Results 11 to 20 of about 524 (199)

A new Mersenne prime [PDF]

Mathematics of Computation, 1991
The number 2 110503
W. N. Colquitt, L. Welsh
openaire   +2 more sources

Acerca de algunos exponentes de Mersenne (About some Mersenne exponents)

Revista Digital Matemática, Educación e Internet
Los números primos de Mersenne crecen de manera vertiginosa y se vuelven intratables con las herramientas de cómputo actuales. En este trabajo se repasan brevemente las cadenas de Mersenne para mostrar cómo ese crecimiento exponencial impone un límite en
Gerardo Miramontes de León
doaj   +3 more sources

Efficient and Constant Time Modular Reduction With Generalized Mersenne Primes

IEEE Access
Many cryptographic applications require a vast number of modular multiplications with a large prime modulus. Generalized Mersennes are a class of primes commonly used in cryptography because of their special forms.
Serdar S. Erdem, Sezer S. Erdem
doaj   +2 more sources

Gaussian Mersenne and Eisenstein Mersenne primes [PDF]

Mathematics of Computation, 2010
The Biquadratic Reciprocity Law is used to produce a deterministic primality test for Gaussian Mersenne norms which is analogous to the Lucas–Lehmer test for Mersenne numbers. It is shown that the proposed test could not have been obtained from the Quadratic Reciprocity Law and Proth’s Theorem.
Pedro Berrizbeitia, Boris Iskra
openaire   +2 more sources

Non-negative Solutions of the Nonlinear Diophantine Equation (8^n)^x + p^y=z^2 for Some Prime Number p

Walailak Journal of Science and Technology, 2021
In this paper, we explain all non-negative integer solutions for the nonlinear Diophantine equation of type 8x + py = z2 when p is an arbitrary odd prime number and incongruent with 1 modulo 8.
Boorapa SINGHA
doaj   +3 more sources

The Power of Hashing with Mersenne Primes

CoRR, 2020
The classic way of computing a $k$-universal hash function is to use a random degree-$(k-1)$ polynomial over a prime field $\mathbb Z_p$. For a fast computation of the polynomial, the prime $p$ is often chosen as a Mersenne prime $p=2^b-1$. In this paper, we show that there are other nice advantages to using Mersenne primes.
Thomas Dybdahl Ahle, Jakob Bæk Tejs Knudsen, Mikkel Thorup   +2 more
openaire   +2 more sources

Prime-Field Masking in Hardware and its Soundness against Low-Noise SCA Attacks

Transactions on Cryptographic Hardware and Embedded Systems, 2023
A recent study suggests that arithmetic masking in prime fields leads to stronger security guarantees against passive physical adversaries than Boolean masking.
Gaëtan Cassiers, Loïc Masure, Charles Momin, Thorben Moos, François-Xavier Standaert   +4 more
doaj   +1 more source

The search for the largest non Mersenne prime number

, 2021
I bring novelties in the search for the largest non mersenne prime number coming if not at the greatest number very close to ...
Luis Felipe massena misiec (8212830)
core   +1 more source

A New Mersenne Prime [PDF]

Mathematics of Computation, 1958
Am 8. September 1957 ergab die schwedische Elektronenrechenmaschine BESK (siehe auch nachstehendes Referat Zbl 0082.25602) nach einer Laufzeit von 5h 30m die Zahl \(2^{3217}-1\) als Primzahl. (Nachgeprüft am 12. September.) Sie ist, mit ihren 969 Stellen vollständig mitgeteilt, nunmehr die größe bekannte Primzahl.
openaire   +2 more sources

Partitions of numbers and the algebraic principle of Mersenne, Fermat and even perfect numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Let ρ be an odd prime greater than or equal to 11. In a previous work, starting from an M-cycle in a finite field 𝔽_ρ, it has been established how the divisors of Mersenne, Fermat and Lehmer numbers arise.
A. M. S. Ramasamy
doaj   +1 more source