Results 21 to 30 of about 82,510 (316)

Lattice Points on the Fermat Factorization Method

Journal of Mathematics, 2022
In this paper, we study algebraic properties of lattice points of the arc on the conics x2−dy2=N especially for d=1, which is the Fermat factorization equation that is the main idea of many important factorization methods like the quadratic field sieve ...
Regis Freguin Babindamana, Gilda Rech Bansimba, Basile Guy Richard Bossoto   +2 more
doaj   +1 more source

Integer Factorization – Cryptology Meets Number Theory

Scientific Journal of Gdynia Maritime University, 2019
Integer factorization is one of the oldest mathematical problems. Initially, the interest in factorization was motivated by curiosity about be­haviour of prime numbers, which are the basic building blocks of all other integers.
Josef Pieprzyk
doaj   +1 more source

A note on solitary numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Does 14 have a friend? Until now, this has been an open question. In this note, we prove that a potential friend F of 14 is an odd, non-square positive integer.
Sagar Mandal
doaj   +1 more source

Lacunaryx: Computing bounded-degree factors of lacunary polynomials [PDF]

, 2015
In this paper, we report on an implementation in the free software Mathemagix of lacunary factorization algorithms, distributed as a library called Lacunaryx.
Grenet, Bruno
core   +2 more sources

Labeled Factorization of Integers [PDF]

The Electronic Journal of Combinatorics, 2009
The labeled factorizations of a positive integer $n$ are obtained as a completion of the set of ordered factorizations of $n$. This follows a new technique for generating ordered factorizations found by extending a method for unordered factorizations that relies on partitioning the multiset of prime factors of $n$.
openaire   +2 more sources

A construction of integer-valued polynomials with prescribed sets of lengths of factorizations [PDF]

, 2013
For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a product of n ...
Ch Frei, F Kainrath, P-J Cahen, Sophie Frisch, ST Chapman   +4 more
core   +2 more sources

Factorization of big integer and the security of RSA

网络与信息安全学报, 2017
Three kinds of methods for integer factorization were proposed and the security of RSA was demarcated.RSA is a well-known cryptographic algorithm,using the analysis result of those methods.Through the work,readers could easily realize that if merely ...
Yan-bing REN
doaj   +3 more sources

A New Idea for RSA Backdoors

Cryptography, 2023
This article proposes a new method to inject backdoors in RSA (the public-key cryptosystem invented by Rivest, Shamir, and Adleman) and other cryptographic primitives based on the integer factorization problem for balanced semi-primes.
Marco Cesati
doaj   +1 more source

Mersenne version of Brocard-Ramanujan equation

Journal of New Results in Science, 2023
In this study, we deal with a special form of the Brocard-Ramanujan equation, which is one of the interesting and still open problems of Diophantine analysis.
Ayşe Nalli, Seyran İbrahimov
doaj   +1 more source

Conjugacy Systems Based on Nonabelian Factorization Problems and Their Applications in Cryptography

Journal of Applied Mathematics, 2014
To resist known quantum algorithm attacks, several nonabelian algebraic structures mounted upon the stage of modern cryptography. Recently, Baba et al. proposed an important analogy from the integer factorization problem to the factorization problem over
Lize Gu, Shihui Zheng
doaj   +1 more source