QRD for Parallel Arithmetic Structures

2017 ◽  
Author(s):  
Martin Langhammer
Keyword(s):  
Parallel Arithmetic ◽  
Arithmetic Structures

A fast parallel arithmetic unit

1956 ◽  
Vol 103 (3S) ◽  
pp. 520-527
Author(s):  
K.D. Tocher ◽  
M. Lehman
Keyword(s):  
Arithmetic Unit ◽  
Parallel Arithmetic

The Improvement of Newton Method and the Validation of Optimization Idea of Blind Walking Repeatedly

2011 ◽  
Vol 250-253 ◽  
pp. 4061-4064
Author(s):  
Chun Ling Zhang
Keyword(s):  
Saddle Point ◽  
Newton Method ◽  
Optimization Problem ◽  
Initial Point ◽  
Optimization Method ◽  
Maximum Point ◽  
Optimal Result ◽  
Feasible Domain ◽  
Parallel Arithmetic ◽  
Newton Direction

The existence of maximum point, oddity point and saddle point often leads to computation failure. The optimization idea is based on the reality that the optimum towards the local minimum related the initial point. After getting several optimal results with different initial point, the best result is taken as the final optimal result. The arithmetic improvement of multi-dimension Newton method is improved. The improvement is important for the optimization method with grads convergence rule or searching direction constructed by grads. A computational example with a saddle point, maximum point and oddity point is studied by multi-dimension Newton method, damped Newton method and Newton direction method. The importance of the idea of blind walking repeatedly is testified. Owing to the parallel arithmetic of modernistic optimization method, it does not need to study optimization problem with seriate feasible domain by modernistic optimization method.

scholarly journals On the elliptic time in the adelic gravity

2016 ◽  
Vol 14 (3) ◽  
pp. 307-318
Author(s):  
George Shabat
Keyword(s):  
Elliptic Curves ◽  
Finite Order ◽  
Body Problem ◽  
Two Body Problem ◽  
Arithmetic Structures

The paper is devoted to the algebraic and arithmetic structures related to the two-body problem and discuss the possible generalizations. The role of the points of finite order on the elliptic curves is emphasized.

Arithmetic structures for AES cryptographic systems

2015 ◽  
Author(s):  
Mostafa Abd-El-Barr ◽  
Aisha Al-Noori
Keyword(s):  
Arithmetic Structures

scholarly journals Polynomial representations of the Diffie-Hellman mapping

2001 ◽  
Vol 63 (3) ◽  
pp. 467-473 ◽  
Author(s):  
Edwin El Mahassni ◽  
Igor Shparlinski
Keyword(s):  
Finite Field ◽  
Lower Bounds ◽  
Primitive Root ◽  
Polynomial Equations ◽  
Arithmetic Complexity ◽  
Diffie Hellman ◽  
Polynomial Representations ◽  
Parallel Arithmetic

We obtain lower bounds on the degrees of polynomials representing the Diffie-Hellman mapping (gx, gy) → gxy, where g is a primitive root of a finite field q of q elements. These bounds are exponential in terms of log q. In particular, these results can be used to obtain lower bounds on the parallel arithmetic complexity of breaking the Diffie-Hellman cryptosystem. The method is based on bounds of numbers of solutions of some polynomial equations.

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