Non-interactive arguments of knowledge are powerful cryptographic tools that can be used
to demonstrate the faithful execution of arbitrary computations with publicly verifiable proofs …

Background Elliptic curve cryptographic schemes were proposed independently in 1985 by
Neal Koblitz (Koblitz 1987) and Victor Miller (Miller 1986). They are the elliptic curve …

Public key cryptography is a major interdisciplinary subject with many real-world
applications, such as digital signatures. A strong background in the mathematics underlying …

In this paper we perform a review of elliptic curve cryptography (ECC) as it is used in
practice today in order to reveal unique mistakes and vulnerabilities that arise in …

Elliptic curves with small embedding degree and large prime-order subgroup are key
ingredients for implementing pairing-based cryptographic systems. Such “pairing-friendly” …

This paper describes the design of a fast software library for the computation of the optimal
ate pairing on a Barreto–Naehrig elliptic curve. Our library is able to compute the optimal ate …

We introduce Four Q, a high-security, high-performance elliptic curve that targets the 128-bit
security level. At the highest arithmetic level, cryptographic scalar multiplications on Four Q …

Safe curves for elliptic-curve cryptography Page 1 Safe curves for elliptic-curve cryptography
Daniel J. Bernstein1,2 and Tanja Lange3,2 1 University of Illinois at Chicago, USA 2 Academia …

Frey and Rück gave a method to transform the discrete logarithm problem in the divisor
class group of a curve over F _q into a discrete logarithm problem in some finite field …

We present an index-calculus algorithm for the computation of discrete logarithms in the
Jacobian of hyperelliptic curves defined over finite fields. The complexity predicts that it is …