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CMA
2010
183views more  CMA 2010»
13 years 1 months ago
Ramanujan's class invariants and their use in elliptic curve cryptography
Complex Multiplication (CM) method is a frequently used method for the generation of elliptic curves (ECs) over a prime field Fp. The most demanding and complex step of this metho...
Elisavet Konstantinou, Aristides Kontogeorgis
ESA
2006
Springer
147views Algorithms» more  ESA 2006»
13 years 8 months ago
Univariate Polynomial Real Root Isolation: Continued Fractions Revisited
We present algorithmic, complexity and implementation results concerning real root isolation of integer univariate polynomials using the continued fraction expansion of real algeb...
Elias P. Tsigaridas, Ioannis Z. Emiris
TCS
2008
13 years 4 months ago
On the complexity of real root isolation using continued fractions
We present algorithmic, complexity and implementation results concerning real root isolation of integer univariate polynomials using the continued fraction expansion of real algeb...
Elias P. Tsigaridas, Ioannis Z. Emiris
TC
2008
13 years 4 months ago
Low-Complexity Bit-Parallel Square Root Computation over GF(2^{m}) for All Trinomials
In this contribution we introduce a low-complexity bit-parallel algorithm for computing square roots over binary extension fields. Our proposed method can be applied for any type ...
Francisco Rodríguez-Henríquez, Guill...
CORR
2008
Springer
132views Education» more  CORR 2008»
13 years 4 months ago
Trading GRH for algebra: algorithms for factoring polynomials and related structures
Abstract. In this paper we develop a general technique to eliminate the assumption of the Generalized Riemann Hypothesis (GRH) from various deterministic polynomial factoring algor...
Gábor Ivanyos, Marek Karpinski, Lajos R&oac...