Efficient probabilistic algorithm for solving quadratic equations over finite fields

1987 ◽  
Vol 23 (17) ◽  
pp. 869 ◽  
Author(s):  
T. Itoh
Keyword(s):  
Finite Fields ◽  
Probabilistic Algorithm ◽  
Quadratic Equations

scholarly journals Constructing Isogenies between Elliptic Curves Over Finite Fields

1999 ◽  
Vol 2 ◽  
pp. 118-138 ◽  
Author(s):  
Steven D. Galbraith
Keyword(s):  
Finite Field ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Endomorphism Ring ◽  
Elliptic Curve Cryptography ◽  
Class Number ◽  
Probabilistic Algorithm ◽  
Worst Case ◽  
Curves Over Finite Fields ◽  
Exponential Complexity

AbstractLet E1 and E2 be ordinary elliptic curves over a finite field Fp such that #E1(Fp) = #E2(Fp). Tate's isogeny theorem states that there is an isogeny from E1 to E2 which is defined over Fp. The goal of this paper is to describe a probabilistic algorithm for constructing such an isogeny.The algorithm proposed in this paper has exponential complexity in the worst case. Nevertheless, it is efficient in certain situations (that is, when the class number of the endomorphism ring is small). The significance of these results to elliptic curve cryptography is discussed.

scholarly journals Factoring Polynomials Using Elliptic Curves

2018 ◽  
Vol 7 (4.10) ◽  
pp. 112
Author(s):  
A. Uma Maheswari ◽  
Prabha Durairaj
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Probabilistic Algorithm ◽  
Numerical Examples ◽  
Polynomials Over Finite Fields ◽  
Factoring Polynomials ◽  
Initial Choice

This paper presents a probabilistic algorithm to factor polynomials over finite fields using elliptic curves. The success of the algorithm depends on the initial choice of elliptic curve parameters. The algorithm is illustrated through numerical examples. 

Finite Fields

1996 ◽  
Author(s):  
Rudolf Lidl ◽  
Harald Niederreiter
Keyword(s):  
Finite Fields
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