Computing cardinalities of -curve reductions over finite fields

We present a specialized point-counting algorithm for a class of elliptic curves over $\mathbb{F}_{p^{2}}$ that includes reductions of quadratic $\mathbb{Q}$-curves modulo inert primes and, more generally, any elliptic curve over $\mathbb{F}_{p^{2}}$ with a low-degree isogeny to its Galois conjugate curve. These curves have interesting cryptographic applications. Our algorithm is a variant of the Schoof–Elkies–Atkin (SEA) algorithm, but with a new, lower-degree endomorphism in place of Frobenius. While it has the same asymptotic asymptotic complexity as SEA, our algorithm is much faster in practice.

What Makes an In-Service Program Click?

In-service programs are in operation, or are springing up, wherever teachers are at work. Mr. Lyon, Dean, State Teachers College, Livingston, Alabama, undertakes to put his finger on some of the elements which make for success, where success is attained in this rapidly expanding educational effort. It is refreshing to note that he seeks evaluations by professional workers engaged at different levels and in different types of service. A cross-sectional rather than a specialized point of view is the interesting result.

Malaria in a gonorrhea clinic

At the moment, clinical medicine is busy revising the old narrowly specialized point of view on diseases and expanding the understanding of local painful disorders by studying the effect of general conditions in the diseased organism on local diseases. This path aims to bring greater clarity to our usually vague and vague ideas about soil, disposition, individuality depending on which the same local process in different cases gives extremely different pictures.