Abstract
In leakage-resilient symmetric cryptography, two important concepts have been proposed in order to decrease the success rate of differential side-channel attacks. The first one is to limit the attacker’s data complexity by restricting the number of observable inputs; the second one is to create correlated algorithmic noise by using parallel S-boxes with equal inputs. The latter hinders the typical divide and conquer approach of differential side-channel attacks and makes key recovery much more difficult in practice. The use of localized electromagnetic (EM) measurements has already been shown to limit the effectiveness of such measures in previous works based on PRESENT S-boxes and 90 nm FPGAs. However, it has been left for future investigation in recent publications based on AES S-boxes. We aim at providing helpful results and insights from LDA-preprocessed, multivariate, localized EM attacks against a 45 nm FPGA implementation using AES S-boxes. We show, that even in the case of densely placed S-boxes (with identical routing constraints), and even when limiting the data complexity to the minimum of only two inputs, the guessing entropy of the key is reduced to only \(2^{48}\), which remains well within the key enumeration capabilities of today’s adversaries. Relaxing the S-box placement constraints further reduces the guessing entropy. Also, increasing the data complexity for efficiency, decreases it down to a direct key recovery. While our results are empirical and reflective of one device and implementation, they emphasize the threat of multivariate localized EM attacks to such AES-based leakage-resilient constructions, more than currently believed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Reducing the data complexity to 1 would mean that only a single observation (with possibly unlimited measurement complexity) would be available to adversaries. This corresponds to a simple power analysis attack scenario which is not generally considered in most contributions in the field of leakage-resilient cryptography.
- 2.
This corresponds to the ranking of the key after a practical laboratory evaluation using localized EM, where the order of the key bytes is discovered during the attacks, but not all correct subkeys are ranked first. In contrast, the previously mentioned \(2^{44}\) corresponds to the remaining search complexity of global attacks, once all key bytes are assumed to be ranked first, despite the correlated algorithmic noise (theoretical best case).
- 3.
The equations show the calculation of the transformation matrix for one S-box. We omitted an additional identifier for the S-box number for the sake of clarity.
- 4.
We used OFB mode, but other modes would work as well.
References
Archambeau, C., Peeters, E., Standaert, F.-X., Quisquater, J.-J.: Template attacks in principal subspaces. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol. 4249, pp. 1–14. Springer, Heidelberg (2006). doi:10.1007/11894063_1
Belaïd, S., De Santis, F., Heyszl, J., Mangard, S., Medwed, M., Schmidt, J.M., Standaert, F.X., Tillich, S.: Towards fresh re-keying with leakage-resilient PRFs: cipher design principles and analysis. J. Cryptograph. Eng. 4(3), 157–171 (2014)
Belaïd, S., Grosso, V., Standaert, F.X.: Masking and leakage-resilient primitives: one, the other(s) or both? Crypt. Commun. 7(1), 163–184 (2015)
Bruneau, N., Guilley, S., Heuser, A., Marion, D., Rioul, O.: Less is more. In: Güneysu, T., Handschuh, H. (eds.) CHES 2015. LNCS, vol. 9293, pp. 22–41. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48324-4_2
Canright, D.: A very compact S-box for AES. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 441–455. Springer, Heidelberg (2005). doi:10.1007/11545262_32
Choudary, O., Kuhn, M.G.: Efficient template attacks. In: Francillon, A., Rohatgi, P. (eds.) CARDIS 2013. LNCS, vol. 8419, pp. 253–270. Springer, Cham (2014). doi:10.1007/978-3-319-08302-5_17
Choudary, O., Kuhn, M.G.: Template attacks on different devices. In: Prouff, E. (ed.) COSADE 2014. LNCS, vol. 8622, pp. 179–198. Springer, Cham (2014). doi:10.1007/978-3-319-10175-0_13
Fisher, R.A.: The use of multiple measurements in taxonomic problems. Ann. Eugenics 7(7), 179–188 (1936)
Gammel, B., Fischer, W., Mangard, S.: Generating a session key for authentication and secure data transfer. US Patent 2014016955, 7 November 2013
