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Non-vanishing of L-Functions and Applications
TLDR
This book systematically develops some methods for proving the non-vanishing of certain L-functions at points in the critical strip. Expand
Refinements of Miller's algorithm for computing the Weil/Tate pairing
TLDR
Three refinements to Miller's algorithm are given, one of which is especially efficient when the underlying elliptic curve is over a finite field of characteristic three, which is a case of particular cryptographic interest. Expand
NONADJACENT RADIX-τ EXPANSIONS OF INTEGERS IN EUCLIDEAN IMAGINARY QUADRATIC NUMBER FIELDS
In the seminal papers [6, 7], Koblitz curves were proposed for cryptographic use. For fast operations on these curves, these papers also initiated a study of the radix-τ expansion of integers in theExpand
Reductions of points on elliptic curves
AbstractLet E be an elliptic curve defined over $${\mathbb{Q}}$$. Let Γ be a subgroup of rank r of the group of rational points $${E(\mathbb{Q})}$$ of E. For any prime p of good reduction, letExpand
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