… An elliptic curve over a field k is a nonsingular projective curve … k is not 2 or 3, it can be realized
as a plane projective curve … elliptic integrals led to elliptic curves, and why ellipses are not …

… If the exchange gives a zero knowledge proof of a proof of … of public parameters for succinct
zero knowledge proofs. In … Scalable zero knowledge via cycles of elliptic curves. In JA …

… implement a zero knowledge protocol based on elliptic curve … Curves which are a fast
alternative to other elliptic curves. To … implementation of the Schnorr protocol over elliptic curves. …

… equals C(α) · G for a random α; and (2) zero knowledge: if at least one party is honest and V
(tr)=1, tr … Virza, “Scalable zero knowledge via cycles of elliptic curves,” in CRYPTO ’14, 2014, …

… This contribution describes how an elliptic curve cryptosystem can … We show that an elliptic
curve scalar multiplication with a … use of curves defined over a subfield such as Koblitz curves. …

… We use the following hardness assumption over elliptic curve groups with pairings, … In
this section we present our zero knowledge polynomial delegation scheme. At a high level, the …

… zero-knowledge argument that one committed matrix is the product of two other committed
matrices. We also offer a sub-linear size zero-knowledge … If G is an elliptic curve of order p, …

… to teach a senior undergraduate course on elliptic curve cryptography. I was so pleased with
… to pursue the theory of elliptic curves over finite fields and their applications to cryptography. …

… Then we discuss equivalences between elliptic curves and lattices, leading up to the j-…
defining the elliptic curve and as an analytic function in the lattice (also defining the elliptic curve). …