This book discusses the current research concerning public key cryptosystems. It begins with an introduction to the basic concepts of multivariate cryptography and the history of this field. Table of Contents 1. Introduction 2. Multivariate Cryptography 3. The Matsumoto-Imai Cryptosystem 4. Hidden Field Equations 5. Oil and Vinegar 6. MQDSS 7. The SimpleMatrix Encryption Scheme 8. …