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math.NT2011
Generalised Mersenne Numbers Revisited
Robert Granger, Andrew Moss
Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is su…
math.NT2011★ 3 cited
An efficient deterministic test for Kloosterman sum zeros
Omran Ahmadi, Robert Granger
We propose a simple deterministic test for deciding whether or not an element $a \in \F_{2^n}^{\times}$ or $\F_{3^n}^{\times}$ is a zero of the corresponding Kloosterman sum over t…
math.NT2011★ 4 cited
On isogeny classes of Edwards curves over finite fields
Omran Ahmadi, Robert Granger
We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class c…