Related papers: Fast Generation of RSA Keys using Smooth Integers
The assumed computationally difficulty of factoring large integers forms the basis of security for RSA public-key cryptography, which specifically relies on products of two large primes or semi-primes. The best-known factoring algorithms…
In this paper, we provide a generalization of Proth's theorem for integers of the form $Kp^n+1$. In particular, a primality test that requires only one modular exponentiation similar to that of Fermat's test without the computation of any…
Unit testing verifies the presence of faults in individual software components. Previous research has been targeting the automatic generation of unit tests through the adoption of random or search-based algorithms. Despite their…
Randomized smoothing (RS) is one of the prominent techniques to ensure the correctness of machine learning models, where point-wise robustness certificates can be derived analytically. While RS is well understood for classification, its…
Algorithmic verification of realistic systems to satisfy safety and other temporal requirements has suffered from poor scalability of the employed formal approaches. To design systems with rigorous guarantees, many approaches still rely on…
Quality randomness is fundamental to cryptographic operations but on embedded systems good sources are (seemingly) hard to find. Rather than use expensive custom hardware, our ERHARD-RNG Pseudo-Random Number Generator (PRNG) utilizes…
The wide deployment of the generative pre-trained transformer (GPT) has raised privacy concerns for both clients and servers. While cryptographic primitives can be employed for secure GPT inference to protect the privacy of both parties,…
Random Number Generators (RNGs) are crucial for applications ranging from cryptography to simulations. Depending on the source of randomness, RNGs are classified into Pseudo-Random Number Generators (PRNGs), True Random Number Generators…
Based on Restricted Boltzmann Machines (RBMs), an improved pseudo-stochastic sequential cipher generator is proposed. It is effective and efficient because of the two advantages: this generator includes a stochastic neural network that can…
The unpredictability of random numbers is fundamental to both digital security and applications that fairly distribute resources. However, existing random number generators have limitations-the generation processes cannot be fully traced,…
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…
Randomness extraction is indispensable for quantum random number generators, serving to eliminate bias and potential information leakage from raw measurement data. Conventional extractors operate in a block-wise fashion, requiring the…
Integer factorization is a fundamental problem in algorithmic number theory and computer science. It is considered as a one way or trapdoor function in the (RSA) cryptosystem. To date, from elementary trial division to sophisticated methods…
Threshold cryptography has gained momentum in the last decades as a mechanism to protect long term secret keys. Rather than having a single secret key, this allows to distribute the ability to perform a cryptographic operation such as…
Pragmatic reasoning helps interlocutors infer intended meaning from ambiguous or underspecified messages by considering shared context and counterfactual alternatives. Similar challenges arise in natural language-to-code generation, where…
Randomness is a vital resource for modern day information processing, especially for cryptography. A wide range of applications critically rely on abundant, high quality random numbers generated securely. Here we show how to expand a random…
Ensuring correctness is crucial for code generation. Formal verification offers a definitive assurance of correctness, but demands substantial human effort in proof construction and hence raises a pressing need for automation. The primary…
Cryptography is the science of encrypting the information so that it is rendered unreadable for an intruder. Cryptographic techniques are of utmost importance in today's world as the information to be sent might be of invaluable importance…
In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear…
Public-key cryptography has become a popular way to motivate the teaching of concepts in elementary number theory, abstract algebra, and introduction to proof courses, as well as in cryptography courses. Unfortunately, many experts expect…