International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Tor Helleseth

Publications

Year
Venue
Title
2017
ASIACRYPT
2010
EPRINT
On isotopisms of commutative presemifields and CCZ-equivalence of functions
Lilya Budaghyan Tor Helleseth
A function $F$ from \textbf{F}$_{p^n}$ to itself is planar if for any $a\in$\textbf{F}$_{p^n}^*$ the function $F(x+a)-F(x)$ is a permutation. CCZ-equivalence is the most general known equivalence relation of functions preserving planar property. This paper considers two possible extensions of CCZ-equivalence for functions over fields of odd characteristics, one proposed by Coulter and Henderson and the other by Budaghyan and Carlet, and we show that they in fact coincide with CCZ-equivalence. We prove that two finite commutative presemifields of odd order are isotopic if and only if they are strongly isotopic. This result implies that two isotopic commutative presemifields always define CCZ-equivalent planar functions (this was unknown for the general case). Further we prove that, for any odd prime $p$ and any positive integers $n$ and $m$, the indicators of the graphs of functions $F$ and $F'$ from \textbf{F}$_{p^n}$ to \textbf{F}$_{p^m}$ are CCZ-equivalent if and only if $F$ and $F'$ are CCZ-equivalent. We also prove that, for any odd prime $p$, CCZ-equivalence of functions from \textbf{F}$_{p^n}$ to \textbf{F}$_{p^m}$, is strictly more general than EA-equivalence when $n\ge3$ and $m$ is greater or equal to the smallest positive divisor of $n$ different from 1.
2009
EPRINT
New commutative semifields defined by PN multinomials
Lilya Budaghyan Tor Helleseth
We introduce infinite families of perfect nonlinear Dembowski-Ostrom multinomials over $F_{p^{2k}}$ where $p$ is any odd prime. We prove that for $k$ odd and $p\ne3$ these PN functions define new commutative semifields (in part by studying the nuclei of these semifields). This implies that these functions are CCZ-inequivalent to all previously known PN mappings.
2004
CRYPTO
1996
CRYPTO

Program Committees

Eurocrypt 1998
Eurocrypt 1993 (Program chair)
Eurocrypt 1992
Eurocrypt 1988