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2016 | OriginalPaper | Buchkapitel

Optimizing S-Box Implementations for Several Criteria Using SAT Solvers

verfasst von : Ko Stoffelen

Erschienen in: Fast Software Encryption

Verlag: Springer Berlin Heidelberg

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Abstract

We explore the feasibility of applying SAT solvers to optimizing implementations of small functions such as S-boxes for multiple optimization criteria, e.g., the number of nonlinear gates and the number of gates. We provide optimized implementations for the S-boxes used in Ascon, ICEPOLE, Joltik/Piccolo, Keccak/Ketje/Keyak, LAC, Minalpher, PRIMATEs, Prøst, and RECTANGLE, most of which are candidates in the secound round of the CAESAR competition. We then suggest a new method to optimize for circuit depth and we make tooling publicly available to find efficient implementations for several criteria. Furthermore, we illustrate with the 5-bit S-box of PRIMATEs how multiple optimization criteria can be combined.

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Literatur
1.
Zurück zum Zitat Albrecht, M.R., Rechberger, C., Schneider, T., Tiessen, T., Zohner, M.: Ciphers for MPC and FHE. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 430–454. Springer, Heidelberg (2015) Albrecht, M.R., Rechberger, C., Schneider, T., Tiessen, T., Zohner, M.: Ciphers for MPC and FHE. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 430–454. Springer, Heidelberg (2015)
3.
Zurück zum Zitat Bard, G.V., Courtois, N.T., Jefferson, C.: Efficient methods for conversion and solution of sparse systems of low-degree multivariate polynomials over GF(2) via SAT-solvers. IACR Cryptology ePrint Archive, Report 2007/024 (2007). http://eprint.iacr.org/ Bard, G.V., Courtois, N.T., Jefferson, C.: Efficient methods for conversion and solution of sparse systems of low-degree multivariate polynomials over GF(2) via SAT-solvers. IACR Cryptology ePrint Archive, Report 2007/024 (2007). http://​eprint.​iacr.​org/​
7.
Zurück zum Zitat Boyar, J., Matthews, P., Peralta, R.: On the shortest linear straight-line program for computing linear forms. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 168–179. Springer, Heidelberg (2008)CrossRef Boyar, J., Matthews, P., Peralta, R.: On the shortest linear straight-line program for computing linear forms. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 168–179. Springer, Heidelberg (2008)CrossRef
8.
Zurück zum Zitat Boyar, J., Peralta, R.: A new combinational logic minimization technique with applications to cryptology. In: Festa, P. (ed.) SEA 2010. LNCS, vol. 6049, pp. 178–189. Springer, Heidelberg (2010)CrossRef Boyar, J., Peralta, R.: A new combinational logic minimization technique with applications to cryptology. In: Festa, P. (ed.) SEA 2010. LNCS, vol. 6049, pp. 178–189. Springer, Heidelberg (2010)CrossRef
9.
Zurück zum Zitat Boyar, J., Peralta, R., Pochuev, D.: On the multiplicative complexity of Boolean functions over the basis \((\wedge,\oplus,1)\). Theoret. Comput. Sci. 235(1), 43–57 (2000)MathSciNetCrossRefMATH Boyar, J., Peralta, R., Pochuev, D.: On the multiplicative complexity of Boolean functions over the basis \((\wedge,\oplus,1)\). Theoret. Comput. Sci. 235(1), 43–57 (2000)MathSciNetCrossRefMATH
10.
Zurück zum Zitat Buchfuhrer, D., Umans, C.: The complexity of Boolean formula minimization. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 24–35. Springer, Heidelberg (2008)CrossRef Buchfuhrer, D., Umans, C.: The complexity of Boolean formula minimization. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 24–35. Springer, Heidelberg (2008)CrossRef
