We describe an enhanced version of the TWINKLE factoring device and analyse to what extent it can be expected to speed up the sieving step of the Quadratic Sieve and Number Field Sieve factoring algorithms. The bottom line of our analysis is that the TWINKLE-assisted factorization of 768-bit numbers is difficult but doable in about 9 months (including the sieving and matrix parts) by a large or...

Membrane proteins within the sieve element-companion cell complex have essential roles in the physiological functioning of the phloem. The monoclonal antibody line RS6, selected from hybridomas raised against sieve elements isolated from California shield leaf (Streptanthus tortuosus; Brassicaceae) tissue cultures, recognizes an antigen in the Arabidopsis (Arabidopsis thaliana) ecotype Columbia...

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 ...

Apart from cut aphid stylets in combination with electrophysiology, no attempts have been made thus far to measure in vivo sucrose-uptake properties of sieve elements. We investigated the kinetics of sucrose uptake by single sieve elements and phloem parenchyma cells in Vicia faba plants. To this end, microelectrodes were inserted into free-lying phloem cells in the main vein of the youngest fu...

The large sieve has its origins in the work of Linnik and Rényi. It was developed to deal with sequences that avoid a positive proportion of residue classes. It was later simplified by Roth, Bombieri, Davenport, Halberstam, Montgomery, Gallagher and many others. For a survey see Montgomery [12] and Bombieri [1]. It is known that Montgomery’s large sieve [12] is a useful method when sifting sequ...

Sieve elements are one of the least understood cell types in plants. Translocation velocities and volume flow to supply sinks with photoassimilates greatly depend on the geometry of the microfluidic sieve tube system and especially on the anatomy of sieve plates and sieve plate pores. Several models for phloem translocation have been developed, but appropriate data on the geometry of pores, pla...

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...