New Results About the Boomerang Uniformity of Permutation Polynomials

Li, Kangquan; Qu, Longjiang; Sun, Bing; Li, Chao

doi:10.1109/tit.2019.2918531

Cited by 71 publications

(66 citation statements)

References 42 publications

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“…Recently, the boomerang uniformity of some permutations has been studied in [3,12,22,23,26,35,38]. However, the analysis has been focused, principally, on the case of quadratic or power functions.…”

Section: Remarks On the Boomerang Uniformity For Some Piecewise Permumentioning

confidence: 99%

“…However, the analysis has been focused, principally, on the case of quadratic or power functions. Only in [22] and in [12], it has been determined the boomerang uniformity of some piecewise functions obtained from the inverse function modified on the subfield F 4 .…”

Section: Remarks On the Boomerang Uniformity For Some Piecewise Permumentioning

confidence: 99%

“…It was noted in [22], that the entry T F (a, b) of the BCT of a function F can be given by the number of solutions (x, y) of the system…”

Section: Remarks On the Boomerang Uniformity For Some Piecewise Permumentioning

confidence: 99%

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Differentially low uniform permutations from known 4-uniform functions

Calderini

2020

Des. Codes Cryptogr.

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Section: Remarks On the Boomerang Uniformity For Some Piecewise Permumentioning

confidence: 99%

Section: Remarks On the Boomerang Uniformity For Some Piecewise Permumentioning

confidence: 99%

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Differentially low uniform permutations from known 4-uniform functions

Calderini

2020

Des. Codes Cryptogr.

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“…Equally as an Sbox with a Difference Distribution Table with small coefficients provides resistance against differential attacks, an Sbox with a Boomerang Connectivity Table (BCT) with small coefficients prevents an attacker from building efficient boomerang-style attacks. A study of some important families of Sboxes has been made in [BC18], [BPT19] and [LQSL19], just to cite a few. Another interesting line of work that followed the paper of Cid et al is the determination of the probability of a boomerang switch E m that covers more than one round, and that was addressed for SPN ciphers in [WP19,SQH19].…”

Section: Emmentioning

confidence: 99%

On the Feistel Counterpart of the Boomerang Connectivity Table

Boukerrou

Huynh

Lallemand

et al. 2020

ToSC

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At Eurocrypt 2018, Cid et al. introduced the Boomerang Connectivity Table (BCT), a tool to compute the probability of the middle round of a boomerang distinguisher from the description of the cipher’s Sbox(es). Their new table and the following works led to a refined understanding of boomerangs, and resulted in a series of improved attacks. Still, these works only addressed the case of Substitution Permutation Networks, and completely left out the case of ciphers following a Feistel construction. In this article, we address this lack by introducing the FBCT, the Feistel counterpart of the BCT. We show that the coefficient at row Δi, ∇o corresponds to the number of times the second order derivative at points Δi, ∇o) cancels out. We explore the properties of the FBCT and compare it to what is known on the BCT. Taking matters further, we show how to compute the probability of a boomerang switch over multiple rounds with a generic formula.

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“…The situation is the same for the BCT. In order to establish the distribution of the non-trivial coefficients of the BCT of a random permutation, we first recall an alternative definition of the BCT that was introduced in [26].…”

Section: Coefficient Distributionsmentioning

confidence: 99%

Anomalies and Vector Space Search: Tools for S-Box Analysis

Bonnetain

Perrin

Tian

2019

Lecture Notes in Computer Science

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S-boxes are functions with an input so small that the simplest way to specify them is their lookup table (LUT). How can we quantify the distance between the behavior of a given S-box and that of an S-box picked uniformly at random? To answer this question, we introduce various "anomalies". These real numbers are such that a property with an anomaly equal to should be found roughly once in a set of 2 random S-boxes. First, we present statistical anomalies based on the distribution of the coefficients in the difference distribution table, linear approximation table, and for the first time, the boomerang connectivity table. We then count the number of S-boxes that have block-cipher like structures to estimate the anomaly associated to those. In order to recover these structures, we show that the most general tool for decomposing S-boxes is an algorithm efficiently listing all the vector spaces of a given dimension contained in a given set, and we present such an algorithm. Combining these approaches, we conclude that all permutations that are actually picked uniformly at random always have essentially the same cryptographic properties and the same lack of structure.

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New Results About the Boomerang Uniformity of Permutation Polynomials

Cited by 71 publications

References 42 publications

Differentially low uniform permutations from known 4-uniform functions

Differentially low uniform permutations from known 4-uniform functions

On the Feistel Counterpart of the Boomerang Connectivity Table

Anomalies and Vector Space Search: Tools for S-Box Analysis

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