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<p>The derivative mapping plays a central role in many applications, including, most noticeably, differential cryptanalysis (Biham and Shamir in J Cryptol 4:3–72, 1991; Nyberg, in: Advances in Cryptology EUROCRYPT’93, Lecture Notes in Computer Science, 1994). The ambiguity and deficiency of functions measure how close the derivative mapping is to be the injection and surjection, respectively. In this paper, by studying some special linearized polynomials, we determine the exact values of ambiguity, deficiency and differential uniformity of some permutation trinomials over <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2370_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {F}_{2^n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <msup> <mn>2</mn> <mi>n</mi> </msup> </msub> </math></EquationSource> </InlineEquation>.</p>

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Determining ambiguity, deficiency and differential uniformity of permutation trinomials over \(\mathbb {F}_{2^n}\)

  • 期刊论文

  • 发表日期：

    2025年1月11日

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  • Yan-Ping Wang,
  • Dabin Zheng,
  • WeiGuo Zhang

摘要

The derivative mapping plays a central role in many applications, including, most noticeably, differential cryptanalysis (Biham and Shamir in J Cryptol 4:3–72, 1991; Nyberg, in: Advances in Cryptology EUROCRYPT’93, Lecture Notes in Computer Science, 1994). The ambiguity and deficiency of functions measure how close the derivative mapping is to be the injection and surjection, respectively. In this paper, by studying some special linearized polynomials, we determine the exact values of ambiguity, deficiency and differential uniformity of some permutation trinomials over \(\mathbb {F}_{2^n}\) F 2 n .