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Ordinary abelian varieties having small embedding degree
TLDR
This paper generalises the results of Miyaji, Nakabayashi and Takano by giving families corresponding to non-prime group orders with embedding degree suitable for pairing applications and considers the case of ordinary abelian varieties of dimension 2. Expand
Tunable Balancing of RSA
TLDR
An analysis of the security of keys generated by the proposed key generation method for RSA moduli, and a new birthday attack on low Hamming-weight private exponents are given. Expand
Salem Numbers of Trace -2 and Traces of Totally Positive Algebraic Integers
TLDR
It is established that the minimal degree for a Salem number of trace -2 is 20, and all Salem numbers of degree 20 and trace -1 are exhibited. Expand
THE PROBABILITY THAT THE NUMBER OF POINTS ON AN ELLIPTIC CURVE OVER A FINITE FIELD IS PRIME
The paper gives a formula for the probability that a randomly chosen elliptic curve over a finite field has a prime number of points. Two heuristic arguments in support of the formula are given asExpand
Speeding Fermat's factoring method
  • J. McKee
  • Computer Science, Mathematics
  • Math. Comput.
  • 1 October 1999
TLDR
A factoring method is presented which, heuristically, splits composite n in O(n 1/4+ ∈) steps, well-suited for use with small computers: the storage required is negligible, and one never needs to work with numbers larger than n itself. Expand
Computing totally positive algebraic integers of small trace
  • J. McKee
  • Computer Science, Mathematics
  • Math. Comput.
  • 1 May 2011
TLDR
A new bound for the Schur-Siegel-Smyth trace problem is produced and many new examples of such polynomials of minimal absolute trace (for given degree) are found. Expand
On the average number of divisors of quadratic polynomials
for some constant A (depending on a, b and c). Apparently this is due to Bellman and Shapiro (unpublished), and Bellman describes the proof as 'not elementary, although not difficult' [1]. The firstExpand
Computing division polynomials
Recurrence relations for the coefficients of the nth division polynomial for elliptic curves are presented. These provide an algorithm for computing the general division polynomial without usingExpand
Constructing k-radius sequences
TLDR
It is shown that f_k(n) ~ n^2/(2k) as n tends to infinity whenever a certain tiling of Z^r exists, which holds for infinitely many k, including all k < 195 and all k such that k+1 or 2k+1 is prime. Expand
There are Salem Numbers of Every Trace
We show that there are Salem numbers of every trace. The nontrivial part of this result is for Salem numbers of negative trace. The proof has two main ingredients. The first is a novel construction,Expand
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