Computing Hilbert Class Polynomials

We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing $H_D$, and we show that all methods have comparable run times

A comparison and a combination of SST and AGM algorithms for counting points of elliptic curves in characteristic 2

International audienceSince the first use of a p-adic method for counting points of elliptic curves, by Satoh in 1999, several variants of his algorithm have been proposed. In the current state, the AGM algorithm, proposed by Mestre is thought to be the fastest in practice, and the algorithm by Satoh­-Skjernaa­-Taguchi has the best asymptotic complexity but requires precomputations. We present an amelioration of the SST algorithm, borrowing ideas from the AGM. We make a precise comparison between this modified SST algorithm and the AGM, thus demonstrating that the former is faster by a significant factor, even for small cryptographic sizes

Mobilizing heads and hearts for wildlife conservation

Highlighting the shared evolutionary relationships between humans and animals — and recognizing that all species, including humans, are unique in their own way — may facilitate caring for and conserving animals by tapping into a human emotion: empathy