Geodesic
On properties of additive differential probabilities of XOR
Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 46-48.

Voir la notice de l'article provenant de la source Math-Net.Ru

The additive differential probability of exclusive-or $\mathrm{adp}^{\oplus}(\alpha, \beta, \gamma)$, where $\alpha, \beta, \gamma \in \mathbb{Z}_{2}^{n}$, is studied. It is used in the analysis of symmetric-key primitives that combine XOR and modular addition, such as Addition-Rotation-XOR (ARX) constructions. We focus on the maximal differentials which are helpful when constructing differential trails. It is proven that $\max_{\alpha, \beta} \mathrm{adp}^{\oplus}(\alpha,\beta,\gamma) = \mathrm{adp}^{\oplus}(0,\gamma,\gamma)$. In addition, there exist either $2$ or $8$ distinct pairs ($\alpha$, $\beta$) such that $\mathrm{adp}^{\oplus}(\alpha,\beta,\gamma) = \mathrm{adp}^{\oplus}(0,\gamma,\gamma)$. Also, we obtain a simplified representation of $\mathrm{adp}^{\oplus}(0,\gamma,\gamma)$ and formula for $\min_{\gamma}\mathrm{adp}^{\oplus}(0,\gamma,\gamma)$.
Mots-clés : ARX, XOR
Keywords: modular addition, differential cryptanalysis. 
@article{PDMA_2021_14_a7,
     author = {N. Mouha and N. A. Kolomeets and D. A. Ahtyamov and I. A. Sutormin and M. A. Panferov and K. M. Titova and T. A. Bonich and E. A. Ishchukova and N. N. Tokareva and B. F. Zhantulikov},
     title = {On properties of additive differential probabilities of {XOR}},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {46--48},
     publisher = {mathdoc},
     number = {14},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2021_14_a7/}
}
TY  - JOUR
AU  - N. Mouha
AU  - N. A. Kolomeets
AU  - D. A. Ahtyamov
AU  - I. A. Sutormin
AU  - M. A. Panferov
AU  - K. M. Titova
AU  - T. A. Bonich
AU  - E. A. Ishchukova
AU  - N. N. Tokareva
AU  - B. F. Zhantulikov
TI  - On properties of additive differential probabilities of XOR
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2021
SP  - 46
EP  - 48
IS  - 14
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2021_14_a7/
LA  - ru
ID  - PDMA_2021_14_a7
ER  - 
%0 Journal Article
%A N. Mouha
%A N. A. Kolomeets
%A D. A. Ahtyamov
%A I. A. Sutormin
%A M. A. Panferov
%A K. M. Titova
%A T. A. Bonich
%A E. A. Ishchukova
%A N. N. Tokareva
%A B. F. Zhantulikov
%T On properties of additive differential probabilities of XOR
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2021
%P 46-48
%N 14
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2021_14_a7/
%G ru
%F PDMA_2021_14_a7
N. Mouha; N. A. Kolomeets; D. A. Ahtyamov; I. A. Sutormin; M. A. Panferov; K. M. Titova; T. A. Bonich; E. A. Ishchukova; N. N. Tokareva; B. F. Zhantulikov. On properties of additive differential probabilities of XOR. Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 46-48. http://geodesic.mathdoc.fr/item/PDMA_2021_14_a7/

[1] Shimizu A., Miyaguchi S., “Fast data encipherment algorithm (FEAL)”, LNCS, 304, 1988, 267–278 | Zbl

[2] Ferguson N., Lucks S., Schneier B., et al., The Skein Hash Function Family, , 2009 http://www.skein-hash.info

[3] Bernstein D. J., Salsa20 Specification, , 2005 https://cr.yp.to/snuffle/spec.pdf

[4] Bernstein D. J., ChaCha, a Variant of Salsa20, , 2008 https://cr.yp.to/chacha/chacha-20080128.pdf

[5] Aumasson J.-P., Meier W., Phan R. C.-W., Henzen L., The Hash Function BLAKE, , 2014 https://www.researchgate.net/publication/316806226_The_Hash_Function_BLAKE

[6] Biham E., Shamir A., “Differential cryptanalysis of DES-like cryptosystems”, J. Cryptology, 4:1 (1991), 3–72 | DOI | MR | Zbl

[7] Lipmaa H., Wallen J., Dumas P., “On the additive differential probability of exclusive-or”, LNCS, 3017, 2004, 317–331 | Zbl

[8] Mouha N., Velichkov V., De Canniere C., Preneel B., “The differential analysis of S-functions”, LNCS, 6544, 2011, 36–56 | MR | Zbl

[9] Horadam A. F., “Basic properties of a certain generalised sequence of numbers”, The Fibonacci Quarterly, 3:3 (1965), 161–176 | MR | Zbl

[10] Mouha N., Kolomeec N., Akhtiamov D., et al., “Maximums of the additive differential probability of Exclusive-Or”, IACR Trans. Symmetric Cryptology, 2021:2 (2021), 292–313 | DOI