Esquemes de compartició de secrets amb corbes el·líptiques

Abstract

[en] In this thesis, we provide a didactic introduction to pairing-based cryptography with elliptic curves, following the premises and methodologies outlined in Lawrence C. Washington’s book Elliptic Curves, Number Theory, and Cryptography. We introduce the algebraic structure of the curve and subsequently, we delve into the key concept of pairing, exploring its applications in the field of computer security. The distinctive element of this work is the presentation and analysis of a cryptographic secret sharing scheme titled Conjunctive Hierarchical Multi-Secret Sharing Scheme using Elliptic Curves, developed by Mohan Chintamani, Prabal Paul, and Laba Sa. With this contribution, we delve into the properties of elliptic curves and pairing, providing a deeper understanding of contemporary cryptographic techniques and their applications.