As a beginning graduate student, I recall being frustrated by a general lack of accessible sources from which I could learn about (theoretical) cryptography. I remember wondering: why aren’t there more books presenting the basics of cryptography at an introductory level? Jumping ahead almost a decade later, as a faculty member my graduate students now ask me: what is the best resource for learning about (various topics in) cryptography? This monograph is intended to serve as an answer to these questions— at least with regard to digital signature schemes.

Given the above motivation, this book has been written with a beginning graduate student in mind: a student who is potentially interested in doing research in the field of cryptography, and who has taken an introductory course on the subject, but is not sure where to turn next. Though intended primarily for that audience, I hope that advanced graduate students and researchers will find the book useful as well. In addition to covering various constructions of digital signature schemes in a unified framework, this text also serves as a compendium of various “folklore” results that are, perhaps, not as well known as they should be. This book could also serve as a textbook for a graduate seminar on advanced cryptography; in such a class, I expect the entire book could be covered at a leisurely pace in one semester with perhaps some time left over for excursions into related topics. I hope it will also prove helpful to graduate students and researchers in other fields, such as computer security or mathematics, who want to obtain a more thorough appreciation of digital signatures and known results in this area.