相关论文: On additive differential probabilities of the comp…

Due to implementation constraints the XOR operation is widely used in order to combine plaintext and key bit-strings in secret-key block ciphers. This choice directly induces the classical version of the differential attack by the use of…

In a XOR-based alternating block cipher the plaintext is masked by a sequence of layers each performing distinct actions: a highly nonlinear permutation, a linear transformation, and the bitwise key addition. When assessing resistance…

Let $\mathcal{R}$ be a commutative ring with unity, and let $P$ be a locally finite poset. The aim of the paper is to provide an explicit description of the additive biderivations of the incidence algebra $I(P, \mathcal{R})$. We demonstrate…

We introduce a truncated addition operation on pairs of N-bit binary numbers that interpolates between ordinary addition mod 2^N and bitwise addition in (Z/2Z)^N. We use truncated addition to analyze hash functions that are built from the…

Composition is one of the most important properties of differential privacy (DP), as it allows algorithm designers to build complex private algorithms from DP primitives. We consider precise composition bounds of the overall privacy loss…

This article describes a lightweight additive homomorphic algorithm with the same encryption and decryption keys. Compared to standard additive homomorphic algorithms like Paillier, this algorithm reduces the computational cost of…

In this brief note, we consider estimation of the bitwise combination $x_1 \lor \dots \lor x_n = \max_i x_i$ observing a set of noisy bits $\tilde x_i \in \{0, 1\}$ that represent the true, unobserved bits $x_i \in \{0, 1\}$ under…

Fix a positive integer $N$. Select an additive composition $\xi$ of $N$ uniformly out of $2^{N-1}$ possibilities. The interplay between the number of parts in $\xi$ and the maximum part in $\xi$ is our focus. It is not surprising that…

The problem is related to all-or-nothing transforms (AONT) suggested by Rivest as a preprocessing for encrypting data with a block cipher. Since then there have been various applications of AONTs in cryptography and security. D'Arco,…

In this paper we investigate some new problems in additive combinatorics. Our problems mainly involve permutations (or circular permutations) $n$ distinct numbers (or elements of an additive abelian group) $a_1,\ldots,a_n$ with adjacent…

We extend the Ax-Katz theorem for a single polynomial from finite fields to the rings Z_m with m composite. This extension not only yields the analogous result, but gives significantly higher divisibility bounds. We conjecture what computer…

This paper presents a novel strategy to decentralize the soft detection procedure in an uplink cell-free massive multiple-input-multiple-output network. We propose efficient approaches to compute the a posteriori probability-per-bit,…

The exact composition of mechanisms for which two differential privacy (DP) constraints hold simultaneously is studied. The resulting privacy region admits an exact representation as a mixture over compositions of mechanisms of…

Let $\R$ be an alternative ring containing a nontrivial idempotent and $\D$ be a multiplicative Lie-type derivation from $\R$ into itself. Under certain assumptions on $\R$, we prove that $\D$ is almost additive. Let $p_n(x_1, x_2, \cdots,…

We consider finite dimensional representations of the dihedral group $D_{2p}$ over an algebraically closed field of characteristic two where $p$ is an odd integer and study the degrees of generating and separating polynomials in the…

Let $M_n$ be an $n$ by $n$ random matrix where each entry is +1 or -1 independently with probability 1/2. Our main result implies that the probability that $M_n$ is singular is at most $(1/\sqrt{2} + o(1))^n$, improving on the previous best…

We consider questions related to the computation of the capacity of codes that avoid forbidden difference patterns. The maximal number of $n$-bit sequences whose pairwise differences do not contain some given forbidden difference patterns…

Let p and r be two primes and n, m be two distinct divisors of pr. Consider the n-th and m-th cyclotomic polynomials. In this paper, we present lower and upper bounds for the coefficients of the inverse of one of them modulo the other one.…

Inspired by Armin Straub's conjecture (arXiv:1601.07161) about the number and maximal size of (2n+1, 2n+3)-core partitions with distinct parts, we develop relatively efficient, symbolic-computational algorithms, based on non-linear…

We address the problem of solving systems of two bivariate polynomials of total degree at most $d$ with integer coefficients of maximum bitsize $\tau$. It is known that a linear separating form, that is a linear combination of the variables…