Related papers: Fast Generation of RSA Keys using Smooth Integers
Random number generators (RNGs) are notoriously challenging to build and test, especially for cryptographic applications. While statistical tests cannot definitively guarantee an RNG's output quality, they are a powerful verification tool…
We establish rigorous error bounds for prime counting using a truncated Gaussian (TG) kernel in the explicit formula framework. Our main theorem proves that the approximation error remains globally below 1/2 for all sufficiently large…
Principal component analysis (PCA) is widely used for dimension reduction and embedding of real data in social network analysis, information retrieval, and natural language processing, etc. In this work we propose a fast randomized PCA…
Quantum random number generators (QRNGs) promise perfectly unpredictable random numbers. However, the security certification of the random numbers in form of a stochastic model often introduces assumptions that are either hardly justified…
Software Testing is a process to identify the quality and reliability of software, which can be achieved through the help of proper test data. However, doing this manually is a difficult task due to the presence of number of predicate nodes…
We present a special-purpose algorithm for factoring semiprimes $N = pq$ in which one prime factor satisfies $p \approx c\,(a/b)^n$ for positive integers $a, b, c, n$ with $a > b$ and $\gcd(a,b) = 1$. Given the correct parameters $(a, b)$,…
Random numbers sequences (RNSs) play a vital role in various scientific and engineering applications. They are critical to the integrity of classical and quantum cryptography, the accuracy of mathematical modeling and Monte Carlo…
An efficient integer factorization algorithm would reduce the security of all variants of the RSA cryptographic scheme to zero. Despite the passage of years, no method for efficiently factoring large semiprime numbers in a classical…
We propose a multi-scale analysis method for studying arithmetic properties of integer sets, such as primality. Our approach organizes information through a hierarchy of nested sequences, where each level enables a hierarchical expression…
This paper considers the phase retrieval problem in which measurements consist of only the magnitude of several linear measurements of the unknown, e.g., spectral components of a time sequence. We develop low-complexity algorithms with…
We present and demonstrate a new protocol for practical quantum cryptography, tailored for an implementation with weak coherent pulses to obtain a high key generation rate. The key is obtained by a simple time-of-arrival measurement on the…
Quantum random number generation is a technique to generate random numbers by extracting randomness from specific quantum processes. As for practical random number generators, they are required not only to have no information leakage but…
We demonstrate extraction of randomness from spontaneous-emission events less than 36 ns in the past, giving output bits with excess predictability below $10^{-5}$ and strong metrological randomness assurances. This randomness generation…
Semi-quantum cryptography involves at least one user who is semi-quantum or "classical" in nature. Such a user can only interact with the quantum channel in a very restricted way. Many semi-quantum key distribution protocols have been…
Generating secure random numbers is vital to the security and privacy infrastructures we rely on today. Having a computer system generate a secure random number is not a trivial problem due to the deterministic nature of computer systems.…
Today, Internet becomes the essential part of our lives. Over 90 percent of the ecommerce is developed on the Internet. A security algorithm became very necessary for producer client transactions assurance and the financial applications…
We discuss a procedure, which should be called Lenstra's fix, for producing secure RSA moduli even when the random number generation is very poor.
Random numbers are widely used for information security, cryptography, stochastic modeling, and quantum simulations. Key technical challenges for physical random number generation are speed and scalability. We demonstrate a method for…
Despite significant advancements in natural language generation, controlling language models to produce texts with desired attributes remains a formidable challenge. In this work, we introduce RSA-Control, a training-free controllable text…
In classical two-party computation, a trusted initializer who prepares certain initial correlations, known as one-time tables, can help make the inputs of both parties information-theoretically secure. We propose some bipartite quantum…