… In this paper, the speed of the arithmetic of twisted Edwards curves is increased by a … is
called extended twisted Edwards coordinates which adds an auxiliary coordinate to twisted Ed…

… We speed up the (complete) formulas for the binary Edwards curve arithmetic which have
been firstly presented in [6] and were the fastest ones on the curves to the best of our …

… In characteristic different from 2, we establish a linear isomorphism with the twisted Edwards
… Binary Edwards curves [3], like the twisted \(\varvec{\mu }_4\)-normal form of this work, cover …

… points on the curve. We will say that an elliptic curve E can be put in twisted Edwards form if
… We will use the term complete Edwards form when a is a square (including the case a = 1 of …

… I will then relate Twisted Edwards curves and Montgomery curves. I will … for Twisted Edwards
curves. In addition, I will compare and contrast Twisted Edwards curves with Edwards curves…

… twisted Edwards curves we introduce in this paper is birationally equivalent to a Montgomery
curve … that the Montgomery form of our curves allows for an equally efficient implementation …

… and doubling formulas for twisted Edwards curves with cost of \(5\… 2 we review twisted Edwards
curves, and in Sect. 3 we … Here, we show that the addition law in twisted Edwards curve \(\…

… twisted Edwards curves. Then we present the explicit formulae for pairing computation on
Edwards curves. … Moreover, when \(j=1728\) and \(j=0\) we consider quartic and sextic twists to …

… 4 DOUBLING IN TWISTED EDWARDS CURVES In this section, we look at the doubling
formula for Twisted Edwards Curves with a particular parameterization and then propose …

… When using an Intel Core i7 processor clocked at 2.7 GHz as test platform, we can compute
more than 38,000 commitments per second on a twisted Edwards curve over a 127-bit field. …