PL EN
REVIEW PAPER
DETERMINISTIC ENCODING ON ELLIPTIC CURVES
 
 
More details
Hide details
1
Uniwersytet Warszawski
 
 
Publication date: 2014-12-05
 
 
SBN 2014;6(2): 125-131
 
KEYWORDS
ABSTRACT
The methods of finding points on elliptic curves over finite fields are presented with special emphasis on deterministic algorithms. Such algorithms were unknown until 2005. Earlier methods were probabilistic in nature and their efficiency was strongly conditioned on unproved Riemann conjectures.
REFERENCES (10)
1.
E. Bach, Explicit bounds for primality testing and related problems, Math. Comp. 55 (1990), 355–380.
 
2.
R.R. Farashahi, P.A. Fouque, I.E.Shparlinski, M. Tibouchi, J.F. Voloch, Indifferentiable deterministic hashing to elliptic and hyperelliptic curves, Math. Comp. 82 (2013), 491–512.
 
3.
H. Hasse, Zur Theorie der abstrakten elliptischen Funktionenkrper. I, II & III, Crelle’s Journal 175 (1936).
 
4.
N. Koblitz, Wykład z teorii liczb i kryptografii, Wydawnictwa Naukowo-Techniczne, Warszawa 2006.
 
5.
N. Koblitz, Algebraiczne aspekty kryptografii, Wydawnictwa Naukowo-Techniczne, Warszawa 2000.
 
6.
A. Schinzel, M. Skałba, On equations y 2 = x n + k in a finite field, Bull. Polish Acad. Sci. Math. 52 (2004), 223–226.
 
7.
A. Shallue, C. van de Woestijne, Construction of rational points on elliptic curves over finite fields, Lecture Notes in Computer Science 4076, Springer 2006, 510–524.
 
8.
D. Shanks, Five number-theoretic algorithms, Congressus Numerantium 7 , Proc. 2 nd Manitoba Conf. on Numerical Math. (University of Manitoba), 1972, 51–70.
 
9.
M. Skałba, Points on elliptic curves over finite fields, Acta Arith. 117 (2005), 293–301.
 
10.
M. Ulas, Rational points on certain hyperelliptic curves over finite fields, Bull. Polish Acad. Sci. Math. 55 (2007), 97–104.
 
ISSN:2082-2677
Journals System - logo
Scroll to top