Geodesic
On the Bit-Slice representations of some nonlinear bijective transformations
Matematičeskie voprosy kriptografii, Tome 15 (2024) no. 1, pp. 97-125 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study how to obtain efficient Bit-Slice representations in some classes of nonlinear bijective transformations having almost optimal cryptographic properties. For some 8-bit instances belonging to these classes, we determine (by combining analytical methods with a open source tool) its low gate count logic circuit representations through binary logic operations $\mathtt{AND, XOR, OR}$ and $\mathtt{NOT}$. In particular, for the S-Box used in the Russian cryptographic standard GOST R 34.12-2015 "Kuznyechik”, we derive a Bit-Slice implementation which consume a total of 176 binary logical operations. The new representation requires 51 Boolean operations less than in previously known one (that need 227 bitwise logical operations, see, for example, [1]). 
@article{MVK_2024_15_1_a5,
     author = {O. C. Puente and R. F. Leal and R. A. de la Cruz Jim\'enez},
     title = {On the {Bit-Slice} representations of some nonlinear bijective transformations},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {97--125},
     year = {2024},
     volume = {15},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MVK_2024_15_1_a5/}
}
TY  - JOUR
AU  - O. C. Puente
AU  - R. F. Leal
AU  - R. A. de la Cruz Jiménez
TI  - On the Bit-Slice representations of some nonlinear bijective transformations
JO  - Matematičeskie voprosy kriptografii
PY  - 2024
SP  - 97
EP  - 125
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MVK_2024_15_1_a5/
LA  - en
ID  - MVK_2024_15_1_a5
ER  - 
%0 Journal Article
%A O. C. Puente
%A R. F. Leal
%A R. A. de la Cruz Jiménez
%T On the Bit-Slice representations of some nonlinear bijective transformations
%J Matematičeskie voprosy kriptografii
%D 2024
%P 97-125
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/MVK_2024_15_1_a5/
%G en
%F MVK_2024_15_1_a5
O. C. Puente; R. F. Leal; R. A. de la Cruz Jiménez. On the Bit-Slice representations of some nonlinear bijective transformations. Matematičeskie voprosy kriptografii, Tome 15 (2024) no. 1, pp. 97-125. http://geodesic.mathdoc.fr/item/MVK_2024_15_1_a5/

[1] Avraamova O. D., Fomin D. B., Serov V. A., Smirnov A. V., Shokov V. N., “A compact Bit-Sliced representation of Kuznyechik S-Box”, Matematicheskie voprosy kriptografii, 12:2 (2021), 21–38 | DOI | MR | Zbl

[2] Barreto P.S.L.M., Rijmen V., “The Whirlpool hashing function”, First open NESSIE Workshop (Leuven, Belgium, 2000), v. 13, 14

[3] Biham Eli, “A fast new DES implementation in software”, FSE 1997, Lect. Notes Comput. Sci., 1267, 1997, 260–272 | DOI | Zbl

[4] Biryukov A., Perrin L., Udovenko A., “Reverse engineering the S-Box of streebog, kuznyechik and STRIBOBr1”, EUROCRYPT 2016, Lect. Notes Comput. Sci., 9665, 2016, 372–402 | DOI | MR | Zbl

[5] Boyar J., Peralta R., “A new combinational logic minimization technique with applications to cryptology”, SEA 2010, Lect. Notes Comput. Sci., 6049, 2010, 178–189 | DOI

[6] Carlet C., Boolean Functions for Cryptography and Coding Theory, Cambridge Univ. Press, Cambridge, 2021 | DOI | MR | Zbl

[7] CircuitVerse simulator, 2023 } {\tt https://circuitverse.org

[8] Dansarie M., “sboxgates: A program for finding low gate count implementations of S-Boxes”, J. Open Source Software, 6(62) (2021), 2946 | DOI

[9] de la Cruz-Jiménez R. A., “Generation of 8-bit S-Boxes having almost optimal cryptographic properties using smaller 4-bit S-Boxes and finite field multiplication”, LATINCRYPT 2017, Lect. Notes Comput. Sci., 11368, 2017, 191–206 | DOI | MR

[10] de la Cruz-Jiménez R. A., On some methods for constructing almost optimal s-boxes and their resilience against side-channel attacks, Cryptology ePrint Archive, Report 2018/618, 2018 http://eprint.iacr.org/2016/493

[11] de la Cruz-Jiménez R. A., “Constructing $8$-bit permutations, $8$-bit involutions and $8$-bit orthomorphisms with almost optimal cryptographic parameters”, Matematicheskie voprosy kriptografii, 12:3 (2021), 89–124 | DOI | MR | Zbl

[12] Dygin D. M., Lavrikov I. V., Marshalko G. B., Rudskoy V. I., Trifonov D. I., Shishkin V. A., “On a new Russian Encryption Standard”, Matematicheskie voprosy kriptografii, 6:2 (2015), 29–34 | DOI | MR | Zbl

[13] Fomin D., Trifonov D., “Computational work for some TU-based permutations”, Current Trends in Cryptology (CTCrypt 2023), 2023 https://ctcrypt.ru/ematerials2023

[14] Ishai Y., Sahai A., Wagner D., “Private circuits: securing hardware against probing attacks”, CRYPTO 2003, Lect. Notes Comput. Sci., 2729, 2003, 463-481 | DOI | MR | Zbl

[15] Knuth D. E., Fascicle 6: Satisfiability, Art of computer programming, 19, Addison-Wesley, Reading, Mass., 2015 | MR

[16] Kwan M., Reducing the gate count of bitslice DES, Cryptology ePrint Archive, Report 2000/051, , 2000 https://eprint.iacr.org/2000/051

[17] Opirskyy I., Sovyn Y., Mykhailova O., “Heuristic method of finding bitliced-description of derivative cryptographic S-Box”, IEEE 16th Int. Conf. Adv. Trends in Radioelectr., Telecomm. Comput. Eng. (TCSET) (Lviv-Slavske, Ukraine, 2022), 104–109

[18] Zhenzhen B. et al., “Peigen - a platform for evaluation, implementation, and generation of S-boxes”, IACR Trans. Symm. Cryptology, 2019:1 (2019), 330–394

[19] PNST 799-2022. Informatsionnye tekhnologii. Kriptograficheskaya zaschita informatsii. Terminy i opredeleniya, Rossiiskii institut standartizatsii, M., 2024