### Structural Evaluation by Generalized Integral Property

Yosuke Todo

##### Abstract

In this paper, we show structural cryptanalyses against two popular networks, i.e., the Feistel Network and the Substitute-Permutation Network (SPN). Our cryptanalyses are distinguishing attacks by an improved integral distinguisher. The integral distinguisher is one of the most powerful attacks against block ciphers, and it is usually constructed by evaluating the propagation characteristic of integral properties, e.g., the ALL or BALANCE property. However, the integral property does not derive useful distinguishers against block ciphers with non-bijective functions and bit-oriented structures. Moreover, since the integral property does not clearly exploit the algebraic degree of block ciphers, it tends not to construct useful distinguishers against block ciphers with low-degree functions. In this paper, we propose a new property called {\it the division property}, which is the generalization of the integral property. It can effectively construct the integral distinguisher even if the block cipher has non-bijective functions, bit-oriented structures, and low-degree functions. From viewpoints of the attackable number of rounds or chosen plaintexts, the division property can construct better distinguishers than previous methods. Although our attack is a generic attack, it can improve several integral distinguishers against specific cryptographic primitives. For instance, it can reduce the required number of chosen plaintexts for the 10-round distinguisher on Keccak-f from $2^{1025}$ to $2^{515}$. For the Feistel cipher, it theoretically proves that Simon 32, 48, 64, 96, and 128 have 9-, 11-, 11-, 13-, and 13-round integral distinguishers, respectively.

Available format(s)
Category
Secret-key cryptography
Publication info
A minor revision of an IACR publication in EUROCRYPT 2015
Keywords
cryptanalysis
Contact author(s)
todo yosuke @ lab ntt co jp
History
2015-07-03: revised
See all versions
Short URL
https://ia.cr/2015/090

CC BY

BibTeX

@misc{cryptoeprint:2015/090,
author = {Yosuke Todo},
title = {Structural Evaluation by Generalized Integral Property},
howpublished = {Cryptology ePrint Archive, Paper 2015/090},
year = {2015},
note = {\url{https://eprint.iacr.org/2015/090}},
url = {https://eprint.iacr.org/2015/090}
}

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