On the Security of Feistel Ciphers with SPN Round Function against Differential, Linear, and Truncated Differential Cryptanalysis

Masayuki KANDA; Tsutomu MATSUMOTO

On the Security of Feistel Ciphers with SPN Round Function against Differential, Linear, and Truncated Differential Cryptanalysis

Masayuki KANDA, Tsutomu MATSUMOTO

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This paper studies security of Feistel ciphers with SPN round function against differential cryptanalysis, linear cryptanalysis, and truncated differential cryptanalysis from the "designer's standpoint." In estimating the security, we use the upper bounds of differential characteristic probability, linear characteristic probability and truncated differential probability, respectively. They are useful to design practically secure ciphers against these cryptanalyses. Firstly, we consider the minimum numbers of differential and linear active s-boxes. They provide the upper bounds of differential and linear characteristic probability, which show the security of ciphers constructed by s-boxes against differential and linear cryptanalysis. We clarify the (lower bounds of) minimum numbers of differential and linear active s-boxes in some consecutive rounds of the Feistel ciphers by using differential and linear branch numbers, P_d, P_l, respectively. Secondly, we discuss the following items on truncated differential probability from the designer's standpoint, and show how the following items affect the upper bound of truncated differential probability; (a) truncated differential probability of effective active-s-box, (b) XOR cancellation probability, and (c) effect of auxiliary functions. Finally, we revise Matsui's algorithm using the above discussion in order to evaluate the upper bound of truncated differential probability, since we consider the upper bound of truncated differential probability as well as that of differential and linear probability.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E85-A No.1 pp.25-37

Publication Date: 2002/01/01

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

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Masayuki KANDA, Tsutomu MATSUMOTO, "On the Security of Feistel Ciphers with SPN Round Function against Differential, Linear, and Truncated Differential Cryptanalysis" in IEICE TRANSACTIONS on Fundamentals, vol. E85-A, no. 1, pp. 25-37, January 2002, doi: .
Abstract: This paper studies security of Feistel ciphers with SPN round function against differential cryptanalysis, linear cryptanalysis, and truncated differential cryptanalysis from the "designer's standpoint." In estimating the security, we use the upper bounds of differential characteristic probability, linear characteristic probability and truncated differential probability, respectively. They are useful to design practically secure ciphers against these cryptanalyses. Firstly, we consider the minimum numbers of differential and linear active s-boxes. They provide the upper bounds of differential and linear characteristic probability, which show the security of ciphers constructed by s-boxes against differential and linear cryptanalysis. We clarify the (lower bounds of) minimum numbers of differential and linear active s-boxes in some consecutive rounds of the Feistel ciphers by using differential and linear branch numbers, P_d, P_l, respectively. Secondly, we discuss the following items on truncated differential probability from the designer's standpoint, and show how the following items affect the upper bound of truncated differential probability; (a) truncated differential probability of effective active-s-box, (b) XOR cancellation probability, and (c) effect of auxiliary functions. Finally, we revise Matsui's algorithm using the above discussion in order to evaluate the upper bound of truncated differential probability, since we consider the upper bound of truncated differential probability as well as that of differential and linear probability.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e85-a_1_25/_p

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@ARTICLE{e85-a_1_25,
author={Masayuki KANDA, Tsutomu MATSUMOTO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Security of Feistel Ciphers with SPN Round Function against Differential, Linear, and Truncated Differential Cryptanalysis},
year={2002},
volume={E85-A},
number={1},
pages={25-37},
abstract={This paper studies security of Feistel ciphers with SPN round function against differential cryptanalysis, linear cryptanalysis, and truncated differential cryptanalysis from the "designer's standpoint." In estimating the security, we use the upper bounds of differential characteristic probability, linear characteristic probability and truncated differential probability, respectively. They are useful to design practically secure ciphers against these cryptanalyses. Firstly, we consider the minimum numbers of differential and linear active s-boxes. They provide the upper bounds of differential and linear characteristic probability, which show the security of ciphers constructed by s-boxes against differential and linear cryptanalysis. We clarify the (lower bounds of) minimum numbers of differential and linear active s-boxes in some consecutive rounds of the Feistel ciphers by using differential and linear branch numbers, P_d, P_l, respectively. Secondly, we discuss the following items on truncated differential probability from the designer's standpoint, and show how the following items affect the upper bound of truncated differential probability; (a) truncated differential probability of effective active-s-box, (b) XOR cancellation probability, and (c) effect of auxiliary functions. Finally, we revise Matsui's algorithm using the above discussion in order to evaluate the upper bound of truncated differential probability, since we consider the upper bound of truncated differential probability as well as that of differential and linear probability.},
keywords={},
doi={},
ISSN={},
month={January},}

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TY - JOUR
TI - On the Security of Feistel Ciphers with SPN Round Function against Differential, Linear, and Truncated Differential Cryptanalysis
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 25
EP - 37
AU - Masayuki KANDA
AU - Tsutomu MATSUMOTO
PY - 2002
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E85-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2002
AB - This paper studies security of Feistel ciphers with SPN round function against differential cryptanalysis, linear cryptanalysis, and truncated differential cryptanalysis from the "designer's standpoint." In estimating the security, we use the upper bounds of differential characteristic probability, linear characteristic probability and truncated differential probability, respectively. They are useful to design practically secure ciphers against these cryptanalyses. Firstly, we consider the minimum numbers of differential and linear active s-boxes. They provide the upper bounds of differential and linear characteristic probability, which show the security of ciphers constructed by s-boxes against differential and linear cryptanalysis. We clarify the (lower bounds of) minimum numbers of differential and linear active s-boxes in some consecutive rounds of the Feistel ciphers by using differential and linear branch numbers, P_d, P_l, respectively. Secondly, we discuss the following items on truncated differential probability from the designer's standpoint, and show how the following items affect the upper bound of truncated differential probability; (a) truncated differential probability of effective active-s-box, (b) XOR cancellation probability, and (c) effect of auxiliary functions. Finally, we revise Matsui's algorithm using the above discussion in order to evaluate the upper bound of truncated differential probability, since we consider the upper bound of truncated differential probability as well as that of differential and linear probability.
ER -