Quantum computers will break today s most popular public-key cryptographic systems including RSA DSA and ECDSA. This book introduces the reader to the next generation of cryptographic algorithms the systems that resist quantum-computer attacks: in particular post-quantum public-key encryption systems and post-quantum public-key signature systems. Leading experts have joined forces for the first time to explain the state of the art in quantum computing hash-based cryptography code-based cryptography lattice-based cryptography and multivariate cryptography. Mathematical foundations and implementation issues are included. This book is an essential resource for students and researchers who want to contribute to the field of post-quantum cryptography.