Abstract
Binary field multiplication is the most fundamental building block of binary field Elliptic Curve Cryptography (ECC) and Galois/Counter Mode (GCM). Both bit-wise scanning and Look-Up Table (LUT) based methods are commonly used for binary field multiplication. In terms of Side Channel Attack (SCA), bit-wise scanning exploits insecure branch operations which leaks information in a form of timing and power consumption. On the other hands, LUT based method is regarded as a relatively secure approach because LUT access can be conducted in a regular and atomic form. This ensures a constant time solution as well. In this paper, we conduct the SCA on the LUT based binary field multiplication. The attack exploits the horizontal Correlation Power Analysis (CPA) on weights of LUT. We identify the operand with only a power trace of binary field multiplication. In order to prevent SCA, we also suggest a mask based binary field multiplication which ensures a regular and constant time solution without LUT and branch statements.
This work was partly supported by Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government (MSIP) (No.10043907, Development of high performance IoT device and Open Platform with Intelligent Software) and the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the ITRC(Information Technology Research Center) support program (IITP-2015-H8501-15-1017) supervised by the IITP(Institute for Information & communications Technology Promotion).
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Normally the degree (t) is set to 4 to get 16 cases because degree 8 needs too large LUT (\(2^{8}=256\)). Since the other degrees including (5, 6, 7) are not the power of two, they are inefficient over 8, 16 or 32-bit machine.
References
Aranha, D.F., Dahab, R., López, J., Oliveira, L.B.: Efficient implementation of elliptic curve cryptography in wireless sensors. Adv. Math. Comm. 4(2), 169–187 (2010)
Brier, E., Clavier, C., Olivier, F.: Correlation power analysis with a leakage model. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 16–29. Springer, Heidelberg (2004)
Chari, S., Jutla, C.S., Rao, J.R., Rohatgi, P.: Towards sound approaches to counteract power-analysis attacks. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 398–412. Springer, Heidelberg (1999)
Chen, C.-N.: Memory address side-channel analysis on exponentiation. In: Lee, J., Kim, J. (eds.) ICISC 2014. LNCS, vol. 8949, pp. 421–432. Springer, Heidelberg (2014)
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)
Gouvêa, C.P.L., López, J.: Implementing GCM on ARMv8. In: Nyberg, K. (ed.) CT-RSA 2015. LNCS, vol. 9048, pp. 167–180. Springer, Heidelberg (2015)
Gueron, S.: AES-GCM software performance on the current high end CPUs as a performance baseline for CAESAR competition
Gueron, S., Kounavis, M.E.: Intel\(\textregistered \) carry-less multiplication instruction and its usage for computing the GCM mode. Intel white paper (2010), September 2012
Hankerson, D., Vanstone, S., Menezes, A.J.: Guide to Elliptic Curve Cryptography. Springer, New York (2004)
Kargl, A., Pyka, S., Seuschek, H.: Fast arithmetic on ATmega128 for elliptic curve cryptography. IACR Cryptology ePrint Archive 2008, 442 (2008)
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)
López, J., Dahab, R.: High-speed software multiplication in F2m. In: Roy, B., Okamoto, E. (eds.) INDOCRYPT 2000. LNCS, vol. 1977, pp. 203–212. Springer, Heidelberg (2000)
Messerges, T.S., Dabbish, E.A., Sloan, R.H.: Investigations of power analysis attacks on smartcards. In: USENIX workshop on smartcard technology, vol. 17, p. 17 (1999)
Oliveira, L.B., Aranha, D.F., Gouvêa, C.P., Scott, M., Câmara, D.F., López, J., Dahab, R.: TinyPBC: pairings for authenticated identity-based non-interactive key distribution in sensor networks. Comput. Commun. 34(3), 485–493 (2011)
Seo, H., Lee, Y., Kim, H., Park, T., Kim, H.: Binary and prime field multiplication for public key cryptography on embedded microprocessors. Secur. Commun. Netw. 7(4), 774–787 (2014)
Seo, H., Liu, Z., Choi, J., Kim, H.: Karatsuba-block-comb technique for elliptic curve cryptography over binary fields. Secur. Commun. Netw. 8(17), 3121–3130 (2015)
Seo, S.C., Han, D.-G., Kim, H.C., Hong, S.: TinyECCK: Efficient elliptic curve cryptography implementation over GF(2m) on 8-bit micaz mote. IEICE Trans. Inf. Syst. 91(5), 1338–1347 (2008)
Shirase, M., Miyazaki, Y., Takagi, T., Han, D.-G.: Efficient implementation of pairing-based cryptography on a sensor node. IEICE Trans. Inf. Syst. 92(5), 909–917 (2009)
Szczechowiak, P., Oliveira, L.B., Scott, M., Collier, M., Dahab, R.: NanoECC: testing the limits of elliptic curve cryptography in sensor networks. In: Verdone, R. (ed.) EWSN 2008. LNCS, vol. 4913, pp. 305–320. Springer, Heidelberg (2008)
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Seo, H. et al. (2016). Secure Binary Field Multiplication. In: Kim, Hw., Choi, D. (eds) Information Security Applications. WISA 2015. Lecture Notes in Computer Science(), vol 9503. Springer, Cham. https://doi.org/10.1007/978-3-319-31875-2_14
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DOI: https://doi.org/10.1007/978-3-319-31875-2_14
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