scholarly journals An Improved Architecture of a Hardware Accelerator for Factoring Integers with Elliptic Curve Method

2018 ◽  
Author(s):  
Michal Andrzejczak
Keyword(s):  
Elliptic Curve ◽  
Hardware Accelerator ◽  
Curve Method ◽  
Elliptic Curve Method

scholarly journals A hyperelliptic smoothness test. I

1993 ◽  
Vol 345 (1676) ◽  
pp. 397-408 ◽  
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Density Theorem ◽  
Probabilistic Algorithm ◽  
Smooth Numbers ◽  
Short Intervals ◽  
Jacobian Varieties ◽  
Genus 2 ◽  
Curve Method ◽  
Elliptic Curve Method

This series of papers is concerned with a probabilistic algorithm for finding small prime factors of an integer. While the algorithm is not practical, it yields an improvement over previous complexity results. The algorithm uses the jacobian varieties of curves of genus 2 in the same way that the elliptic curve method uses elliptic curves. In this first paper in the series a new density theorem is presented for smooth numbers in short intervals. It is a key ingredient of the analysis of the algorithm.

Implementation of Embedded Mobile Device Elliptic Curve Algorithm Fast Generating Algorithm

2013 ◽  
Vol 694-697 ◽  
pp. 2599-2603
Author(s):  
Li Hong Zhang ◽  
Shu Qian Chen
Keyword(s):  
Embedded Systems ◽  
Elliptic Curve ◽  
Mobile Device ◽  
Operating Efficiency ◽  
Elliptic Curve Cryptosystem ◽  
Generation Algorithm ◽  
Curve Method ◽  
Security Guarantees ◽  
Elliptic Curve Method ◽  
Improved Algorithm

Elliptic curve cryptosystem is used in the process of embedded systems, the selection and generation algorithm of the elliptic curve will directly affect the efficiency of systems. From Elliptic Curve's selection, Elliptic Curve's structure, Elliptic Curve's generation, this paper discussed the realization of a random elliptic curve method of Embedded Mobile Device, the SEA algorithm and its improved algorithm. The results show that this method can achieve a quick implementation of the elliptic curve method to improve the operating efficiency of embedded systems in the same security guarantees.

scholarly journals Area–time efficient hardware architecture for factoring integers with the elliptic curve method

2005 ◽  
Vol 152 (1) ◽  
pp. 67 ◽  
Author(s):  
J. Pelzl ◽  
M. imka ◽  
T. Kleinjung ◽  
J. Franke ◽  
C. Priplata ◽  
...  
Keyword(s):  
Elliptic Curve ◽  
Hardware Architecture ◽  
Curve Method ◽  
Elliptic Curve Method
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