Related papers: A kilobit hidden SNFS discrete logarithm computati…
Pairing based cryptography is in a dangerous position following the breakthroughs on discrete logarithms computations in finite fields of small characteristic. Remaining instances are built over finite fields of large characteristic and…
Large integer factorization is a prominent research challenge, particularly in the context of quantum computing. This holds significant importance, especially in information security that relies on public key cryptosystems. The classical…
We describe implementations for solving the discrete logarithm problem in the class group of an imaginary quadratic field and in the infrastructure of a real quadratic field. The algorithms used incorporate improvements over previously-used…
There are various approaches to exploiting "hidden structure" in instances of hard combinatorial problems to allow faster algorithms than for general unstructured or random instances. For SAT and its counting version #SAT, hidden structure…
This paper introduces a new public key cryptosystem based on two hard problems : the cube root extraction modulo a composite moduli (which is equivalent to the factorisation of the moduli) and the discrete logarithm problem. These two hard…
Machine learning models are increasingly used in high-stakes decision-making systems. In such applications, a major concern is that these models sometimes discriminate against certain demographic groups such as individuals with certain…
The discrete logarithm in a finite group of large order has been widely applied in public key cryptosystem. In this paper, we will present a probabilistic algorithm for discrete logarithm.
Recent breakthrough methods \cite{gggz,joux,bgjt} on computing discrete logarithms in small characteristic finite fields share an interesting feature in common with the earlier medium prime function field sieve method \cite{jl}. To solve…
With the development of machine learning, it is difficult for a single server to process all the data. So machine learning tasks need to be spread across multiple servers, turning the centralized machine learning into a distributed one.…
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 discrete logarithm problem is one of the backbones in public key cryptography. In this paper we study the discrete logarithm problem in the group of circulant matrices over a finite field. This gives rise to secure and fast public key…
Differentially private SGD (DPSGD) has recently shown promise in deep learning. However, compared to non-private SGD, the DPSGD algorithm places computational overheads that can undo the benefit of batching in GPUs. Micro-batching is a…
We study the problem of differentially private (DP) mechanisms for representing sets of size $k$ from a large universe. Our first construction creates $(\epsilon,\delta)$-DP representations with error probability of $1/(e^\epsilon + 1)$…
Differentially private collaborative filtering is a challenging task, both in terms of accuracy and speed. We present a simple algorithm that is provably differentially private, while offering good performance, using a novel connection of…
Interval-valued computing is a relatively new computing paradigm. It uses finitely many interval segments over the unit interval in a computation as data structure. The satisfiability of Quantified Boolean formulae and other hard problems,…
Prime numbers are fundamental in number theory and play a significant role in various areas, from pure mathematics to practical applications, including cryptography. In this contribution, we introduce a multithreaded implementation of the…
Currently, public-key compression of supersingular isogeny Diffie-Hellman (SIDH) and its variant, supersingular isogeny key encapsulation (SIKE) involve pairing computation and discrete logarithm computation. In this paper, we propose novel…
A backdoor in a finite-domain CSP instance is a set of variables where each possible instantiation moves the instance into a polynomial-time solvable class. Backdoors have found many applications in artificial intelligence and elsewhere,…
We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete…
Factorisation of integers $n$ is of number theoretic and cryptographic significance. The Number Field Sieve (NFS) introduced circa 1990, is still the state of the art algorithm, but no rigorous proof that it halts or generates relationships…