11.
Zurück zum Zitat Chambers, B., Manolios, P., Vroon, D.: Faster SAT solving with better CNF generation. In: Proceedings of the Conference on Design, Automation and Test in Europe, DATE 2009, 3001 Leuven, Belgium, Belgium, pp. 1590–1595. European Design and Automation Association (2009) Chambers, B., Manolios, P., Vroon, D.: Faster SAT solving with better CNF generation. In: Proceedings of the Conference on Design, Automation and Test in Europe, DATE 2009, 3001 Leuven, Belgium, Belgium, pp. 1590–1595. European Design and Automation Association (2009)
12.
Zurück zum Zitat Courtois, N., Hulme, D., Mourouzis, T.: Solving circuit optimisation problems in cryptography and cryptanalysis. Cryptology ePrint Archive, Report 2011/475 (2011). http://eprint.iacr.org/ Courtois, N., Hulme, D., Mourouzis, T.: Solving circuit optimisation problems in cryptography and cryptanalysis. Cryptology ePrint Archive, Report 2011/475 (2011). http://​eprint.​iacr.​org/​
13.
Zurück zum Zitat Courtois, N., Mourouzis, T., Hulme, D.: Exact logic minimization and multiplicative complexity of concrete algebraic and cryptographic circuits. Int. J. Adv. Intell. Syst. 6(3 and 4), 165–176 (2013) Courtois, N., Mourouzis, T., Hulme, D.: Exact logic minimization and multiplicative complexity of concrete algebraic and cryptographic circuits. Int. J. Adv. Intell. Syst. 6(3 and 4), 165–176 (2013)
15.
Zurück zum Zitat Fuhs, C., Schneider-Kamp, P.: Optimizing the AES S-box using SAT. In: IWIL@ LPAR, pp. 64–70. Citeseer (2010) Fuhs, C., Schneider-Kamp, P.: Optimizing the AES S-box using SAT. In: IWIL@ LPAR, pp. 64–70. Citeseer (2010)
16.
Zurück zum Zitat Fuhs, C., Schneider-Kamp, P.: Synthesizing shortest linear straight-line programs over GF(2) using SAT. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 71–84. Springer, Heidelberg (2010)CrossRef Fuhs, C., Schneider-Kamp, P.: Synthesizing shortest linear straight-line programs over GF(2) using SAT. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 71–84. Springer, Heidelberg (2010)CrossRef
20.
Zurück zum Zitat Mourouzis, T.: Optimizations in Algebraic and Differential Cryptanalysis. PhD thesis, UCL (University College London) (2015) Mourouzis, T.: Optimizations in Algebraic and Differential Cryptanalysis. PhD thesis, UCL (University College London) (2015)
22.
Zurück zum Zitat Shibutani, K., Isobe, T., Hiwatari, H., Mitsuda, A., Akishita, T., Shirai, T.: Piccolo: an ultra-lightweight blockcipher. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 342–357. Springer, Heidelberg (2011)CrossRef Shibutani, K., Isobe, T., Hiwatari, H., Mitsuda, A., Akishita, T., Shirai, T.: Piccolo: an ultra-lightweight blockcipher. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 342–357. Springer, Heidelberg (2011)CrossRef
24.
Zurück zum Zitat Zhang, W., Bao, Z., Lin, D., Rijmen, V., Yang, B., Verbauwhede, I.: RECTANGLE: a bit-slice ultra-lightweight block cipher suitable for multiple platforms. Cryptology ePrint Archive, Report 2014/084 (2014). http://eprint.iacr.org/ Zhang, W., Bao, Z., Lin, D., Rijmen, V., Yang, B., Verbauwhede, I.: RECTANGLE: a bit-slice ultra-lightweight block cipher suitable for multiple platforms. Cryptology ePrint Archive, Report 2014/084 (2014). http://​eprint.​iacr.​org/​
Metadaten
Titel
Optimizing S-Box Implementations for Several Criteria Using SAT Solvers
verfasst von
Ko Stoffelen
Copyright-Jahr
2016
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-52993-5_8