Strict Evaluation of the Maximum Average of Differential Probability and the Maximum Average of Linear Probability

Kazumaro AOKI; Kazuo OHTA

Strict Evaluation of the Maximum Average of Differential Probability and the Maximum Average of Linear Probability

Kazumaro AOKI, Kazuo OHTA

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Nyberg and Knudsen proved that the maximum average of differential probability (ADP_max) and the maximum average of linear probability (ALP_max) of Feistel cipher with over 4 rounds can be evaluated as ADP_max 2DCP²_max and ALP_max 2LCP²_max using the maximum of defferential characteristic probability (DCP_max) and the maximum of linear characteristic probability (LCP_max) per round. This paper shows ADP_max DCP²_max and ALP_max LCP²_max if the F function is a bijection and the Feistel cipher has more than 3 rounds. The results prove that Feistel ciphers are stronger against differential and linear cryptanalyses than previously thought. Combining this result with that of Luby and Rackoff, the implication is that the 3-round Feistel cipher could be used as a building block cipher for the construction of provable secure block cipher algorithm.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E80-A No.1 pp.2-8

Publication Date: 1997/01/25

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

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Kazumaro AOKI, Kazuo OHTA, "Strict Evaluation of the Maximum Average of Differential Probability and the Maximum Average of Linear Probability" in IEICE TRANSACTIONS on Fundamentals, vol. E80-A, no. 1, pp. 2-8, January 1997, doi: .
Abstract: Nyberg and Knudsen proved that the maximum average of differential probability (ADP_max) and the maximum average of linear probability (ALP_max) of Feistel cipher with over 4 rounds can be evaluated as ADP_max 2DCP²_max and ALP_max 2LCP²_max using the maximum of defferential characteristic probability (DCP_max) and the maximum of linear characteristic probability (LCP_max) per round. This paper shows ADP_max DCP²_max and ALP_max LCP²_max if the F function is a bijection and the Feistel cipher has more than 3 rounds. The results prove that Feistel ciphers are stronger against differential and linear cryptanalyses than previously thought. Combining this result with that of Luby and Rackoff, the implication is that the 3-round Feistel cipher could be used as a building block cipher for the construction of provable secure block cipher algorithm.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e80-a_1_2/_p

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@ARTICLE{e80-a_1_2,
author={Kazumaro AOKI, Kazuo OHTA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Strict Evaluation of the Maximum Average of Differential Probability and the Maximum Average of Linear Probability},
year={1997},
volume={E80-A},
number={1},
pages={2-8},
abstract={Nyberg and Knudsen proved that the maximum average of differential probability (ADP_max) and the maximum average of linear probability (ALP_max) of Feistel cipher with over 4 rounds can be evaluated as ADP_max 2DCP²_max and ALP_max 2LCP²_max using the maximum of defferential characteristic probability (DCP_max) and the maximum of linear characteristic probability (LCP_max) per round. This paper shows ADP_max DCP²_max and ALP_max LCP²_max if the F function is a bijection and the Feistel cipher has more than 3 rounds. The results prove that Feistel ciphers are stronger against differential and linear cryptanalyses than previously thought. Combining this result with that of Luby and Rackoff, the implication is that the 3-round Feistel cipher could be used as a building block cipher for the construction of provable secure block cipher algorithm.},
keywords={},
doi={},
ISSN={},
month={January},}

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TY - JOUR
TI - Strict Evaluation of the Maximum Average of Differential Probability and the Maximum Average of Linear Probability
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2
EP - 8
AU - Kazumaro AOKI
AU - Kazuo OHTA
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E80-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 1997
AB - Nyberg and Knudsen proved that the maximum average of differential probability (ADP_max) and the maximum average of linear probability (ALP_max) of Feistel cipher with over 4 rounds can be evaluated as ADP_max 2DCP²_max and ALP_max 2LCP²_max using the maximum of defferential characteristic probability (DCP_max) and the maximum of linear characteristic probability (LCP_max) per round. This paper shows ADP_max DCP²_max and ALP_max LCP²_max if the F function is a bijection and the Feistel cipher has more than 3 rounds. The results prove that Feistel ciphers are stronger against differential and linear cryptanalyses than previously thought. Combining this result with that of Luby and Rackoff, the implication is that the 3-round Feistel cipher could be used as a building block cipher for the construction of provable secure block cipher algorithm.
ER -