euler totient function
Recently Published Documents


TOTAL DOCUMENTS

39
(FIVE YEARS 13)

H-INDEX

3
(FIVE YEARS 1)

2021 ◽  
Vol 52 (1) ◽  
pp. 17-94
Author(s):  
Javier Diaz-Vargas ◽  
Carlos Jacob Rubio-Barrios ◽  
Horacio Tapia-Recillas

2021 ◽  
Author(s):  
Michael Prendergast

This paper describes a new method for performing secure encryption of blocks of streaming data. This algorithm is an extension of the RSA encryption algorithm. Instead of using a public key (e,n) where n is the product of two large primes and e is relatively prime to the Euler Totient function, φ(n), one uses a public key (n,m,E), where m is the rank of the matrix E and E is an invertible matrix in GL(m,φ(n)). When m is 1, this last condition is equivalent to saying that E is relatively prime to φ(n), which is a requirement for standard RSA encryption. Rather than a secret private key (d,φ(n)) where d is the inverse of e (mod φ(n)), the private key is (D,φ(n)), where D is the inverse of E (mod (φ(n)). The key to making this generalization work is a matrix generalization of the scalar exponentiation operator that maps the set of m-dimensional vectors with integer coefficients modulo n, onto itself.


Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1796
Author(s):  
Štěpán Hubálovský ◽  
Eva Trojovská

Let Fn be the nth Fibonacci number. The order of appearance z(n) of a natural number n is defined as the smallest positive integer k such that Fk≡0(modn). In this paper, we shall find all positive solutions of the Diophantine equation z(φ(n))=n, where φ is the Euler totient function.


Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1083 ◽  
Author(s):  
Daeyeoul Kim ◽  
Umit Sarp ◽  
Sebahattin Ikikardes

In this paper, according to some numerical computational evidence, we investigate and prove certain identities and properties on the absolute Möbius divisor functions and Euler totient function when they are iterated. Subsequently, the relationship between the absolute Möbius divisor function with Fermat primes has been researched and some results have been obtained.


2019 ◽  
Vol 15 (07) ◽  
pp. 1463-1468
Author(s):  
Dominik Burek ◽  
Błażej Żmija

A composite positive integer [Formula: see text] has the Lehmer property if [Formula: see text] divides [Formula: see text] where [Formula: see text] is an Euler totient function. In this paper, we shall prove that if [Formula: see text] has the Lehmer property, then [Formula: see text], where [Formula: see text] is the number of prime divisors of [Formula: see text]. We apply this bound to repunit numbers and prove that there are at most finitely many numbers with the Lehmer property in the set [Formula: see text] where [Formula: see text] denotes the highest power of 2 that divides [Formula: see text], and [Formula: see text] is a fixed real number.


2019 ◽  
Vol 30 (4) ◽  
pp. 536-541 ◽  
Author(s):  
J. Wu

Sign in / Sign up

Export Citation Format

Share Document