… elliptic curves In our underlying preprocessing \(\text{ zk-SNARK }\), the verifier \(V\) consists
mainly of operations in an elliptic curve … multiple, suitably-chosen elliptic curves, that lie on a …

… of zero knowledge proofs (ZKP). In this paper, we study well-established ZKP protocols
based on the discrete logarithm problem and we adapt them to the Elliptic Curve Cryptography (…

… of elliptic curves. In Section 4, we present a deterministic algorithm for generating twisted
Edwards elliptic curves … checks that a twisted Edwards elliptic curve should pass. We base this …

… The protocol presented in this paper takes benefit of the usage of the elliptic curve version
of the Schnorr’s zero knowledge protocol [8]. Notice that, since security is based on the ECDLP…

… elliptic curve operations more generally are an increasingly important part of zero knowledge
… elliptic curves. To prove ECIPs more efficiently, I represent a collection of points that sum to …

… for perfect zero-knowledge proofs called "blobs" using the discrete log problem. Contrary
to what they remark on p. 73 of [2], we argue that the Mordell group of an elliptic curve is more …

… a novel, alternative zero-knowledge identification protocol has been proposed whose security
relies on the difficulty of solving the discrete logarithm problem over elliptic curves. It has …

… on the elliptic curve y2 ≡ x3 + 1 mod P, where P = ln − 1 and P ≡ 2 mod 3. One can
sample a random nontrivial point ρ = (x, y) on the curve of by picking y ← ZP and setting x ≡ y …

… For both NTT and MSM, we evaluate them with different underlying elliptic curves: BN-128,
BLS12-381, and MNT4753, where the bitwidth λ = 256, 384, and 768, respectively. For BN-…

… In this paper, we give an overview on the elliptic curves designed for different … of elliptic
curves tailored for SNARKs, at three stages of the process: curves to instantiate a SNARK, curves …