Results 11 to 20 of about 3,178 (169)
Primality Proving via One Round in ECPP and One Iteration in AKS [PDF]
, 2003 In this paper, a random primality proving algorithm is proposed, which generates prime certificate of length O(log n). The certificate can be verified in deterministic time O(log^4 n).
Cheng, Qi
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Solving some specific tasks by Euler's and Fermat's Little theorem
Ratio Mathematica, 2019 Euler's and Fermat's Little theorems have a great use in number theory. Euler's theorem is currently widely used in computer science and cryptography, as one of the current encryption methods is an exponential cipher based on the knowledge of number ...
Viliam Ďuriš
doaj +1 more source
An Introduction to Quantum Complexity Theory [PDF]
, 1999 We give a basic overview of computational complexity, query complexity, and communication complexity, with quantum information incorporated into each of these scenarios.
Cleve, Richard
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Characterization of prime and composite numbers using the notion of successive sum of integers and the consequence in primality testing [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we give a characterization of primes and composite natural numbers using the notion of the sum of successive natural numbers. We prove essentially that an odd natural number N≥3 is prime if and only if the unique decomposition of N as a ...
Fateh Mustapha Dehmeche +2 more
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Two Compact Incremental Prime Sieves [PDF]
, 2015 A prime sieve is an algorithm that finds the primes up to a bound $n$. We say that a prime sieve is incremental, if it can quickly determine if $n+1$ is prime after having found all primes up to $n$. We say a sieve is compact if it uses roughly $\sqrt{n}$
Sorenson, Jonathan P.
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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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METHOD OF TESTING LARGE NUMBERS FOR PRIMALITY
Сучасні інформаційні системиThe current stage of scientific and technological development entails ensuring information security across all domains of human activity. Confidential data and wireless channels of remote control systems are particularly sensitive to various types of ...
Vladimir Pevnev +3 more
doaj +1 more source
Constructing elliptic curves of prime order [PDF]
, 2007 We present a very efficient algorithm to construct an elliptic curve E and a finite field F such that the order of the point group E(F) is a given prime number N.
Broker, Reinier, Stevenhagen, Peter
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A deterministic version of Pollard's p-1 algorithm
, 2009 In this article we present applications of smooth numbers to the unconditional derandomization of some well-known integer factoring algorithms. We begin with Pollard's $p-1$ algorithm, which finds in random polynomial time the prime divisors $p$ of an ...
Zralek, Bartosz
core +5 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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