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STOC
1991
ACM
87views Algorithms» more  STOC 1991»
13 years 8 months ago
Constructing Nonresidues in Finite Fields and the Extended Riemann Hypothesis
We describe a new deterministic algorithm for the problem of constructing k-th
Johannes Buchmann, Victor Shoup
CORR
2008
Springer
129views Education» more  CORR 2008»
13 years 5 months ago
Factoring Polynomials over Finite Fields using Balance Test
We study the problem of factoring univariate polynomials over finite fields. Under the assumption of the Extended Riemann Hypothesis (ERH), Gao [Gao01] designed a polynomial time ...
Chandan Saha
CORR
2008
Springer
132views Education» more  CORR 2008»
13 years 5 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...
CORR
2010
Springer
192views Education» more  CORR 2010»
13 years 2 months ago
Constructing elliptic curve isogenies in quantum subexponential time
Given two elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit an isogeny between them, but finding such an isog...
Andrew M. Childs, David Jao, Vladimir Soukharev
CORR
2004
Springer
104views Education» more  CORR 2004»
13 years 4 months ago
Ramanujan Graphs and the Random Reducibility of Discrete Log on Isogenous Elliptic Curves
Cryptographic applications using an elliptic curve over a finite field filter curves for suitability using their order as the primary criterion: e.g. checking that their order has...
David Jao, Stephen D. Miller, Ramarathnam Venkates...