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» Efficient computation of the characteristic polynomial
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CMA
2010
183views more  CMA 2010»
14 years 8 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
CASC
2010
Springer
160views Mathematics» more  CASC 2010»
14 years 10 months ago
Factorization of Polynomials and GCD Computations for Finding Universal Denominators
We discuss the algorithms which, given a linear difference equation with rational function coefficients over a field k of characteristic 0, compute a polynomial U(x) ∈ k[x] (a ...
Sergei A. Abramov, A. Gheffar, D. E. Khmelnov
ACMSE
2006
ACM
15 years 3 months ago
Revisiting a limit on efficient quantum computation
In this paper, we offer an exposition of a theorem originally due to Adleman, Demarrais and Huang that shows that the quantum complexity class BQP (Bounded-error Quantum Polynomia...
Tarsem S. Purewal Jr.
ARITH
2007
IEEE
15 years 3 months ago
Efficient polynomial L-approximations
We address the problem of computing a good floating-point-coefficient polynomial approximation to a function, with respect to the supremum norm. This is a key step in most process...
Nicolas Brisebarre, Sylvain Chevillard
CORR
2004
Springer
94views Education» more  CORR 2004»
14 years 11 months ago
Quantum Computing, Postselection, and Probabilistic Polynomial-Time
I study the class of problems efficiently solvable by a quantum computer, given the ability to "postselect" on the outcomes of measurements. I prove that this class coin...
Scott Aaronson