901 research outputs found
Fast algorithms for computing isogenies between elliptic curves
We survey algorithms for computing isogenies between elliptic curves defined
over a field of characteristic either 0 or a large prime. We introduce a new
algorithm that computes an isogeny of degree ( different from the
characteristic) in time quasi-linear with respect to . This is based in
particular on fast algorithms for power series expansion of the Weierstrass
-function and related functions
Generalization of the Lee-O'Sullivan List Decoding for One-Point AG Codes
We generalize the list decoding algorithm for Hermitian codes proposed by Lee
and O'Sullivan based on Gr\"obner bases to general one-point AG codes, under an
assumption weaker than one used by Beelen and Brander. Our generalization
enables us to apply the fast algorithm to compute a Gr\"obner basis of a module
proposed by Lee and O'Sullivan, which was not possible in another
generalization by Lax.Comment: article.cls, 14 pages, no figure. The order of authors was changed.
To appear in Journal of Symbolic Computation. This is an extended journal
paper version of our earlier conference paper arXiv:1201.624
Faster 64-bit universal hashing using carry-less multiplications
Intel and AMD support the Carry-less Multiplication (CLMUL) instruction set
in their x64 processors. We use CLMUL to implement an almost universal 64-bit
hash family (CLHASH). We compare this new family with what might be the fastest
almost universal family on x64 processors (VHASH). We find that CLHASH is at
least 60% faster. We also compare CLHASH with a popular hash function designed
for speed (Google's CityHash). We find that CLHASH is 40% faster than CityHash
on inputs larger than 64 bytes and just as fast otherwise
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