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In this paper, we study the cryptographic properties of an infinite class of balanced vectorial Boolean functions recently introduced by Feng, Liao and Yang. These functions provably achieve an optimum algebraic immunity. We give a simpler proof of this fact and we prove that these functions have also an optimum algebraic degree and a non-weak nonlinearity.
Binary covering arrays have been extensively studied in many different contexts, but the explicit construction of small binary covering arrays with strength larger than three remains poorly understood. Connections with existentially closed graphs and Hadamard matrices are examined, particularly those arising from the Paley graphs and tournaments. Computational results on arrays generated by column...
In this paper, a class of three-weight linear codes and a class of four-weight linear codes over GF(q) are presented and their weight distributions are determined. These codes are punctured from the irreducible cyclic codes, and contain optimal codes. Their duals contain also optimal codes.
We consider binary fingerprinting codes that trace at least one of t pirates using the marking assumption. Ensembles of binary equal-weight codes are considered along with a new efficient decoding algorithm. The design substantially increases the code rates of the former fingerprinting constructions. In particular, for large t, the new t-fingerprinting codes have code rate of t− 2ln 2 and...
A synchronization pattern is a sequence of dots in which the out-of-phase autocorrelation function takes the values zero or one. These patterns have numerous applications in information theory. Recently, two-dimensional synchronization patterns have found application in key predistribution for wireless sensor networks. This application has raised some new questions. We will discuss some of the old...
Client-to-client password-authenticated key agreement (C2C-PAKA) protocol deals with the authenticated key agreement process between two clients of different realms, who only share their passwords with their own servers. Recently, Byun et al. [13] proposed an efficient C2C-PAKA protocol and carried a claimed proof of security in a formal model of communication and adversarial capabilities. In this...
Motivated by a recent application to hash functions suggested by O. Chevassut, P.-A. Fouque, P. Gaudry and D. Pointcheval, we study the frequency with which both an elliptic curve over a finite field, and its quadratic twist are cryptographically suitable. Here, we obtain heuristic estimates for the number of such curves for which both the curve and its twist have a number of points which is prime...
We briefly survey some recent progress on list decoding algorithms for binary codes. The results discussed include: Algorithms to list decode binary Reed-Muller codes of any order up to the minimum distance, generalizing the classical Goldreich-Levin algorithm for RM codes of order 1 (Hadamard codes). These algorithms are “local” and run in time polynomial in the message length...
In this paper we prove two results related to low-density parity-check (LDPC) codes. The first is to show that the generating function attached to the pseudo-codewords of an LDPC code is a rational function, answering a question raised in [6]. The combinatorial information of its numerator and denominator is also discussed. The second concerns an infinite family of q-regular bipartite graphs...
The constraints of lightweight distributed computing environments such as wireless sensor networks lend themselves to the use of symmetric cryptography to provide security services. The lack of central infrastructure after deployment of such networks requires the necessary symmetric keys to be predistributed to participating nodes. The rich mathematical structure of combinatorial designs has resulted...
In this paper, we consider the norm-trace curves which are defined by the equation over where q is a power of a prime number and r ≥ 2 is an integer. We determine the Weierstrass semigroup of the triple of points $\left(P_{\infty}, P_{00}, P_{0b} \right)$ on this curve.
The aim of this article is to describe a new hash algorithm using polynomials over finite fields. In software, it runs at speeds comparable to SHA-384. Hardware implementation of a slightly modified version of the algorithm presented here runs at significantly faster speeds, namely at 2 Gbits/sec on an FPGA Virtex V of frequency 300 MHz. Modelling suggests that this speed can be increased to 3.4 Gbits/sec...
This survey paper gives an overview of algebraic unitary codes. It describes the coding problem involved, and present several algebraic approaches yielding interesting constructions, as well as the latest bounds.
The authentication codes based on the rational normal curves in projective spaces over finite fields were the first construction of the non-Cartesian t-fold perfect authentication codes for arbitrary positive integer t. In this paper it shows that the subfield rational normal curves provide a new family of such codes, its expected probabilities of successful deception for optimal spoofing attacks...
We give two impossibility results regarding strong encryption over an infinite enumerable domain. The first one relates to statistically secure one-time encryption. The second one relates to computationally secure encryption resisting adaptive chosen ciphertext attacks in streaming mode with bounded resources: memory, time delay or output length. Curiously, both impossibility results can be achieved...
The minimum distance between bent and resilient functions is studied. This problem is converted into two problems. One is to construct a special matrix, which leads to a combinatorial problem; the other is the existence of bent functions with specified types. Then the relation of these two problems is studied. For the 1-resilient functions, we get a solution to the first combinatorial problem. By...
Approximate message authentication codes (AMAC) arise naturally in biometric and multimedia applications where plaintexts are fuzzy and a tagged message (x′, t) where t is the calculated tag for a message x that is ‘close’ to x′ should pass the verification test. Fuzziness of plaintexts can be due to a variety of factors including applying acceptable transforms such as compression and decompression...
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