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Abstract
The threat posed by side channels requires ciphers that can be efficiently protected in both software and hardware against such attacks. In this paper, we proposed a novel Sbox construction based on iterations of shift-invariant quadratic permutations and linear diffusions. Owing to the selected quadratic permutations, all of our Sboxes enable uniform 3-share threshold implementations, which provide first order SCA protections without any fresh randomness. More importantly, because of the “shift-invariant” property, there are ample implementation trade-offs available, in software as well as hardware. We provide implementation results (software and hardware) for a four-bit and an eight-bit Sbox, which confirm that our constructions are competitive and can be easily adapted to various platforms as claimed. We have successfully verified their resistance to first order attacks based on real acquisitions. Because there are very few studies focusing on software-based threshold implementations, our software implementations might be of independent interest in this regard.
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Notes
- 1.
Technically, glitches still exist within one instruction. However, the threat that glitches may bring—mixing between different data shares—does not usually show up.
- 2.
Note that here we only need\(x_0\) to appear, rather than appearing as a linear term [15].
- 3.
Unlike its hardware counterpart, “coupling” effect [28] and “voltage fluctuation” are not the only concerns for the software TI. An AND instruction may not have the same leakage as 32 1-bit-AND gates, unless all the other combinational logic cells in the ALU are actually “silent”.
- 4.
Note that this does not mean each Sbox can be computed only 109 cycles: if there is only one Sbox to compute, it will still take 870 cycles, as most of the bit-width will be wasted.
- 5.
Depending on the specific implementation, such “extra logic” can actually predominates the overall area cost. To this end, we would like the stress that our serial implementation is only worthwhile if it has a significant advantage in area cost.
References
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
Nikova, S., Rijmen, V., Schläffer, M.: Secure hardware implementation of nonlinear functions in the presence of glitches. J. Cryptol.24(2), 292–321 (2011)
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
De Meyer, L., Bilgin, B.: Classification of balanced quadratic functions. IACR Cryptology ePrint Archive, Report 2018/113 (2018)
Bozilov, D., Bilgin, B., Sahin, H.A.: A note on 5-bit quadratic permutations’ classification. IACR Trans. Symmetric Cryptol.2017(1), 398–404 (2017)
Beyne, T., Bilgin, B.: Uniform first-order threshold implementations. In: Avanzi, R., Heys, H. (eds.) SAC 2016. LNCS, vol. 10532, pp. 79–98. Springer, Cham (2017).https://doi.org/10.1007/978-3-319-69453-5_5
De Meyer, L., Moradi, A., Wegener, F.: Spin me right round rotational symmetry for FPGA-specific AES. IACR Trans. Cryptogr. Hardw. Embed. Syst.2018(3), 596–626 (2018)
Daemen, J.: Changing of the guards: a simple and efficient method for achieving uniformity in threshold sharing. In: Fischer, W., Homma, N. (eds.) CHES 2017. LNCS, vol. 10529, pp. 137–153. Springer, Cham (2017).https://doi.org/10.1007/978-3-319-66787-4_7
Boss, E., Grosso, V., Güneysu, T., Leander, G., Moradi, A., Schneider, T.: Strong 8-bit Sboxes with efficient masking in hardware extended version. J. Cryptogr. Eng.7(2), 149–165 (2017)
Meyer, L.D., Varici, K.: More constructions for strong 8-bit S-boxes with efficient masking in hardware. In: Proceedings of the 38th Symposium on Information Theory in the Benelux, Delft, NE, p. 11. Werkgemeenschap voor Informatie- en Communicatietheorie (2017)
Sasdrich, P., Bock, R., Moradi, A.: Threshold implementation in software. In: Fan, J., Gierlichs, B. (eds.) COSADE 2018. LNCS, vol. 10815, pp. 227–244. Springer, Cham (2018).https://doi.org/10.1007/978-3-319-89641-0_13
Jungk, B., Petri, R., Stottinger, M.: Efficient side-channel protections of ARX ciphers. IACR Trans. Cryptogr. Hardw. Embed. Syst.2018(3), 627–653 (2018)
Balasch, J., Gierlichs, B., Reparaz, O., Verbauwhede, I.: DPA, bitslicing and masking at 1 GHz. In: Güneysu, T., Handschuh, H. (eds.) CHES 2015. LNCS, vol. 9293, pp. 599–619. Springer, Heidelberg (2015).https://doi.org/10.1007/978-3-662-48324-4_30
