Related papers: Fast polynomial arithmetic in homomorphic encrypti…
Promise CSPs are a relaxation of constraint satisfaction problems where the goal is to find an assignment satisfying a relaxed version of the constraints. Several well-known problems can be cast as promise CSPs including approximate graph…
This paper establishes a novel upper bound-termed the arithmetic Singleton bound-on the Hamming distance of any simple-root constacyclic code over a finite field. The key technical ingredient is the notion of multiple equal-difference (MED)…
We study the complexity of securely evaluating arithmetic circuits over finite rings. This question is motivated by natural secure computation tasks. Focusing mainly on the case of two-party protocols with security against malicious…
We present a new scheme for quantum homomorphic encryption which is compact and allows for efficient evaluation of arbitrary polynomial-sized quantum circuits. Building on the framework of Broadbent and Jeffery and recent results in the…
Cover-free families are set systems used as solutions for a large variety of problems, and in particular, problems where we deal with $n$ elements and want to identify $d$ invalid ones among them by performing only $t$ tests ($t \leq n$).…
We present a set of new, efficient high-order symplectic methods designed for Hamiltonian systems with cubic or quartic potentials. By demonstrating that polynomial potentials require fewer order conditions, we develop schemes that…
Applying machine learning algorithms to private data, such as financial or medical data, while preserving their confidentiality, is a difficult task. Homomorphic Encryption (HE) is acknowledged for its ability to allow computation on…
Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We…
Ring Learning With Error (RLWE) algorithm is used in Post Quantum Cryptography (PQC) and Homomorphic Encryption (HE) algorithm. The existing classical crypto algorithms may be broken in quantum computers. The adversaries can store all…
We present an algorithm that computes the product of two n-bit integers in O(n log n (4\sqrt 2)^{log^* n}) bit operations. Previously, the best known bound was O(n log n 6^{log^* n}). We also prove that for a fixed prime p, polynomials in…
An efficient randomized polynomial identity test for noncommutative polynomials given by noncommutative arithmetic circuits remains an open problem. The main bottleneck to applying known techniques is that a noncommutative circuit of size…
The problem to construct optimal conflict-avoiding codes of even lengths and the Hamming weight $3$ is completely settled. On the contrary, it is still open for odd lengths. It turns out that the prime lengths are the fundamental cases…
Treewidth and hypertree width have proven to be highly successful structural parameters in the context of the Constraint Satisfaction Problem (CSP). When either of these parameters is bounded by a constant, then CSP becomes solvable in…
The point of this paper is to use affine automorphisms from algebraic geometry to build cryptographic multivariate mappings. We will construct groups G,H, both isomorphic to the cyclic group with a prime number of elements and multilinear…
Data privacy concerns often prevent the use of cloud-based machine learning services for sensitive personal data. While homomorphic encryption (HE) offers a potential solution by enabling computations on encrypted data, the challenge is to…
A method is described which allows to evaluate efficiently a polynomial in a (possibly trivial) extension of the finite field of its coefficients. Its complexity is shown to be lower than that of standard techniques when the degree of the…
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
Many hard graph problems, such as Hamiltonian Cycle, become FPT when parameterized by treewidth, a parameter that is bounded only on sparse graphs. When parameterized by the more general parameter clique-width, Hamiltonian Cycle becomes…
The problem of finding a maximum $2$-matching without short cycles has received significant attention due to its relevance to the Hamilton cycle problem. This problem is generalized to finding a maximum $t$-matching which excludes specified…
Trigraph list homomorphism problems (also known as list matrix partition problems) have generated recent interest, partly because there are concrete problems that are not known to be polynomial time solvable or NP-complete. Thus while…