Abstract
On an embedded device, an implementation of cryptographic operation, like an RSA modular exponentiation [12], can be attacked by side channel analysis. In particular, recent improvements on horizontal power analysis [3, 10] render ineffective the usual counter-measures which randomize the data at the very beginning of the computations [2, 4]. To counteract horizontal analysis it is necessary to randomize the computations all along the exponentiation. The leak resistant arithmetic (LRA) proposed in [1] implements modular arithmetic in residue number system (RNS) and randomizes the computations by randomly changing the RNS bases. We propose in this paper a variant of the LRA in RNS: we propose to change only one or a few moduli of the RNS basis. This reduces the cost of the randomization and makes it possible to be executed at each loop of a modular exponentiation.
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.
Similar content being viewed by others
References
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)
Ciet, M., Joye, M.: (Virtually) free randomization techniques for elliptic curve cryptography. In: Qing, S., Gollmann, D., Zhou, J. (eds.) ICICS 2003. LNCS, vol. 2836, pp. 348–359. Springer, Heidelberg (2003)
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)
Coron, J.-S.: Resistance against differential power analysis for elliptic curve cryptosystems. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 292–302. Springer, Heidelberg (1999)
Garner, H.L.: The Residue Number System. IRE Trans. on Elctronic Computers 8, 140–147 (1959)
Joye, M., Yen, S.-M.: The Montgomery Powering Ladder. In: Kaliski, B.S., Koç, K., Paar, C. (eds.) Cryptographic Hardware and Embedded Systems - CHES 2002. LNCS, vol. 2523, pp. 291–302. Springer, Heidelberg (2003)
Kawamura, S., Koike, M., Sano, F., Shimbo, A.: Cox-rower architecture for fast parallel montgomery multiplication. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 523–538. Springer, Heidelberg (2000)
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)
Montgomery, P.: Modular Multiplication Without Trial Division. Math. Computation, 519–521 (1985)
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)
Posch, K.C., Posch, R.: Modulo Reduction in Residue Number Systems. IEEE Trans. Parallel Distrib. Syst. 6(5), 449–454 (1995)
Rivest, R.L., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public-Key Cryptosystems. Communications of the ACM 21, 120–126 (1978)
Walter, C.D.: Sliding windows succumbs to big mac attack. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 286–299. Springer, Heidelberg (2001)
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
Negre, C., Perin, G. (2015). Trade-Off Approaches for Leak Resistant Modular Arithmetic in RNS. In: Foo, E., Stebila, D. (eds) Information Security and Privacy. ACISP 2015. Lecture Notes in Computer Science(), vol 9144. Springer, Cham. https://doi.org/10.1007/978-3-319-19962-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-19962-7_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19961-0
Online ISBN: 978-3-319-19962-7
eBook Packages: Computer ScienceComputer Science (R0)