fujino, T.: On measurable side-channel leaks inside ASIC design primitives. In: Bertoni, G., Coron, J.-S. (eds.) CHES 2013. LNCS, vol. 8086, pp. 159–178. Springer, Heidelberg (2013)
Okeya, K., Sakurai, K.: A second-order DPA attack breaks a window-method based countermeasure against side channel attacks. In: Chan, A.H., Gligor, V.D. (eds.) ISC 2002. LNCS, vol. 2433, p. 389. Springer, Heidelberg (2002)
AIST, Side-Channel Attack Standard Evaluation Board. http://www.risec.aist.go.jp/project/sasebo/
Acknowledgement
The authors would like to thank the anonymous reviewers at COSADE 2015 for their valuable comments. The study was conducted as a part of the CREST Dependable VLSI Systems Project funded by the Japan Science and Technology Agency.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Sugawara, T., Suzuki, D., Saeki, M. (2015). Two Operands of Multipliers in Side-Channel Attack. In: Mangard, S., Poschmann, A. (eds) Constructive Side-Channel Analysis and Secure Design. COSADE 2015. Lecture Notes in Computer Science(), vol 9064. Springer, Cham. https://doi.org/10.1007/978-3-319-21476-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-21476-4_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21475-7
Online ISBN: 978-3-319-21476-4
eBook Packages: Computer ScienceComputer Science (R0)