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ANTS
2004
Springer
95views Algorithms» more  ANTS 2004»
9 years 7 months ago
Using Primitive Subgroups to Do More with Fewer Bits
Abstract. This paper gives a survey of some ways to improve the efficiency of discrete log-based cryptography by using the restriction of scalars and the geometry and arithmetic of...
Karl Rubin, Alice Silverberg
ANTS
2004
Springer
103views Algorithms» more  ANTS 2004»
9 years 7 months ago
A Comparison of CEILIDH and XTR
We give a comparison of the performance of the recently proposed torus-based public key cryptosystem CEILIDH, and XTR. Underpinning both systems is the mathematics of the two dimen...
Robert Granger, Dan Page, Martijn Stam
ANTS
2004
Springer
149views Algorithms» more  ANTS 2004»
9 years 9 months ago
A Binary Recursive Gcd Algorithm
The binary algorithm is a variant of the Euclidean algorithm that performs well in practice. We present a quasi-linear time recursive algorithm that computes the greatest common di...
Damien Stehlé, Paul Zimmermann
ANTS
2004
Springer
105views Algorithms» more  ANTS 2004»
9 years 9 months ago
Algorithmic Aspects of Cubic Function Fields
Abstract. This paper presents an investigative account of arbitrary cubic function fields. We present an elementary classification of the signature of a cubic extension of a rati...
Renate Scheidler
ANTS
2004
Springer
106views Algorithms» more  ANTS 2004»
9 years 9 months ago
The Discrete Logarithm in Logarithmic -Class Groups and Its Applications in K-theory
We present an algorithm for the computation of the discrete logarithm in logarithmic -Class Groups. This is applied to the calculation to the -rank of the wild kernel WK2 of a numb...
Sebastian Pauli, Florence Soriano-Gafiuk
ANTS
2004
Springer
233views Algorithms» more  ANTS 2004»
9 years 9 months ago
Computing Order Statistics in the Farey Sequence
We study the problem of computing the k-th term of the Farey sequence of order n, for given n and k. Several methods for generating the entire Farey sequence are known. However, th...
Corina E. Patrascu, Mihai Patrascu
ANTS
2004
Springer
91views Algorithms» more  ANTS 2004»
9 years 9 months ago
Low-Dimensional Lattice Basis Reduction Revisited
Phong Q. Nguyen, Damien Stehlé
ANTS
2004
Springer
93views Algorithms» more  ANTS 2004»
9 years 9 months ago
Nonic 3-adic Fields
We compute all nonic extensions of Q3 and find that there are 795 of them up to isomorphism. We describe how to compute the associated Galois group of such a field, and also the ...
John W. Jones, David P. Roberts
ANTS
2004
Springer
111views Algorithms» more  ANTS 2004»
9 years 9 months ago
A Method to Solve Cyclotomic Norm Equations
We present a technique to recover f ∈ Q(ζp) where ζp is a primitive pth root of unity for a prime p, given its norm g = f ∗ ¯f in the totally real field Q(ζp + ζ−1 p )....
Nick Howgrave-Graham, Michael Szydlo
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