The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

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

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 …

We propose an index calculus algorithm for the discrete logarithm problem on general
abelian varieties of small dimension. The main difference with the previous approaches is …

TEXT: Over a period of sixteen years elliptic curve cryptography went from being an
approach that many people mistrusted or misunderstood to being a public key technology …

Efficient algorithms for abelian varieties and their moduli spaces Page 1 HAL Id: tel-03498268
https://hal.science/tel-03498268 Submitted on 20 Dec 2021 HAL is a multi-disciplinary open …

Galbraith, Lin, and Scott recently constructed efficiently computable endomorphisms for a
large family of elliptic curves defined over IF q 2 and showed, in the case where q is a prime …

Pairing-based cryptographic protocols are typically vulnerable to small-subgroup attacks in
the absence of protective measures. Subgroup membership testing is one of the feasible …

We examine several versions of the one-more-discrete-log and one-more-Diffie-Hellman
problems. In attempting to evaluate their intractability, we find conflicting evidence of the …

Diffie–Hellman key exchange is at the foundations of public-key cryptography, but
conventional group-based Diffie–Hellman is vulnerable to Shor's quantum algorithm. A …