Sieve methods
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Sieve Methods
Preface Sieve methods have had a long and fruitful history. The sieve of Eratosthenes (around 3rd century B.C.) was a device to generate prime numbers. Later Legendre used it in his studies of the prime number counting function π(x). Sieve methods bloomed and became a topic of intense investigation after the pioneering work of Viggo Brun (see [Bru16],[Bru19], [Bru22]). Using his formulation of ...
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A sieve is a technique for bounding the size of a set after the elements with “undesirable properties” (usually of a number theoretic nature) have been removed. The undesirable properties could be divisibility by a prime from a given set, other multiplicative constraints (divisibility by a perfect square for example) or inclusion in a set of residue classes. The methods usually involve some kin...
متن کاملThe Sieve Re-Imagined: Integer Factorization Methods
In this paper, I explain the Quadratic Sieve, its Multiple Polynomial variation, the Number Field Sieve, and give some worked examples of the afore-mentioned algorithms. Using my own Maple implementation of the Quadratic Sieve, I explore the effect of altering one of the parameters of the Quadratic Sieve algorithm, with respect to both time and success rate.
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In order to assess the security of cryptosystems based on the discrete logarithm problem in non-prime finite fields, as are the torus-based or pairing-based ones, we investigate thoroughly the case in Fp6 with the Number Field Sieve. We provide new insights, improvements, and comparisons between different methods to select polynomials intended for a sieve in dimension 3 using a special-q strate...
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In order to assess the security of cryptosystems based on the discrete logarithm problem in non-prime finite fields, as are the torus-based or pairing-based ones, we investigate thoroughly the case in Fp6 with the Number Field Sieve. We provide new insights, improvements, and comparisons between different methods to select polynomials intended for a sieve in dimension 3 using a special-q strate...
متن کاملEffect of Inlet Downcomer on the Hydrodynamic Parameters of Sieve Trays Using CFD Analysis
Nowadays distillation is recognized as one of the economical and the most trustable separation methods in chemical, petroleum, gas and petrochemical industries. It is almost used as a first and the most applicable choice in separation methods. In this article the effect of inlet downcomer on the hydrodynamics of industrial sieve tray has been elaborated. The study was carried out by using a 3-D...
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