Geodesic
Some conditions for the applicability of the integral cryptanalysis to $4$-rounds of AES-like ciphers
Prikladnaya Diskretnaya Matematika. Supplement, no. 15 (2022), pp. 57-62 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A number of necessary conditions and one sufficient condition are obtained so that the integral cryptanalysis can be applied to block algorithms constructed similarly to the AES algorithm (i.e., SQUARE, Rijndael, Crypton) with a reduced number of rounds to four, which are denoted as $f_1,f_2,f_3,f_4$. For example, it was proved that if we consider the multiset $\{y_{j}(x)\in V_{8}:x\in I_{i}\}$, where $I_{i} =\{(B_{0},\ldots,B_{i-1},z,B_{i+1},\ldots,B_{15}):z\in V_{8}\}$, the subvector $B_{i} =z$, $i\in\{0,\ldots,15\}$, takes all possible values from $V_{8}$, and the other data block subvectors are fixed, $(y_{0}(x),\ldots ,y_{15}(x))=f_{4} \circ f_{3} \circ f_{2} \circ f_{1}(x,k_{0}^{*})$, $k_{0}^{*} $ is the true key, then a necessary condition for obtaining information about the fourth round key $k_{4, j} $ by the integral method is: the subset $ Y_{j} ^{*} =\{\alpha \in V_{8} :|\{x\in I_{i} :y_{j}(x)=\alpha\}| =2k-1,k\in\mathbb{N}\}$ is not empty. The experimental data on the application of the integral method to the Rijndael algorithm are presented.
Keywords: block cipher, AES, SQUARE, Rijndael, Crypton, integral cryptanalysis.
Mots-clés : spectral coefficient 
@article{PDMA_2022_15_a14,
     author = {K. N. Pankov},
     title = {Some conditions for the applicability of the integral cryptanalysis to $4$-rounds of {AES-like} ciphers},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {57--62},
     year = {2022},
     number = {15},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2022_15_a14/}
}
TY  - JOUR
AU  - K. N. Pankov
TI  - Some conditions for the applicability of the integral cryptanalysis to $4$-rounds of AES-like ciphers
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2022
SP  - 57
EP  - 62
IS  - 15
UR  - http://geodesic.mathdoc.fr/item/PDMA_2022_15_a14/
LA  - ru
ID  - PDMA_2022_15_a14
ER  - 
%0 Journal Article
%A K. N. Pankov
%T Some conditions for the applicability of the integral cryptanalysis to $4$-rounds of AES-like ciphers
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2022
%P 57-62
%N 15
%U http://geodesic.mathdoc.fr/item/PDMA_2022_15_a14/
%G ru
%F PDMA_2022_15_a14
K. N. Pankov. Some conditions for the applicability of the integral cryptanalysis to $4$-rounds of AES-like ciphers. Prikladnaya Diskretnaya Matematika. Supplement, no. 15 (2022), pp. 57-62. http://geodesic.mathdoc.fr/item/PDMA_2022_15_a14/

[1] Zhukov A. E., “Legkovesnaya kriptografiya. Ch. 1”, Voprosy kiberbezopasnosti, 2015, no. 1(9), 26–43

[2] Zhukov A. E., “Legkovesnaya kriptografiya. Ch. 2”, Voprosy kiberbezopasnosti, 2015, no. 2(10), 2–10

[3] Romanchenko A. M., “Metod otsenivaniya rezultatov kriptoanaliza blochnogo shifra”, Trudy SPIIRAN, 2015, no. 2(39), 101–108

[4] Hu Y., Zhang Y., and Xiao G., “Integral cryptanalysis of SAFER+”, IET Electronics Let., 35:17 (1999), 1458–1459 | DOI

[5] Daemen J., Knudsen L. R., and Rijmen V., “The block cipher Square”, LNCS, 2365, 2002, 112–127

[6] Lai X., “Higher order derivatives and differential cryptanalysis”, Communications and Cryptography, Springer Intern. Ser. Engin. Comput. Sci., 276, 1994, 227–233 | Zbl

[7] Collard B. and Standaert F.-X., “A statistical saturation attack against the block cipher PRESENT”, LNCS, 5473, 2009, 195–210 | MR | Zbl

[8] Shnaier B., Prikladnaya kriptografiya: protokoly, algoritmy i iskhodnyi kod, Alfa-kniga, M., 2019, 1024 pp.

[9] Alda F., Aragona R., Nicolodi L., and Sala M., “Implementation and improvement of the partial sum attack on 6-round AES”, Physical and Data-Link Security Techniques for Future Communication Systems, Lecture Notes in Electr. Eng., 358, 2016, 181–195 | MR

[10] Sorokin M. A., Pudovkina M. A., “O pochti sovershennykh nelineinykh preobrazovaniyakh i razdelyayuschem svoistve multimnozhestv”, Prikladnaya diskretnaya matematika. Prilozhenie, 2019, no. 12, 237–239

[11] ElSheikh M. and Youssef A. M., “Integral cryptanalysis of reduced-round tweakable TWINE”, LNCS, 12579, 2020, 485–504 | MR

[12] Hebborn P., Lambin B., Leander G., and Todo Y., “Strong and tight security guarantees against integral distinguishers”, LNCS, 13090, 2021, 362–391 | MR

[13] Knudsen L. R. and Wagner D., “Integral cryptanalysis (extended abstract)”, LNCS, 2365, 2002, 112–127 | Zbl

[14] Kiryukhin V. A., “Related-key attack on 5-round Kuznyechik”, Matematicheskie voprosy kriptografii, 11:2 (2020), 53–67 | MR | Zbl

[15] Ferguson N., Kelsey J., Schneier B., et al., “Improved cryptanalysis of Rijndael”, LNCS, 1978, 2000, 213–230

[16] D'Halluin C., Bijnens G., Rijmen V., and Preneel B., “Attack on six rounds of Crypton”, LNCS, 1636, 1999, 46–59 | Zbl

[17] Los A. B., Nesterenko A. Yu., Rozhkov M. I., Kriptograficheskie metody zaschity informatsii, Yurait, M., 2018, 473 pp.

[18] Pankov K. N., “Otsenki skorosti skhodimosti v predelnykh teoremakh dlya sovmestnykh raspredelenii chasti kharakteristik sluchainykh dvoichnykh otobrazhenii”, Prikladnaya diskretnaya matematika, 2012, no. 4(18), 14–30 | MR | Zbl

[19] Pankov K. N., “Utochnennye asimptoticheskie otsenki dlya chisla $(n,m,k)$-ustoichivykh dvoichnykh otobrazhenii”, Prikladnaya diskretnaya matematika. Prilozhenie, 2017, no. 10, 46–49

[20] Babenko L. K., Ischukova E. A., Sovremennye algoritmy blochnogo shifrovaniya i metody ikh analiza, Gelios ARV, M., 2006, 376 pp.