Related papers: Cryptanalysis of RSA Cryptosystem: Prime Factoriza…
In topologically-protected quantum computation, quantum gates can be carried out by adiabatically braiding two-dimensional quasiparticles, reminiscent of entangled world lines. Bonesteel et al. [Phys. Rev. Lett. 95, 140503 (2005)], as well…
In this paper, we present attacks on three types of RSA modulus when the least significant bits of the prime factors of RSA modulus satisfy some conditions. Let $p,$ and $q$ be primes of the form $p=a^{m_1}+r_p$ and $q=b^{m_2}+r_q$…
Today, prime numbers attained exceptional situation in the area of numbers theory and cryptography. As we know, the trend for accessing to the largest prime numbers due to using Mersenne theorem, although resulted in vast development of…
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…
RSA is an incredibly successful and useful asymmetric encryption algorithm. One of the types of implementation flaws in RSA is low entropy of the key generation, specifically the prime number creation stage. This can occur due to flawed…
Prime factorization on quantum processors is typically implemented either via circuit-based approaches such as Shor's algorithm or through Hamiltonian optimization methods based on adiabatic, annealing, or variational techniques. While…
This manuscript describes a technique for computing partial rank-revealing factorizations, such as, e.g, a partial QR factorization or a partial singular value decomposition. The method takes as input a tolerance $\varepsilon$ and an…
Prime numbers play a very vital role in modern cryptography and especially the difficulties involved in factoring numbers composed of product of two large prime numbers have been put to use in many modern cryptographic designs. Thus, the…
Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…
Predicting the cheapest sample size for the optimal stratification in multivariate survey design is a problem in cases where the population frame is large. A solution exists that iteratively searches for the minimum sample size necessary to…
With meteoric developments in communication systems and data storage technologies, the need for secure data transmission is more crucial than ever. The level of security provided by any cryptosystem relies on the sensitivity of the private…
The Grey Wolf Optimizer (GWO) is a swarm intelligence meta-heuristic algorithm inspired by the hunting behaviour and social hierarchy of grey wolves in nature. This paper analyses the use of chaos theory in this algorithm to improve its…
Cryptographic Self-Selection is a paradigm employed by modern Proof-of-Stake consensus protocols to select a block-proposing "leader." Algorand [Chen and Micali, 2019] proposes a canonical protocol, and Ferreira et al. [2022] establish…
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…
We factorize a 48-bit integer using 10 trapped-ion qubits on a Quantinuum's quantum computer. This result outperforms the recent achievement by B. Yan et al., arXiv:2212.12372 (2022), increasing the success probability by a factor of 6 with…
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…
Sparse coding is a core building block in many data analysis and machine learning pipelines. Typically it is solved by relying on generic optimization techniques, that are optimal in the class of first-order methods for non-smooth, convex…
Testing provides means pertaining to assuring software performance. The total aim of software industry is actually to make a certain start associated with high quality software for the end user. However, associated with software testing has…
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…