It is of interest in cryptographic applications to obtain practical performance improvements for the discrete logarithm problem over prime fields Fp with p of size ≤ 500 bits. The linear sieve and the cubic sieve methods described in Coppersmith, Odlyzko and Schroeppel’s paper [3] are two practical algorithms for computing discrete logarithms over prime fields. The cubic sieve algorithm is asym...

This review deals with aspects of the cellular and molecular biology of the sieve element/companion cell complex, the functional unit of sieve tubes in angiosperms. It includes the following issues: (a) evolution of the sieve elements; (b) the specific structural outfit of sieve elements and its functional significance; (c) modes of cellular and molecular interaction between sieve element and c...

Macro-sieve electrodes were implanted in the sciatic nerve of five adult male Lewis rats following spinal cord injury to assess the ability of the macro-sieve electrode to interface regenerated peripheral nerve fibers post-spinal cord injury. Each spinal cord injury was performed via right lateral hemisection of the cord at the T9-10 site. Five months post-implantation, the ability of the macro...

According to an established concept, injury of the phloem triggers local sieve plate occlusion including callose-mediated constriction and, possibly, protein plugging of the sieve pores. Sieve plate occlusion can also be achieved by distant stimuli, depends on the passage of electropotential waves (EPWs), and is reversible in intact plants. The time-course of the wound response was studied in s...

We report the factorization of a 135-digit integer by the triple-large-prime variation of the multiple polynomial quadratic sieve. Previous workers [6][10] had suggested that using more than two large primes would be counterproductive, because of the greatly increased number of false reports from the sievers. We provide evidence that, for this number and our implementation, using three large pr...

Sieve tubes are comprised of sieve elements, enucleated cells that are incapable of RNA and protein synthesis. The proteins in sieve elements are supplied from the neighboring companion cells through plasmodesmata. In rice plants, it was unclear whether or not all proteins produced in companion cells had the same distribution pattern in the sieve element-companion cell complex. In this study, t...

Phytoplasmas, biotrophic wall-less prokaryotes, only reside in sieve elements of their host plants. The essentials of the intimate interaction between phytoplasmas and their hosts are poorly understood, which calls for research on potential ultrastructural modifications. We investigated modifications of the sieve-element ultrastructure induced in tomato plants by 'Candidatus Phytoplasma solani,...

The sieve is a morphological scale-space operator that filters an input signal by removing intensity extrema at a specific scale. In images, this processing can be carried out along a path -the 1D sieveor over a connected graph -the 2D sieve. The 2D version of the sieve generally performs better; it is however much more complex to implement. In this paper we present the 1.5D sieve, a Hamiltonia...

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 √ n space or less. In this paper we present two new results: • We describe the rolling sieve, a practical, incremental prime sieve that takes O(n log logn) ti...

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.