Related papers: Comparing the difficulty of factorization and disc…

In late 2012 and early 2013 the discrete logarithm problem (DLP) in finite fields of small characteristic underwent a dramatic series of breakthroughs, culminating in a heuristic quasi-polynomial time algorithm, due to Barbulescu, Gaudry,…

The inference of Large language models (LLMs) requires immense computation and memory resources. To curtail these costs, quantisation has merged as a promising solution, but existing LLM quantisation mainly focuses on 8-bit. In this work,…

We give new characterizations of the sample complexity of answering linear queries (statistical queries) in the local and central models of differential privacy: *In the non-interactive local model, we give the first approximate…

Shor's algorithm is one of the most promising applications of quantum computers. However, since $\sim 10^6$ physical qubits are believed to be required for established approaches, the algorithm will need to be distributed across many…

The RSA cryptosystem could be easily broken with large scale general purpose quantum computers running Shor's factorization algorithm. Being such devices still in their infancy, a quantum annealing approach to integer factorization has…

Let f be an arbitrary positive integer valued function. The goal of this note is to show that one can construct a finitely generated group in which the discrete log problem is polynomially equivalent to computing the function f. In…

This paper elaborates on a sieving technique that has first been applied in 2018 for improving bounds on deterministic integer factorization. We will generalize the sieve in order to obtain a polynomial-time reduction from integer…

Factorization and multiplication of dense matrices and tensors are critical, yet extremely expensive pieces of the scientific toolbox. Careful use of low rank approximation can drastically reduce the computation and memory requirements of…

In recent years, advancements in quantum chip technology, such as Willow, have contributed to reducing quantum computation error rates, potentially accelerating the practical adoption of quantum computing. As a result, the design of quantum…

Differential privacy for the 2020 census required an estimated 90 terabytes of randomness [GL20], an amount which may be prohibitively expensive or entirely infeasible to generate. Motivated by these practical concerns, [CSV25] initiated…

In this paper we address two different problems related with the factorization of an RSA module N. First we can show that factoring is equivalent in deterministic polynomial time to counting points on a pair of twisted Elliptic curves…

Factoring large integers using a quantum computer is an outstanding research problem that can illustrate true quantum advantage over classical computers. Exponential time order is required in order to find the prime factors of an integer by…

This paper explores vulnerabilities in RSA cryptosystems that arise from improper prime number selection during key generation. We examine two primary attack vectors: Fermat's factorization method, which exploits RSA keys generated with…

We revisit Schnorr's lattice-based integer factorization algorithm, now with an effective point of view. We present effective versions of Theorem 2 of Schnorr's "Factoring integers and computing discrete logarithms via diophantine…

The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…

The theoretical aspects of four integer factorization algorithms are discussed in details in this note. The focus is on the performances of these algorithms on the subset of hard to factor balanced integers N = pq, p < q < 2p. The running…

The Implicit Factorization Problem was first introduced by May and Ritzenhofen at PKC'09. This problem aims to factorize two RSA moduli $N_1=p_1q_1$ and $N_2=p_2q_2$ when their prime factors share a certain number of least significant bits…

The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore…

Digitized adiabatic quantum factorization is a hybrid algorithm that exploits the advantage of digitized quantum computers to implement efficient adiabatic algorithms for factorization through gate decompositions of analog evolutions. In…

This paper presents a novel algorithm for the modulus operation for FPGA implementation. The proposed algorithm use only addition, subtraction, logical, and bit shift operations, avoiding the complexities and hardware costs associated with…