On probability of one-bit difference propagation through modulo addition and subtraction
Prikladnaâ diskretnaâ matematika, no. 4 (2012), pp. 53-60.

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

In this paper, a proof is given for the fact that the probability of one-bit difference propagation through modulo addition and subtraction is equal to 1 if the bit is the most significant one, and 1/2 otherwise. This theoretical fact is verified too with the experimental data.
Keywords: block cipher, differential cryptanalysis, difference propagation.
@article{PDM_2012_4_a3,
     author = {A. I. Pestunov},
     title = {On probability of one-bit difference propagation through modulo addition and subtraction},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {53--60},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2012_4_a3/}
}
TY  - JOUR
AU  - A. I. Pestunov
TI  - On probability of one-bit difference propagation through modulo addition and subtraction
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2012
SP  - 53
EP  - 60
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2012_4_a3/
LA  - ru
ID  - PDM_2012_4_a3
ER  - 
%0 Journal Article
%A A. I. Pestunov
%T On probability of one-bit difference propagation through modulo addition and subtraction
%J Prikladnaâ diskretnaâ matematika
%D 2012
%P 53-60
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2012_4_a3/
%G ru
%F PDM_2012_4_a3
A. I. Pestunov. On probability of one-bit difference propagation through modulo addition and subtraction. Prikladnaâ diskretnaâ matematika, no. 4 (2012), pp. 53-60. http://geodesic.mathdoc.fr/item/PDM_2012_4_a3/

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

[2] Wagner D., “The boomerang attack”, LNCS, 1636, 1999, 156–170 | Zbl

[3] Kelsey J., Kohno T., Schneier B., “Amplified boomerang attacks against reduced-round MARS and Serpent”, LNCS, 1978, 2001, 75–93 | Zbl

[4] Biham E., Biryukov A., Shamir A., “Cryptanalysis of Skipjack reduced to 31 round using impossible differentials”, LNCS, 1592, 1999, 12–23 | Zbl

[5] Pestunov A. I., “Blochnye shifry i ikh kriptoanaliz”, Vychislitelnye tekhnologii, 12:4, spets. vyp. (2007), 42–49 | Zbl

[6] Lai X., Massey J., “Markov ciphers and differential cryptanalysis”, LNCS, 547, 1991, 17–38 | MR | Zbl

[7] Nyberg K., Knudsen L., “Provable security against a differential attack”, J. Cryptology, 8 (1995), 27–37 | MR | Zbl

[8] Vaudenay S., “Decorrelation: a theory for block cipher security”, J. Cryptology, 16 (2003), 249–286 | DOI | MR | Zbl

[9] Agibalov G. P., “Elementy teorii differentsialnogo kriptoanaliza iterativnykh blochnykh shifrov s additivnym raundovym klyuchom”, Prikladnaya diskretnaya matematika, 2008, no. 1(1), 34–42

[10] Biryukov A., Kushilevitz E., “Improved cryptanalysis of RC5”, LNCS, 1403, 1998, 85–99 | Zbl

[11] Pestunov A. I., “Differentsialnyi kriptoanaliz blochnogo shifra MARS”, Prikladnaya diskretnaya matematika, 2009, no. 4(6), 56–63

[12] Pestunov A. I., “Differentsialnyi kriptoanaliz blochnogo shifra CAST-256”, Bezopasnost informatsionnykh tekhnologii, 2009, no. 4, 57–62

[13] Borovkov A. A., Teoriya veroyatnostei, Nauka, M., 1976, 352 pp. | MR | Zbl

[14] Borovkov A. A., Matematicheskaya statistika, Nauka, M., 1984, 472 pp. | MR | Zbl

[15] Burwick C. et al., MARS – a candidate cipher for AES, NIST AES Proposal, 1999

[16] Pestunov A. I., “Statisticheskii analiz sovremennykh blochnykh shifrov”, Vychislitelnye tekhnologii, 12:2 (2007), 122–129 | Zbl

[17] Brian Gladman's Home Page, , 2012 www.gladman.me.uk