Glowacz, C., Grosso, V., Poussier, R., Schüth, J., Standaert, F.-X.: Simpler and more efficient rank estimation for side-channel security assessment. In: Leander, G. (ed.) FSE 2015. LNCS, vol. 9054, pp. 117–129. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48116-5_6
Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. J. ACM (JACM) 33(4), 792–807 (1986)
Heyszl, J., Mangard, S., Heinz, B., Stumpf, F., Sigl, G.: Localized electromagnetic analysis of cryptographic implementations. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 231–244. Springer, Heidelberg (2012). doi:10.1007/978-3-642-27954-6_15
Kirschbaum, M.: Power analysis resistant logic styles - design, implementation, and evaluation. Ph.D. thesis (2011)
Kocher, P.C.: Leak-resistant cryptographic indexed key update, US Patent 6,539,092, 25 March 2003
Mangard, S., Oswald, E., Popp, T.: Power Analysis Attacks. Springer, New York (2008)
Medwed, M., Standaert, F.-X., Großschädl, J., Regazzoni, F.: Fresh re-keying: security against side-channel and fault attacks for low-cost devices. In: Bernstein, D.J., Lange, T. (eds.) AFRICACRYPT 2010. LNCS, vol. 6055, pp. 279–296. Springer, Heidelberg (2010). doi:10.1007/978-3-642-12678-9_17
Medwed, M., Standaert, F.-X., Joux, A.: Towards super-exponential side-channel security with efficient leakage-resilient PRFs. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 193–212. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33027-8_12
Medwed, M., Standaert, F.-X., Nikov, V., Feldhofer, M.: Unknown-input attacks in the parallel setting: improving the security of the CHES 2012 leakage-resilient PRF. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 602–623. Springer, Heidelberg (2016). doi:10.1007/978-3-662-53887-6_22
Petit, C., Standaert, F.X., Pereira, O., Malkin, T.G., Yung, M.: A block cipher based pseudo random number generator secure against side-channel key recovery. In: Proceedings of the 2008 ACM Symposium on Information, Computer and Communications Security, pp. 56–65. ACM (2008)
Pietrzak, K.: A leakage-resilient mode of operation. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 462–482. Springer, Heidelberg (2009). doi:10.1007/978-3-642-01001-9_27
Standaert, F.-X., Archambeau, C.: Using subspace-based template attacks to compare and combine power and electromagnetic information leakages. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 411–425. Springer, Heidelberg (2008). doi:10.1007/978-3-540-85053-3_26
Standaert, F.-X., Pereira, O., Yu, Y.: Leakage-resilient symmetric cryptography under empirically verifiable assumptions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 335–352. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40041-4_19
Standaert, F.X., Pereira, O., Yu, Y., Quisquater, J.J., Yung, M., Oswald, E.: Leakage resilient cryptography in practice. In: Sadeghi, A.R., Naccache, D. (eds.) Towards Hardware-Intrinsic Security. Information Security and Cryptography, pp. 99–134. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14452-3_5
Taha, M.M.I., Schaumont, P.: Key updating for leakage resiliency with application to AES modes of operation. IEEE Trans. Inf. Forensics Secur. 10(3), 519–528 (2015)
Acknowledgements
The work presented in this contribution was supported by the German Federal Ministry of Education and Research in the project ALESSIO through grant number 16KIS0629.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendices
A Floorplanning
Layout of one S-box in the Xilinx IDE.
Position of 16 S-boxes on the floorplan of the Xilinx Spartan 6 FPGA. The entire AES is placed within the black box.
B SNR Heat Maps for All S-Boxes
SNR heat maps of unconstrained placement.
SNR heat maps of dense hard-macro placement.
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Unterstein, F., Heyszl, J., De Santis, F., Specht, R. (2017). Dissecting Leakage Resilient PRFs with Multivariate Localized EM Attacks. In: Guilley, S. (eds) Constructive Side-Channel Analysis and Secure Design. COSADE 2017. Lecture Notes in Computer Science(), vol 10348. Springer, Cham. https://doi.org/10.1007/978-3-319-64647-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-64647-3_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-64646-6
Online ISBN: 978-3-319-64647-3
eBook Packages: Computer ScienceComputer Science (R0)