Elliptic curves over finite fields

Handbook of elliptic and hyperelliptic curve cryptography: Part 1 presents the following content: Chapter 1 introduction to public-key cryptography, chapter 2 algebraic background, chapter 3 background on p-adic numbers, chapter 4 background on curves and jacobians, chapter 5 varieties over special fields, chapter 6 background on pairings, chapter 7 background on weil descent, chapter 8 cohomological backgroundon point counting, chapter 9 exponentiation, chapter 10 integer arithmetic, chapter 11 finite field arithmetic, chapter 12 arithmetic of p-adic numbers, chapter 13 arithmetic of ellip...

423p runthenight08 12-04-2023 8 5   Download

"Ebook Elliptic curves number theory and cryptography (Second edition)" present Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermat’s Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices.

524p haphuonglan2021 25-04-2021 48 14   Download

In the underlying finite field arithmetic of an elliptic curve cryptosystem, field multiplication is the next computational costly operation other than field inversion. We present two novel algorithms for efficient implementation of field multiplication and modular reduction used frequently in an elliptic curve cryptosystem defined over GF (2n ).

10p dunglh2013 02-04-2014 53 0   Download

Implementation of the cryptographic algorisms based on elliptic curves (ECs) over VFFs provides significantly higher performance than the implementation of the EC-based algorithms, in which the ECs are defined over the ground fields and extension finite fields of polynomials.

6p dunglh2013 02-04-2014 56 0   Download