Introduction to Quantum Computation and Quantum Cryptographic Protocols

Anthony Leverrier

Caamaño Mayorga, Renzo Sebastián

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.

Thomas Vidick, Stephanie Wehner

This book offers an accessible and engaging introduction to quantum cryptography, assuming no prior knowledge in quantum computing. Essential background theory and mathematical techniques are introduced and applied in the analysis and design of quantum cryptographic protocols. The title explores several important applications such as quantum key distribution, quantum money, and delegated quantum computation, while also serving as a self-contained introduction to the field of quantum computing. With frequent illustrations and simple examples relevant to quantum cryptography, this title focuses on building intuition and challenges readers to understand the basis of cryptographic security. Frequent worked examples and mid-chapter exercises allow readers to extend their understanding, and in-text quizzes, end-of-chapter homework problems, and recommended further reading reinforce and broaden understanding. Online resources available to instructors include interactive computational problems in Julia, videos, lecture slides, and a fully worked solutions manual.

André Chailloux

Manuel Calixto

Thomas Vidick, Stephanie Wehner

This book offers an accessible and engaging introduction to quantum cryptography, assuming no prior knowledge in quantum computing. Essential background theory and mathematical techniques are introduced and applied in the analysis and design of quantum cryptographic protocols. The title explores several important applications such as quantum key distribution, quantum money, and delegated quantum computation, while also serving as a self-contained introduction to the field of quantum computing. With frequent illustrations and simple examples relevant to quantum cryptography, this title focuses on building intuition and challenges readers to understand the basis of cryptographic security. Frequent worked examples and mid-chapter exercises allow readers to extend their understanding, and in-text quizzes, end-of-chapter homework problems, and recommended further reading reinforce and broaden understanding. Online resources available to instructors include interactive computational problems in Julia, videos, lecture slides, and a fully worked solutions manual.