de Groot, W., Papagiannopoulos, K., de La Piedra, A., Schneider, E., Batina, L.: Bitsliced masking and ARM: friends or foes? In: Bogdanov, A. (ed.) LightSec 2016. LNCS, vol. 10098, pp. 91–109. Springer, Cham (2017).https://doi.org/10.1007/978-3-319-55714-4_7
Daemen, J.: Cipher and hash function design, strategies based on linear and differential cryptanalysis. Ph.D. thesis, K. U. Leuven (1995).http://jda.noekeon.org/
Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: Keccak. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 313–314. Springer, Heidelberg (2013).https://doi.org/10.1007/978-3-642-38348-9_19
Kutzner, S., Nguyen, P.H., Poschmann, A., Wang, H.: On 3-share threshold implementations for 4-bit S-boxes. In: Prouff, E. (ed.) COSADE 2013. LNCS, vol. 7864, pp. 99–113. Springer, Heidelberg (2013).https://doi.org/10.1007/978-3-642-40026-1_7
Gupta, N., Jati, A., Chattopadhyay, A., Sanadhya, S.K., Chang, D.: Threshold implementations of GIFT: a trade-off analysis. IACR Cryptology ePrint Archive, Report 2017/1040 (2017)
Nyberg, K.: Differentially uniform mappings for cryptography. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 55–64. Springer, Heidelberg (1994).https://doi.org/10.1007/3-540-48285-7_6
Božilov, D., Bilgin, B., Sahin, H.: A note on 5-bit quadratic permutations’ classification. IACR Trans. Symmetric Cryptol.2017(1), 398–404 (2017)
Meyer, L.D., Bilgin, B.: Classification of balanced quadratic functions. Cryptology ePrint Archive, Report 2018/113 (2018).https://eprint.iacr.org/2018/113
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
Mariot, L., Picek, S., Leporati, A., Jakobovic, D.: Cellular automata based S-boxes. Cryptogr. Commun.11, 41–62 (2018)
Khovratovich, D., Nikolić, I.: Rotational cryptanalysis of ARX. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 333–346. Springer, Heidelberg (2010).https://doi.org/10.1007/978-3-642-13858-4_19
Leander, G., Poschmann, A.: On the classification of 4 bit S-boxes. In: Carlet, C., Sunar, B. (eds.) WAIFI 2007. LNCS, vol. 4547, pp. 159–176. Springer, Heidelberg (2007).https://doi.org/10.1007/978-3-540-73074-3_13
ARM: Arm and thumb-2 instruction set.http://infocenter.arm.com/help/topic/com.arm.doc.qrc0006e/QRC0006_UAL16.pdf
ARM: Thumb 16-bit instruction set.http://infocenter.arm.com/help/topic/com.arm.doc.qrc0001m/QRC0001_UAL.pdf
De Cnudde, T., Bilgin, B., Gierlichs, B., Nikov, V., Nikova, S., Rijmen, V.: Does coupling affect the security of masked implementations? In: Guilley, S. (ed.) COSADE 2017. LNCS, vol. 10348, pp. 1–18. Springer, Cham (2017).https://doi.org/10.1007/978-3-319-64647-3_1
Goudarzi, D., Rivain, M.: How fast can higher-order masking be in software? In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10210, pp. 567–597. Springer, Cham (2017).https://doi.org/10.1007/978-3-319-56620-7_20
Balasch, J., Gierlichs, B., Grosso, V., Reparaz, O., Standaert, F.-X.: On the cost of lazy engineering for masked software implementations. In: Joye, M., Moradi, A. (eds.) CARDIS 2014. LNCS, vol. 8968, pp. 64–81. Springer, Cham (2015).https://doi.org/10.1007/978-3-319-16763-3_5
Wegener, F., Moradi, A.: A first-order SCA resistant AES without fresh randomness. In: Fan, J., Gierlichs, B. (eds.) COSADE 2018. LNCS, vol. 10815, pp. 245–262. Springer, Cham (2018).https://doi.org/10.1007/978-3-319-89641-0_14
Bilgin, B., Gierlichs, B., Nikova, S., Nikov, V., Rijmen, V.: Trade-offs for threshold implementations illustrated on AES. IEEE Trans. CAD Integr. Circuits Syst.34(7), 1188–1200 (2015)
Goodwill, G., Jun, B., Jaffe, J., Rohatgi, P.: A testing methodology for side channel resistance validation. Technical report, CRI (2011)
Ding, A.A., Zhang, L., Durvaux, F., Standaert, F.-X., Fei, Y.: Towards sound and optimal leakage detection procedure. In: Eisenbarth, T., Teglia, Y. (eds.) CARDIS 2017. LNCS, vol. 10728, pp. 105–122. Springer, Cham (2018).https://doi.org/10.1007/978-3-319-75208-2_7
Acknowledgements
We would like to thank all anonymous reviewers for improving the quality of this paper as well as providing insights from some other perspectives. This work has been funded in part by EPSRC under grant agreement EP/N011635/1 (LADA).
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University of Bristol, Bristol, UK
Si Gao, Arnab Roy & Elisabeth Oswald
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Gao, S., Roy, A., Oswald, E. (2019). Constructing TI-Friendly Substitution Boxes Using Shift-Invariant Permutations. In: Matsui, M. (eds) Topics in Cryptology – CT-RSA 2019. CT-RSA 2019. Lecture Notes in Computer Science(), vol 11405. Springer, Cham. https://doi.org/10.1007/978-3-030-12612-4_22
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