Related papers: Fast Generation of RSA Keys using Smooth Integers
Many modern asymmetric encryption methods rely on prime numbers, as they have distinctive properties. For instance, the security of RSA cryptosystem relies on the computational difficulty of factoring a large composite number in its prime…
The security of RSA algorithm depends upon the positive integer N, which is the multiple of two precise large prime numbers. Factorization of such great numbers is a problematic process. There are many algorithms has been implemented in the…
Prime factorization has been a buzzing topic in the field of number theory since time unknown. However, in recent years, alternative avenues to tackle this problem are being explored by researchers because of its direct application in the…
In this paper we present the experimental results that more clearly than any theory suggest an answer to the question: when in detection of large (probably) prime numbers to apply, a very resource demanding, Miller-Rabin algorithm. Or, to…
This article proposes a new method to inject backdoors in RSA and other cryptographic primitives based on the Integer Factorization problem for balanced semi-primes. The method relies on mathematical congruences among the factors of the…
The key-generation algorithm for the RSA cryptosystem is specified in several standards, such as PKCS#1, IEEE 1363-2000, FIPS 186-3, ANSI X9.44, or ISO/IEC 18033-2. All of them substantially differ in their requirements. This indicates that…
The security of any cryptosystem relies on the secrecy of the system's secret keys. Yet, recent experimental work demonstrates that tens of thousands of devices on the Internet use RSA and DSA secrets drawn from a small pool of candidate…
Modern-day computer security relies heavily on cryptography as a means to protect the data that we have become increasingly reliant on. The main research in computer security domain is how to enhance the speed of RSA algorithm. The…
This paper explores vulnerabilities in RSA cryptosystems that arise from improper prime number selection during key generation. We examine two primary attack vectors: Fermat's factorization method, which exploits RSA keys generated with…
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…
We introduce a prime number generator in the form of a stochastic algorithm. The character of such algorithm gives rise to a continuous phase transition which distinguishes a phase where the algorithm is able to reduce the whole system of…
Generating secure random numbers is a central problem in cryptography that needs a reliable source of enough computing entropy. Without enough entropy available - meaning no good source of secure random numbers - a device is susceptible to…
In this paper, we analyze several variants of a simple method for generating prime numbers with fewer random bits. To generate a prime $p$ less than $x$, the basic idea is to fix a constant $q\propto x^{1-\varepsilon}$, pick a uniformly…
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…
Cryptographic primitives have been used for various non-cryptographic objectives, such as eliminating or reducing randomness and interaction. We show how to use cryptography to improve the time complexity of solving computational problems.…
In this expository paper we describe four primality tests. The first test is very efficient, but is only capable of proving that a given number is either composite or 'very probably' prime. The second test is a deterministic polynomial time…
RSA is one of the most popular Public Key Cryptography based algorithm mainly used for digital signatures, encryption/decryption etc. It is based on the mathematical scheme of factorization of very large integers which is a…
Primality testing is an especially useful topic for public-key cryptography. In this paper, a novel primality test algorithm based on the Pell's cubic will be introduced, and its necessary primality conditions will be proved using three…
This paper presents a new technique of generating large prime numbers using a smaller one by employing Goldbach partitions. Experiments are presented showing how this method produces candidate prime numbers that are subsequently tested…
Numerous methods have been considered to create a fast integer factorization algorithm. Despite its apparent simplicity, the difficulty to find such an algorithm plays a crucial role in modern cryptography, notably, in the security of RSA…