Boolean functions are essential to systems for secure and reliable communication. This
comprehensive survey of Boolean functions for cryptography and coding covers the whole …

We study the structure of non-expanding sets in the Grassmann graph. We put forth a
hypothesis stating that every small set whose expansion is smaller than 1− δ must be …

We investigate Boolean degree 1 functions for several classical association schemes,
including Johnson graphs, Grassmann graphs, graphs from polar spaces, and bilinear forms …

We initiate the study of Boolean function analysis on high-dimensional expanders. We
describe an analog of the Fourier expansion and of the Fourier levels on simplicial …

We study the main cryptographic features of Boolean functions (balancedness, nonlinearity,
algebraic immunity) when, for a given number $ n $ of variables, the input to these functions …

We prove hypercontractive inequalities on high dimensional expanders. As in the settings of
the p-biased hypercube, the symmetric group, and the Grassmann scheme, our inequalities …

Let κ∈ N+ ℓ satisfy κ 1+⋯+ κ ℓ= n, and let U κ denote the multislice of all strings u∈[ℓ] n
having exactly κ i coordinates equal to i, for all i∈[ℓ]. Consider the Markov chain on U κ …

The FLIP cipher was proposed at Eurocrypt 2016 for the purpose of meliorating the
efficiency of fully homomorphic cryptosystems. Weightwise perfectly balanced Boolean …

In this paper, we firstly introduce a kind of weightwise almost perfectly balanced Boolean
functions. And then, a construction of weightwise perfectly balanced Boolean functions on 2 …

In this paper, we first introduce a class of quartic Boolean functions. And then, the
construction of weightwise perfectly balanced Boolean functions on $2^ m $ variables are …