Related papers: An asymmetric primitive based on the Bivariate Fun…
Additive Fourier Transform is sdudied. A fast multiplication algorithm for polynomials over the binary field is given. The bit complexity of the algorithm is $O(n(log n)(\log\log n)^2)$.
In this short letter we present the construction of a bi-stochastic kernel p for an arbitrary data set X that is derived from an asymmetric affinity function {\alpha}. The affinity function {\alpha} measures the similarity between points in…
In this work, we consider the proportion of smooth (free of large prime factors) values of a binary form $F(X_1,X_2)\in\Z[X_1,X_2]$. In a particular case, we give an asymptotic equivalent for this proportion which depends on $F$. This is…
We present a conceptual framework for extending homomorphic encryption beyond arithmetic or Boolean operations into the domain of intuitionistic logic proofs and, by the Curry-Howard correspondence, into the domain of typed functional…
We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…
The discrete logarithm problem in a finite group is the basis for many protocols in cryptography. The best general algorithms which solve this problem have time complexity of $\mathcal{O}(\sqrt{N}\log N)$, and a space complexity of…
A symmetric encryption method based on properties of quasicrystals is proposed. The advantages of the cipher are strict aperiodicity and everywhere discontinuous property as well as the speed of computation, simplicity of implementation and…
An inherently parallel algorithm is proposed that efficiently performs selection: finding the K-th largest member of a set of N members. Selection is a common component of many more complex algorithms and therefore is a widely studied…
This paper uses a variant of the notion of \emph{inaccessible entropy} (Haitner, Reingold, Vadhan and Wee, STOC 2009), to give an alternative construction and proof for the fundamental result, first proved by Rompel (STOC 1990), that…
Memory-hard functions (MHF) are functions whose evaluation cost is dominated by memory cost. MHFs are egalitarian, in the sense that evaluating them on dedicated hardware (like FPGAs or ASICs) is not much cheaper than on off-the-shelf…
Although one-way functions are well-established as the minimal primitive for classical cryptography, a minimal primitive for quantum cryptography is still unclear. Universal extrapolation, first considered by Impagliazzo and Levin (1990),…
A fundamental problem in computer science is to find all the common zeroes of $m$ quadratic polynomials in $n$ unknowns over $\mathbb{F}_2$. The cryptanalysis of several modern ciphers reduces to this problem. Up to now, the best complexity…
Recent work by Pijnenburg and Poettering (ESORICS'20) explores the novel cryptographic Encrypt-to-Self primitive that is dedicated to use cases of symmetric encryption where encryptor and decryptor coincide. The primitive is envisioned to…
In this paper we compute the Fourier spectra of some recently discovered binomial APN functions. One consequence of this is the determination of the nonlinearity of the functions, which measures their resistance to linear cryptanalysis.…
We propose a new cryptosystem based on polycyclic groups. The cryptosystem is based on the fact that the word problem can be solved effectively in polycyclic groups, while the known solutions to the conjugacy problem are far less efficient.
We define a pseudorandom function (PRF) $F: \mathcal{K} \times \mathcal{X} \rightarrow \mathcal{Y}$ to be bi-homomorphic when it is fully Key homomorphic and partially Input Homomorphic (KIH), i.e., given $F(k_1, x_1)$ and $F(k_2, x_2)$,…
We prove a complexity dichotomy theorem for a class of Holant problems on 3-regular bipartite graphs. Given an arbitrary nonnegative weighted symmetric constraint function $f = [x_0, x_1, x_2, x_3]$, we prove that the bipartite Holant…
King and Saia were the first to break the quadratic word complexity bound for Byzantine Agreement in synchronous systems against an adaptive adversary, and Algorand broke this bound with near-optimal resilience (first in the synchronous…
In recent years, although some homomorphic encryption algorithms have been proposed to provide additive homomorphic encryption and multiplicative homomorphic encryption. However, similarity measures are required for searches and queries…
In this work we advance the understanding of the fundamental limits of computation for Binary Polynomial Optimization (BPO), which is the problem of maximizing a given polynomial function over all binary points. In our main result we…