42 research outputs found
A complete characterization of plateaued Boolean functions in terms of their Cayley graphs
In this paper we find a complete characterization of plateaued Boolean
functions in terms of the associated Cayley graphs. Precisely, we show that a
Boolean function is -plateaued (of weight ) if and only
if the associated Cayley graph is a complete bipartite graph between the
support of and its complement (hence the graph is strongly regular of
parameters ). Moreover, a Boolean function is
-plateaued (of weight ) if and only if the associated
Cayley graph is strongly -walk-regular (and also strongly
-walk-regular, for all odd ) with some explicitly given
parameters.Comment: 7 pages, 1 figure, Proceedings of Africacrypt 201
Constructive Relationships Between Algebraic Thickness and Normality
We study the relationship between two measures of Boolean functions;
\emph{algebraic thickness} and \emph{normality}. For a function , the
algebraic thickness is a variant of the \emph{sparsity}, the number of nonzero
coefficients in the unique GF(2) polynomial representing , and the normality
is the largest dimension of an affine subspace on which is constant. We
show that for , any function with algebraic thickness
is constant on some affine subspace of dimension
. Furthermore, we give an algorithm
for finding such a subspace. We show that this is at most a factor of
from the best guaranteed, and when restricted to the
technique used, is at most a factor of from the best
guaranteed. We also show that a concrete function, majority, has algebraic
thickness .Comment: Final version published in FCT'201
On Hardware Implementation of Tang-Maitra Boolean Functions
In this paper, we investigate the hardware circuit complexity of the class of Boolean functions recently introduced by Tang and Maitra (IEEE-TIT 64(1): 393 402, 2018). While this class of functions has very good cryptographic properties, the exact hardware requirement is an immediate concern as noted in the paper itself. In this direction, we consider different circuit architectures based on finite field arithmetic and Boolean optimization. An estimation of the circuit complexity is provided for such functions given any input size n. We study different candidate architectures for implementing these functions, all based on the finite field arithmetic. We also show different implementations for both ASIC and FPGA, providing further analysis on the practical aspects of the functions in question and the relation between these implementations and the theoretical bound. The practical results show that the Tang-Maitra functions are quite competitive in terms of area, while still maintaining an acceptable level of throughput performance for both ASIC and FPGA implementations
Bison: Instantiating the Whitened Swap-Or-Not Construction
International audienceWe give the first practical instance-bison-of the Whitened Swap-Or-Not construction. After clarifying inherent limitations of the construction, we point out that this way of building block ciphers allows easy and very strong arguments against differential attacks
Unsolved Problems Related to the Covering Radius of Codes
Introduction Codes with low covering radius have applications in source coding and data compression (see [6]). Although there has been considerable activity in recent years in studying these codes ([2]-[4], [6], [7], [9], [10], [12], [13]), many open questions remain. The following are some of the most important. Other problems may be found in [2], [6]. 1. What is the solution to Berlekamp's light-bulb game? In the Math. Dept. Commons Room at Bell Labs in Murray Hill there is a light-bulb game built by Elwyn Berlekamp nearly twenty years ago. There are 100 light-bulbs, arranged in a 10 × 10 array. At the back of the box there are 100 individual switches, one for each bulb. On the front there are 20 switches, one for each row and column. Throwing one of the rear switches changes the state of a single bulb, while throwing one of the front switches changes the state of a whole row or column. Suppose some subset S of the 100 bulbs ar