Relationships between CCZ and EA equivalence classes and corresponding code invariants

Kathy J. Horadam; Mercé Villanueva

doi:10.1007/978-3-319-12325-7_1

Relationships between CCZ and EA equivalence classes and corresponding code invariants

Research output: Contribution to journal › Article › Research › peer-review

Abstract

© Springer International Publishing Switzerland 2014. The purpose of this paper is to provide a brief survey of CCZ and EA equivalence for functions f : G → N where G and N are finite and N is abelian, and, for the case f : ℤmp → ℤmp, to investigate two codes derived from f, inspired by these equivalences. In particular we show the dimension of the kernel of each code determines a new invariant of the corresponding equivalence class. We present computational results for p = 2 and small m.

Original language	English
Pages (from-to)	3-17
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8865
DOIs	https://doi.org/10.1007/978-3-319-12325-7_1
Publication status	Published - 1 Jan 2014

Keywords

APN function
CCZ equivalence class
Code invariant
Differential cryptanalysis
EA-equivalence class

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10.1007/978-3-319-12325-7_1

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Relationships between CCZ and EA equivalence classes and corresponding code invariants. / Horadam, Kathy J.; Villanueva, Mercé.

In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 8865, 01.01.2014, p. 3-17.

Research output: Contribution to journal › Article › Research › peer-review

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N2 - © Springer International Publishing Switzerland 2014. The purpose of this paper is to provide a brief survey of CCZ and EA equivalence for functions f : G → N where G and N are finite and N is abelian, and, for the case f : ℤmp → ℤmp, to investigate two codes derived from f, inspired by these equivalences. In particular we show the dimension of the kernel of each code determines a new invariant of the corresponding equivalence class. We present computational results for p = 2 and small m.

AB - © Springer International Publishing Switzerland 2014. The purpose of this paper is to provide a brief survey of CCZ and EA equivalence for functions f : G → N where G and N are finite and N is abelian, and, for the case f : ℤmp → ℤmp, to investigate two codes derived from f, inspired by these equivalences. In particular we show the dimension of the kernel of each code determines a new invariant of the corresponding equivalence class. We present computational results for p = 2 and small m.

KW - APN function

KW - CCZ equivalence class

KW - Code invariant

KW - Differential cryptanalysis

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