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» On the least prime primitive root modulo a prime
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ANTS
2006
Springer
105views Algorithms» more  ANTS 2006»
13 years 9 months ago
A Modular Method for Computing the Splitting Field of a Polynomial
We provide a modular method for computing the splitting field Kf of an integral polynomial f by suitable use of the byproduct of computation of its Galois group Gf by p-adic Staudu...
Guénaël Renault, Kazuhiro Yokoyama
JSC
2010
155views more  JSC 2010»
13 years 4 months ago
Algorithms for solving linear systems over cyclotomic fields
We consider the problem of solving a linear system Ax = b over a cyclotomic field. What makes cyclotomic fields of special interest is that we can easily find a prime p that sp...
Liang Chen, Michael B. Monagan
ARESEC
2011
117views more  ARESEC 2011»
12 years 5 months ago
Non-Parallelizable and Non-Interactive Client Puzzles from Modular Square Roots
—Denial of Service (DoS) attacks aiming to exhaust the resources of a server by overwhelming it with bogus requests have become a serious threat. Especially protocols that rely o...
Yves Igor Jerschow, Martin Mauve
STOC
1993
ACM
121views Algorithms» more  STOC 1993»
13 years 9 months ago
On the generation of multivariate polynomials which are hard to factor
In this paper we consider the di culty of factoring multivariate polynomials F(x y z :::) modulo n. We consider in particular the case in which F is a product of two randomly chose...
Adi Shamir
ANTS
2004
Springer
111views Algorithms» more  ANTS 2004»
13 years 11 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