Two New Measures for Permutations: Ambiguity and Deficiency

Panario, Daniel; Sakzad, Amin; Stevens, Brett; Wang, Qiang

doi:10.1109/tit.2011.2159478

Cited by 23 publications

(48 citation statements)

References 16 publications

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“…In [12] we show that, for certain permutation functions that are related to S-boxes in cryptosystems, ambiguity and deficiency correlate well with formal measures of linearity. That is, functions with low ambiguity and low deficiency have low linearity and are thus more resistant to linear cryptanalysis.…”

Section: Results On Ambiguity and Deficiencymentioning

confidence: 87%

“…The ambiguity and deficiency of some well-known permutations such as twisted binomials and Möbius transformations have been computed in [12]. These are evaluated on both additive and multiplicative groups of the finite field F q .…”

Section: Results On Ambiguity and Deficiencymentioning

confidence: 99%

“…It has been also shown that some of them have optimal ambiguity and optimal deficiency. The optimum ambiguity and deficiency of a mapping can be derived using the following theorem cited from [12].…”

Section: Results On Ambiguity and Deficiencymentioning

confidence: 99%

“…Functions with optimum ambiguity, OA * G (f ) = 1, have been constructed in [12]. If we suppose that G = F q , q = p e , then the ambiguity and deficiency depend on the characteristic p of F q .…”

Section: Results On Ambiguity and Deficiencymentioning

confidence: 99%

“…For example adding a fixed element or applying an automorphism of G to the left or right of f , does not affect these two measures for permutations on G [12].…”

Section: B Definitions Of Ambiguity and Deficiencymentioning

confidence: 99%

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Ambiguity and deficiency of permutations from finite fields

Panario

Sakzad

Stevens

et al. 2011

2011 IEEE Information Theory Workshop

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The concepts of ambiguity and deficiency for a given bijection on a finite Abelian group were recently introduced [13]. In this work we investigate the ambiguity and deficiency of some well-known polynomials which satisfy Dn(x+y, xy) = x n +y n for every x, y ∈ Fq and n ∈ N, as well as linearized polynomials and Dembowski-Ostrom polynomials (DO polynomials). For some specific values of n (related to q) these polynomials generate permutations on Fq. We derive explicitly the ambiguity and deficiency of some of them. Numerical results on the ambiguity and deficiency of the others are also provided. Some of these polynomials are almost perfect nonlinear (APN) functions.

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Section: Results On Ambiguity and Deficiencymentioning

confidence: 87%

Section: Results On Ambiguity and Deficiencymentioning

confidence: 99%

Section: Results On Ambiguity and Deficiencymentioning

confidence: 99%

Section: Results On Ambiguity and Deficiencymentioning

confidence: 99%

“…For example adding a fixed element or applying an automorphism of G to the left or right of f , does not affect these two measures for permutations on G [12].…”

Section: B Definitions Of Ambiguity and Deficiencymentioning

confidence: 99%

See 3 more Smart Citations