Abstract
Threshold implementations have emerged as one of the most popular masking countermeasures for hardware implementations of cryptographic primitives. In this work, we first provide a generic construction for \(d+1\) TI sharing which achieves the minimal number of output shares for any n-input Boolean function of degree \(t=n-1\) and for any d. Secondly, we demonstrate the applicability of our results on a first-order and second-order \(d+1\) low-latency PRINCE implementation.
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Banik, S., et al.: Midori: a block cipher for low energy. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9453, pp. 411–436. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48800-3_17
Bertoni, G., Daemen, J., Peeters, M., Assche, G.V.: The Keccak reference, January 2011. http://keccak.noekeon.org/
Bilgin, B., Gierlichs, B., Nikova, S., Nikov, V., Rijmen, V.: Higher-order threshold implementations. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 326–343. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45608-8_18
Bilgin, B., Nikova, S., Nikov, V., Rijmen, V., Stütz, G.: Threshold implementations of all \(3 \times 3\) and \(4 \times 4\) S-boxes. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 76–91. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33027-8_5
Bogdanov, A., et al.: PRESENT: an ultra-lightweight block cipher. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 450–466. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74735-2_31
Borghoff, J., et al.: PRINCE – a low-latency block cipher for pervasive computing applications. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 208–225. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34961-4_14
Cooper, J., DeMulder, E., Goodwill, G., Jaffe, J., Kenworthy, G., Rohatgi, P.: Test Vector Leakage Assessment (TVLA) methodology in practice. In: International Cryptographic Module Conference (2013)
Groß, H., Iusupov, R., Bloem, R.: Generic low-latency masking in hardware. IACR Trans. Cryptogr. Hardw. Embed. Syst.-TCHES 2, 1–21 (2018)
Gross, H., Mangard, S.: Reconciling \(d+1\) masking in hardware and software. In: Fischer, W., Homma, N. (eds.) CHES 2017. LNCS, vol. 10529, pp. 115–136. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66787-4_6
Groß, H., Mangard, S., Korak, T.: Domain-oriented masking: compact masked hardware implementations with arbitrary protection order. In: Proceedings of the ACM Workshop on Theory of Implementation Security, TIS@CCS 2016, Vienna, Austria, p. 3, October 2016
Ishai, Y., Sahai, A., Wagner, D.: Private circuits: securing hardware against probing attacks. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 463–481. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45146-4_27
Knežević, M., Nikov, V., Rombouts, P.: Low-latency encryption – is “Lightweight = Light + Wait”? In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 426–446. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33027-8_25
Moos, T., Moradi, A., Schneider, T., Standaert, F.X.: Glitch-resistant masking revisited - or why proofs in the robust probing model are needed. IACR Trans. Cryptogr. Hardw. Embed. Syst.-TCHES 2, 256–292 (2019)
Moradi, A., Schneider, T.: Side-channel analysis protection and low-latency in action. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 517–547. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_19
Nikova, S., Rechberger, C., Rijmen, V.: Threshold Implementations against side-channel attacks and glitches. In: Ning, P., Qing, S., Li, N. (eds.) ICICS 2006. LNCS, vol. 4307, pp. 529–545. Springer, Heidelberg (2006). https://doi.org/10.1007/11935308_38
Poschmann, A., Moradi, A., Khoo, K., Lim, C.W., Wang, H., Ling, S.: Side-channel resistant crypto for less than 2,300 GE. J. Cryptol. 24(2), 322–345 (2011). https://doi.org/10.1007/s00145-010-9086-6
Reparaz, O., Bilgin, B., Nikova, S., Gierlichs, B., Verbauwhede, I.: Consolidating masking schemes. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 764–783. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47989-6_37
Reparaz, O., Gierlichs, B., Verbauwhede, I.: Fast leakage assessment. In: Fischer, W., Homma, N. (eds.) CHES 2017. LNCS, vol. 10529, pp. 387–399. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66787-4_19
Ueno, R., Homma, N., Aoki, T.: A systematic design of tamper-resistant Galois-field arithmetic circuits based on threshold implementation with (d + 1) input shares. In: 2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL), pp. 136–141 (2017)
Ueno, R., Homma, N., Aoki, T.: Toward more efficient DPA-resistant AES hardware architecture based on threshold implementation. In: Guilley, S. (ed.) COSADE 2017. LNCS, vol. 10348, pp. 50–64. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-64647-3_4
Acknowledgements
We would like to thank Amir Moradi and Tobias Schneider for providing us with HDL code of PRINCE TI presented in [14]. Also we would like to thank the reviewers for helping us to improve the paper.
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Božilov, D., Knežević, M., Nikov, V. (2020). Optimized Threshold Implementations: Minimizing the Latency of Secure Cryptographic Accelerators. In: Belaïd, S., Güneysu, T. (eds) Smart Card Research and Advanced Applications. CARDIS 2019. Lecture Notes in Computer Science(), vol 11833. Springer, Cham. https://doi.org/10.1007/978-3-030-42068-0_2
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