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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 …

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 …

One of the most promising avenues for realising scalable proof systems relies on the
existence of 2-cycles of pairing-friendly elliptic curves. Such a cycle consists of two elliptic …

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 …

We investigate methods for providing easy-to-check proofs of computational effort. Originally
intended for discouraging spam, the concept has wide applicability as a method for …

Efficiently computable homomorphisms allow elliptic curve point multiplication to be
accelerated using the Gallant–Lambert–Vanstone (GLV) method. Iijima, Matsuo, Chao and …

Many index calculus algorithms generate multiplicative relations between smoothness basis
elements by using a process called Sieving. This process allows us to quickly filter potential …

Let A/F _p and A'/F _p be superspecial principally polarized abelian varieties of dimension
g> 1. For any prime ℓ ≠ p, we give an algorithm that finds a path ϕ: A → A'in the (ℓ,\dots, ℓ) …