# CCZ equivalence of power functions

CCZ equivalence of power functions Let $$F\simeq {{\mathrm{GF}}}(p^n)$$ F ≃ GF ( p n ) be a finite field of characteristic p and $$p_k$$ p k and $$p_\ell$$ p ℓ be power functions on F defined by $$p_k(x)=x^k$$ p k ( x ) = x k and $$p_\ell (x)=x^\ell$$ p ℓ ( x ) = x ℓ respectively. We show, that $$p_k$$ p k and $$p_\ell$$ p ℓ are CCZ equivalent, if and only if there exists a positive integer $$0\le a< n$$ 0 ≤ a < n , such that $$\ell \equiv p^a k \pmod {p^n-1}$$ ℓ ≡ p a k ( mod p n - 1 ) or $$k\ell \equiv p^a \pmod {p^n-1}$$ k ℓ ≡ p a ( mod p n - 1 ) . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Designs, Codes and Cryptography Springer Journals

# CCZ equivalence of power functions

, Volume 86 (3) – Mar 7, 2017
28 pages

/lp/springer_journal/ccz-equivalence-of-power-functions-XSUXFfhTA2
Publisher
Springer Journals
Subject
Mathematics; Combinatorics; Coding and Information Theory; Data Structures, Cryptology and Information Theory; Data Encryption; Discrete Mathematics in Computer Science; Information and Communication, Circuits
ISSN
0925-1022
eISSN
1573-7586
D.O.I.
10.1007/s10623-017-0350-8
Publisher site
See Article on Publisher Site

### Abstract

Let $$F\simeq {{\mathrm{GF}}}(p^n)$$ F ≃ GF ( p n ) be a finite field of characteristic p and $$p_k$$ p k and $$p_\ell$$ p ℓ be power functions on F defined by $$p_k(x)=x^k$$ p k ( x ) = x k and $$p_\ell (x)=x^\ell$$ p ℓ ( x ) = x ℓ respectively. We show, that $$p_k$$ p k and $$p_\ell$$ p ℓ are CCZ equivalent, if and only if there exists a positive integer $$0\le a< n$$ 0 ≤ a < n , such that $$\ell \equiv p^a k \pmod {p^n-1}$$ ℓ ≡ p a k ( mod p n - 1 ) or $$k\ell \equiv p^a \pmod {p^n-1}$$ k ℓ ≡ p a ( mod p n - 1 ) .

### Journal

Designs, Codes and CryptographySpringer Journals

Published: Mar 7, 2017

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