On properties of additive differential probabilities of XOR
The additive differential probability of exclusive-or adp®(a,e,Y), where a,e,Y e Zn, 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 maxadp®(a,e, y) = adp®(0,Y,Y). In addition, there exist either 2 or 8 distinct pairs (a, а,в в) such that adp®(a,e,Y) = adp®(0,Y,Y)• Also, we obtain a simplified representation of adp®(0, y, Y) and formula for minadp®(0, y, y). Y
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Keywords
differential cryptanalysis, modular addition, ARX, XORAuthors
| Name | Organization | |
| Mouha N. | Strativia company | nicky@mouha.be |
| Kolomeec N. A. | Institute of Mathematics. S. L. Sobolev SB RAS | kolomeec@math.nsc.ru |
| Ahtyamov D. A. | Hebrew University | akhtyamoff1997@gmail.com |
| Sutormin I. A. | Institute of Mathematics. S. L. Sobolev SB RAS | ivan.sutormin@gmail.com |
| Panferov M. A. | Novosibirsk State University | m.panferov@g.nsu.ru |
| Titova K. M. | Novosibirsk State University | sitnich@gmail.com |
| Bonich T. A. | Novosibirsk State University | t.bonich@g.nsu.ru |
| Ishchukova E. A. | South Federal University | uaishukova@sfedu.ru |
| Tokareva N. N. | Institute of Mathematics. S. L. Sobolev SB RAS; Novosibirsk State University; JetBrains Research Crypto Lab | tokareva@math.nsc.ru |
| Zhantulikov B. F. | Novosibirsk State University | b.zhantulikov@g.nsu.ru |
References
Mouha N., Kolomeec N., Akhtiamov D., et al. Maximums of the additive differential probability of Exclusive-Or // IACR Trans. Symmetric Cryptology. 2021. V. 2021. No. 2. P. 292-313.
Horadam A. F. Basic properties of a certain generalised sequence of numbers // The Fibonacci Quarterly. 1965. V. 3. No. 3. P. 161-176.
Mouha N., Velichkov V., De Canniere C., and Preneel B. The differential analysis of S-func-tions // LNCS. 2011. V. 6544. P. 36-56.
Lipmaa H., Wallen J., and Dumas P. On the additive differential probability of exclusive-or // LNCS. 2004. V. 3017. P. 317-331.
Biham E. and Shamir A. Differential cryptanalysis of DES-like cryptosystems // J. Cryptology. 1991. V. 4. No. 1. P. 3-72.
Aumasson J.-P., Meier W., Phan R. C.-W., and Henzen L. The Hash Function BLAKE. https://www.researchgate.net/publication/316806226_The_Hash_Function_BLAKE. 2014.
Bernstein D. J. ChaCha, a Variant of Salsa20. https://cr.yp.to/chacha/chacha-20080128.pdf. 2008.
Ferguson N., Lucks S., Schneier B., et al. The Skein Hash Function Family. http://www.skein-hash.info. 2009.
Bernstein D. J. Salsa20 Specification. https://cr.yp.to/snuffle/spec.pdf. 2005.
Shimizu A. and Miyaguchi S. Fast data encipherment algorithm (FEAL) // 1988. LNCS. 1988. V.304. P. 267-278.
On properties of additive differential probabilities of XOR | Applied Discrete Mathematics. Supplement. 2021. № 14. DOI: 10.17223/2226308X/14/7
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