This book constitutes the refereed proceedings of the 9th International Workshop on Post-Quantum Cryptography, PQCrypto 2018, held in Fort Lauderdale, FL, USA, in April 2018. The 24 revised full papers presented were carefully reviewed and selected from 97 submissions. The papers are organized in topical sections on Code-based Cryptography; Cryptanalysis; Hash-based Cryptography; Isogenies in Cryptography; Lattice-based Cryptography; Multivariate Cryptography; Protocols; Quantum Algorithms.

Group theoretic problems have propelled scientific achievements across a wide range of fields, including mathematics, physics, chemistry, and the life sciences. Many cryptographic constructions exploit the computational hardness of group theoretical problems, and the area is viewed as a potential source of quantum-resilient cryptographic primitives for the future. Group Theoretic Cryptography supplies an ideal introduction to cryptography for those who are interested in group theory and want to learn about the possible interplays between the two fields. Assuming an undergraduate-level understanding of linear algebra and discrete mathematics, it details the specifics of using non-Abelian groups in the field of cryptography. Moreover, the book evidences how group theoretic techniques help us gain new insight into well known, seemingly unrelated, cryptographic constructions, such as DES. The book starts with brief overviews of the fundamentals of group theory, complexity theory, and cryptography. Part two is devoted to public-key encryption, including provable security guarantees, public-key encryption in the standard model, and public-key encryption using infinite groups. The third part of the book covers secret-key encryption. It examines block ciphers, like the Advanced Encryption Standard, and cryptographic hash functions and message authentication codes. The last part delves into a number of cryptographic applications which are nowadays as relevant as encryption-identification protocols, key establishment, and signature schemes are covered. The book supplies formal security analyses and highlights potential vulnerabilities for cryptographic constructions involving group theory. Summaries and references for further reading, as well as exercises, are included at the end of each chapter. Selected solutions for exercises are provided in the back of the book.

This book constitutes the refereed proceedings of the 9th International Workshop on Post-Quantum Cryptography, PQCrypto 2018, held in Fort Lauderdale, FL, USA, in April 2018. The 24 revised full papers presented were carefully reviewed and selected from 97 submissions. The papers are organized in topical sections on Lattice-based Cryptography, Learning with Errors, Cryptanalysis, Key Establishment, Isogeny-based Cryptography, Hash-based cryptography, Code-based Cryptography.