Related papers: A Novel Application of Boolean Functions with High…
Boolean networks have been used in a variety of settings, as models for general complex systems as well as models of specific systems in diverse fields, such as biology, engineering, and computer science. Traditionally, their properties as…
Symmetric key cryptography stands as a fundamental cornerstone in ensuring security within contemporary electronic communication frameworks. The cryptanalysis of classical symmetric key ciphers involves traditional methods and techniques…
We address the challenge of implementing reliable computation of Boolean functions in future nanocircuit fabrics. Such fabrics are projected to have very high defect rates. We overcome this limitation by using a combination of cheap but…
In this note, we go further on the "basis exchange" idea presented in \cite{LiNa1} by using Mobious inversion. We show that the matrix $S_1(f)S_0(f)^{-1}$ has a nice form when $f$ is chosen to be the majority function, where $S_1(f)$ is the…
We introduce and study the minimum distance function of a graded ideal in a polynomial ring with coefficients in a field, and show that it generalizes the minimum distance of projective Reed-Muller-type codes over finite fields. This gives…
Systems of Boolean equations of low degree arise in a natural way when analyzing block ciphers. The cipher's round functions relate the secret key to auxiliary variables that are introduced by each successive round. In algebraic…
In this paper, we study the relationship between algebraic manipulation detection (AMD) codes and highly nonlinear functions. As applications, on one hand, a generic construction for systematic AMD codes is introduced based on highly…
We introduce a new class of rate one-half binary codes: {\bf complementary information set codes.} A binary linear code of length $2n$ and dimension $n$ is called a complementary information set code (CIS code for short) if it has two…
The nonlinear filter model is an old and well understood approach to the design of secure stream ciphers. Extensive research over several decades has shown how to attack stream ciphers based on this model and has identified the security…
In this paper, we establish a new bound tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a…
This article addresses a fundamental problem faced by the ab initio community: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a novel, basis-set independent,…
Minimal models of a Boolean formula play a pivotal role in various reasoning tasks. While previous research has primarily focused on qualitative analysis over minimal models; our study concentrates on the quantitative aspect, specifically…
Bent functions, or equivalently, Hadamard difference sets in the elementary Abelian group $(\gf(2^{2m}), +)$, have been employed to construct symmetric and quasi-symmetric designs having the symmetric difference property. The main objective…
We wish to generate list-decodable codes over small alphabets using as little randomness as possible. Specifically, we hope to generate codes achieving what we term the Elias bound, which means that they are $(\rho,L)$-list-decodable with…
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arithmetic, BMF employs the Boolean OR and AND operations for the…
Semi-bent Boolean functions are interesting from a cryptographic standpoint, since they possess several desirable properties such as having a low and flat Walsh spectrum, which is useful to resist linear cryptanalysis. In this paper, we…
In [2] we show how to construct information sets for Reed-Muller codes only in terms of their basic parameters. In this work we deal with the corresponding problem for q-ary Generalized Reed-Muller codes of first and second order. We see…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…
We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes our method exploits…