Related papers: A Factoring and Discrete Logarithm based Cryptosys…
Homomorphic encryption is a very useful gradient protection technique used in privacy preserving federated learning. However, existing encrypted federated learning systems need a trusted third party to generate and distribute key pairs to…
Quantum computations are very important branch of modern cryptology. According to the number of working physical qubits available in general-purpose quantum computers and in quantum annealers, there is no coincidence, that nowadays quantum…
A fault injection framework for the decryption algorithm of the Niederreiter public-key cryptosystem using binary irreducible Goppa codes and classical decoding techniques is described. In particular, we obtain low-degree polynomial…
As society becomes more reliant on computers, cryptographic security becomes increasingly important. Current encryption schemes include the ElGamal signature scheme, which depends on the complexity of the discrete logarithm problem. It is…
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…
Iterative clustering algorithms help us to learn the insights behind the data. Unfortunately, this may allow adversaries to infer the privacy of individuals with some background knowledge. In the worst case, the adversaries know the…
In this paper we describe a deep learning--based probabilistic algorithm for integer factorisation. We use Lawrence's extension of Fermat's factorisation algorithm to reduce the integer factorisation problem to a binary classification…
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…
The semidirect discrete logarithm problem (SDLP) is the following analogue of the standard discrete logarithm problem in the semidirect product semigroup $G\rtimes \mathrm{End}(G)$ for a finite semigroup $G$. Given $g\in G, \sigma\in…
RSA cryptography is still widely used. Some of its applications (e.g., distributed signature schemes, cryptosystems) do not allow the RSA modulus to be generated by a centralized trusted entity. Instead, the factorization must remain…
Clustering is a fundamental problem in data analysis. In differentially private clustering, the goal is to identify $k$ cluster centers without disclosing information on individual data points. Despite significant research progress, the…
In this paper, a new algorithm to solve the discrete logarithm problem is presented which is similar to the usual baby-step giant-step algorithm. Our algorithm exploits the order of the discrete logarithm in the multiplicative group of a…
We revisit Fermat's factorization method for a positive integer $n$ that is a product of two primes $p$ and $q$. Such an integer is used as the modulus for both encryption and decryption operations of an RSA cryptosystem. The security of…
The elliptic curve discrete logarithm problem is of fundamental importance in public-key cryptography. It is in use for a long time. Moreover, it is an interesting challenge in computational mathematics. Its solution is supposed to provide…
The Diophantine Equation Hard Problem (DEHP) is a potential cryptographic problem on the Diophantine equation $U=\sum \limits_{i=1}^n {V_i x_{i}}$. A proper implementation of DEHP would render an attacker to search for private parameters…
We discuss a new attack, termed a dimension or linear decomposition attack, on several known group-based cryptosystems. This attack gives a polynomial time deterministic algorithm that recovers the secret shared key from the public data in…
The ability to hide information from unauthorized individuals has been a prevalent issue over the years. Countless algorithms such as DES, AES and SHA have been developed. These algorithms depend on varying key length and key management…
We consider the problems of Private and Secure Matrix Multiplication (PSMM) and Fully Private Matrix Multiplication (FPMM), for which matrices privately selected by a master node are multiplied at distributed worker nodes without revealing…
Considering the difficult problem under classical computing model can be solved by the quantum algorithm in polynomial time, t-multiple discrete logarithm problems presented. The problem is non-degeneracy and unique solution. We talk about…
Differentially private (DP) decentralized Federated Learning (FL) allows local users to collaborate without sharing their data with a central server. However, accurately quantifying the privacy budget of private FL algorithms is challenging…