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When a group acts on a set, it naturally partitions it into orbits, giving rise to orbit problems. These are natural algorithmic problems, as symmetries are central in numerous questions and structures in physics, mathematics, computer…
Homomorphic encryption is one of the main solutions for building secure and privacy-preserving solutions for Machine Learning as a Service. This motivates the development of homomorphic algorithms for the main building blocks of AI,…
The classical heuristic complexity of the Number Field Sieve (NFS) is the solution of an optimization problem that involves an unknown function, usually noted $o(1)$ and called $\xi(N)$ throughout this paper, which tends to zero as the…
Prime factorization is an outstanding problem in arithmetic, with important consequences in a variety of fields, most notably cryptography. Here we employ the intriguing analogy between prime factorization and optical interferometry in…
Being able to compute efficiently a low-weight multiple of a given binary polynomial is often a key ingredient of correlation attacks to LFSR-based stream ciphers. The best known general purpose algorithm is based on the generalized…
Threshold fully homomorphic encryption (ThFHE) enables multiple parties to compute functions over their sensitive data without leaking data privacy. Most of existing ThFHE schemes are restricted to full threshold and require the…
This document describes the symmetric encryption algorithm called Puzzle. It is free and open. The objective of this paper is to get an opinion about its security from the cryptology community. It is separated in two parts, a technical…
We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens…
Distributed state estimation arises in many applications such as position estimation in robot swarms, clock synchronization for processor networks, and data fusion. One characteristic is that agents only have access to noisy measurements of…
cryptographic hash function is a deterministic procedure that compresses an arbitrary block of numerical data and returns a fixed-size bit string. There exist many hash functions: MD5, HAVAL, SHA, ... It was reported that these hash…
This paper gives the definition and property of a bit-pair shadow, and devises the three algorithms of a public key cryptoscheme called JUOAN that is based on a multivariate permutation problem and an anomalous subset product problem to…
Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…
We present a FFT-based algorithm for the computation of a polynomial's coefficients from its roots, and apply it to obtain the coefficients of interpolation polynomials, to invert Vandermondians and to evaluate the symmetric functions of a…
We propose a multi-bit leveled fully homomorphic encryption scheme using multivariate polynomial evaluations. The security of the scheme depends on the hardness of the Learning with Errors (LWE) problem. For homomorphic multiplication, the…
In this paper some cryptographic properties of Boolean functions, including weight, balancedness and nonlinearity, are studied, particularly focusing on splitting functions and cubic Boolean functions. Moreover, we present some quantities…
We introduce efficient $(1+\varepsilon)$-approximation algorithms for the binary matrix factorization (BMF) problem, where the inputs are a matrix $\mathbf{A}\in\{0,1\}^{n\times d}$, a rank parameter $k>0$, as well as an accuracy parameter…
With the development of cloud computing, the storage and processing of massive visual media data has gradually transferred to the cloud server. For example, if the intelligent video monitoring system cannot process a large amount of data…
Cuckoo hashing is a powerful primitive that enables storing items using small space with efficient querying. At a high level, cuckoo hashing maps $n$ items into $b$ entries storing at most $\ell$ items such that each item is placed into one…
Fully homomorphic encryption (FHE) is a powerful encryption technique that allows for computation to be performed on ciphertext without the need for decryption. FHE will thus enable privacy-preserving computation and a wide range of…
This article presents examples of an application of the finite field method for the computation of the characteristic polynomial of the matching arrangement of a graph. Weight functions on edges of a graph with weights from a finite field…