Related papers: Notions for RSA integers
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…
In the RSA cryptosystem integers of the form n=p.q with p and q primes of comparable size (`RSA-integers') play an important role. It is a folklore result of cryptographers that C_r(x), the number of integers n<=x that are of the form n=pq…
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.
Primality generation is the cornerstone of several essential cryptographic systems. The problem has been a subject of deep investigations, but there is still a substantial room for improvements. Typically, the algorithms used have two parts…
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…
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…
For a real parameter $r$, the RSA integers are integers which can be written as the product of two primes $pq$ with $p<q\leq rp$, which are named after the importance of products of two primes in the RSA-cryptography. Several authors…
One of the main problems in cryptography is to give criteria to provide good comparators of cipher systems. The security of a cipher system must include the security of the algorithm, the security of the key generator and management module…
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…
Cryptographic standards serve two important goals: making different implementations interoperable and avoiding various known pitfalls in commonly used schemes. This chapter discusses Public-Key Cryptography Standards (PKCS) which have…
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…
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…
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 proposes an alternative approach to formally establishing the correctness of the RSA public key cryptosystem. The methodology presented herein deviates slightly from conventional proofs found in existing literature. Specifically,…
In this paper, we gave a preliminary dynamical analysis on the RSA cryptosystem and obtained a computational formulae of the number of the fixed points of $k$ order of the RSA. Thus, the problem in [8, 9] has been solved.
Many variants of RSA cryptosystem exist in the literature. One of them is RSA over polynomials based on Galois approach. In standard RSA modulus is product of two large primes whereas in the Galois approach author considered the modulus as…
In symmetric key cryptography the sender as well as the receiver possess a common key. Asymmetric key cryptography involves generation of two distinct keys which are used for encryption and decryption correspondingly. The sender converts…
Given the escalating importance of cybersecurity, it becomes increasingly beneficial for a diverse community to comprehend fundamental security mechanisms. Among these, the RSA algorithm stands out as a crucial component in public-key…
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…
In this paper we present a new efficient algorithm for factoring the RSA and the Rabin moduli in the particular case when the difference between their two prime factors is bounded. As an extension, we also give some theoretical results on…