The Best Differential Characteristic Search of FEAL

Kazumaro AOKI; Kunio KOBAYASHI; Shiho MORIAI

The Best Differential Characteristic Search of FEAL

Kazumaro AOKI, Kunio KOBAYASHI, Shiho MORIAI

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This paper presents the results of the best differential characteristic search of FEAL. The search algorithm for the best differential characteristic (best linear expression) was already presented by Matsui, and improvements on this algorithm were presented by Moriai et al. We further improve the speed of the search algorithm. For example, the search time for the 7-round best differential characteristic of FEAL is reduced to about 10 minutes (Pentium/166 MHz), which is about 2^{12. 6} times faster than Matsui's algorithm. Moreover, we determine all the best differential characteristics of FEAL for up to 32 rounds assuming all S-boxes are independent. As a result, we confirm that the N-round (7N32) best differential characteristic probability of FEAL is 2^-2N, which was found by Biham. For N=6, we find 6-round differential characteristics with a greater probability, 2^-11, than that previously discovered, 2^-12.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E81-A No.1 pp.98-104

Publication Date: 1998/01/25

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Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)

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Kazumaro AOKI, Kunio KOBAYASHI, Shiho MORIAI, "The Best Differential Characteristic Search of FEAL" in IEICE TRANSACTIONS on Fundamentals, vol. E81-A, no. 1, pp. 98-104, January 1998, doi: .
Abstract: This paper presents the results of the best differential characteristic search of FEAL. The search algorithm for the best differential characteristic (best linear expression) was already presented by Matsui, and improvements on this algorithm were presented by Moriai et al. We further improve the speed of the search algorithm. For example, the search time for the 7-round best differential characteristic of FEAL is reduced to about 10 minutes (Pentium/166 MHz), which is about 2^{12. 6} times faster than Matsui's algorithm. Moreover, we determine all the best differential characteristics of FEAL for up to 32 rounds assuming all S-boxes are independent. As a result, we confirm that the N-round (7N32) best differential characteristic probability of FEAL is 2^-2N, which was found by Biham. For N=6, we find 6-round differential characteristics with a greater probability, 2^-11, than that previously discovered, 2^-12.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e81-a_1_98/_p

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@ARTICLE{e81-a_1_98,
author={Kazumaro AOKI, Kunio KOBAYASHI, Shiho MORIAI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The Best Differential Characteristic Search of FEAL},
year={1998},
volume={E81-A},
number={1},
pages={98-104},
abstract={This paper presents the results of the best differential characteristic search of FEAL. The search algorithm for the best differential characteristic (best linear expression) was already presented by Matsui, and improvements on this algorithm were presented by Moriai et al. We further improve the speed of the search algorithm. For example, the search time for the 7-round best differential characteristic of FEAL is reduced to about 10 minutes (Pentium/166 MHz), which is about 2^{12. 6} times faster than Matsui's algorithm. Moreover, we determine all the best differential characteristics of FEAL for up to 32 rounds assuming all S-boxes are independent. As a result, we confirm that the N-round (7N32) best differential characteristic probability of FEAL is 2^-2N, which was found by Biham. For N=6, we find 6-round differential characteristics with a greater probability, 2^-11, than that previously discovered, 2^-12.},
keywords={},
doi={},
ISSN={},
month={January},}

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TY - JOUR
TI - The Best Differential Characteristic Search of FEAL
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 98
EP - 104
AU - Kazumaro AOKI
AU - Kunio KOBAYASHI
AU - Shiho MORIAI
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E81-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 1998
AB - This paper presents the results of the best differential characteristic search of FEAL. The search algorithm for the best differential characteristic (best linear expression) was already presented by Matsui, and improvements on this algorithm were presented by Moriai et al. We further improve the speed of the search algorithm. For example, the search time for the 7-round best differential characteristic of FEAL is reduced to about 10 minutes (Pentium/166 MHz), which is about 2^{12. 6} times faster than Matsui's algorithm. Moreover, we determine all the best differential characteristics of FEAL for up to 32 rounds assuming all S-boxes are independent. As a result, we confirm that the N-round (7N32) best differential characteristic probability of FEAL is 2^-2N, which was found by Biham. For N=6, we find 6-round differential characteristics with a greater probability, 2^-11, than that previously discovered, 2^-12.
ER -