On the theory, design and optimization of Classical and Quantum algorithms for Isogeny-based Cryptography

In this work, we present the theory behind Elliptic Curve Cryptography (ECC) and Isogeny-based cryptography. We start with a quick introduction to Complexity Theory and Cryptography. We give a detailed description of elliptic curves and discuss how they are used to create secure protocols. We present the strength of this scheme and also its weaknesses regarding quantum computation. To show the necessity for other protocols, we review some basic concepts of Quantum Computing and present how Shor's Quantum Algorithm breaks ECC. Then, we survey the rich theory of isogenies between ordinary and supersingular elliptic curves to end with cryptographic protocols, that use these isogenies to create post-quantum cryptographic systems.

• المؤلف الرئيسي: Caamaño Mayorga, Renzo Sebastián (author)
• التنسيق: bachelorThesis
• اللغة: eng
• منشور في: 2021
• الموضوعات: Curvas elípticas; Isogenias; Criptosistemas de clave pública cuántico-resistentes; Algoritmo de Shor; Elliptic curves; Isogenies; Quantum-resistant public-key cryptosystems; Shor's Algorithm
• الوصول للمادة أونلاين: http://repositorio.yachaytech.edu.ec/handle/123456789/304