Results 11 to 20 of about 2,393 (165)
On the Distribution of Atkin and Elkies Primes [PDF]
, 2011 Given an elliptic curve E over a finite field F_q of q elements, we say that an odd prime ell not dividing q is an Elkies prime for E if t_E^2 - 4q is a square modulo ell, where t_E = q+1 - #E(F_q) and #E(F_q) is the number of F_q-rational points on E ...
Shparlinski, Igor E. +1 more
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Partitions of numbers and the algebraic principle of Mersenne, Fermat and even perfect numbers [PDF]
Notes on Number Theory and Discrete MathematicsLet 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
ON A NEW CLASS OF SMARANDACHE PRIME NUMBERS [PDF]
, 2005 The purpose of this note is to report on the discovery of some new prime numbers that were built from factorials, the Smarandache Consecutive Sequence, and the Smarandache Reverse ...
Earls, Jason
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International Journal of Mathematics and Mathematical Sciences, 2015 Elliptic curves have a wide variety of applications in computational number theory such as elliptic curve cryptography, pairing based cryptography, primality tests, and integer factorization.
Keisuke Hakuta
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Experimental Evidence of Quantum Randomness Incomputability
, 2010 In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e.\ it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an asymptotic property -
Calude, Cristian S. +3 more
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Deterministic elliptic curve primality proving for a special sequence of numbers
, 2013 We give a deterministic algorithm that very quickly proves the primality or compositeness of the integers N in a certain sequence, using an elliptic curve E/Q with complex multiplication by the ring of integers of Q(sqrt(-7)). The algorithm uses O(log N)
Everest +5 more
core +2 more sources
Four primality testing algorithms [PDF]
, 2008 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.
Schoof, Rene
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On Taking Square Roots without Quadratic Nonresidues over Finite Fields
, 2009 We present a novel idea to compute square roots over finite fields, without being given any quadratic nonresidue, and without assuming any unproven hypothesis. The algorithm is deterministic and the proof is elementary.
Sze, Tsz-Wo
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Trust‐region filter algorithms utilizing Hessian information for gray‐box optimization
AIChE Journal, EarlyView.Abstract Optimizing industrial processes often involves gray‐box models that couple algebraic glass‐box equations with black‐box components lacking analytic derivatives. Such systems challenge derivative‐based solvers. The classical trust‐region filter (TRF) algorithm provides a robust framework but requires extensive parameter tuning and numerous ...
Gul Hameed +4 more
wiley +1 more source
A trust‐region funnel algorithm for gray‐box optimization
AIChE Journal, EarlyView.Abstract Gray‐box optimization, where parts of optimization problems are represented by algebraic models while others are treated as black‐box models lacking analytic derivatives, remains a challenge. Trust‐region (TR) methods provide a robust framework for gray‐box problems through local reduced models (RMs) for black‐box components, but they are ...
Gul Hameed +4 more
wiley +1 more source