Henri Cohen

Kim Nguyen

Frederik Vercauteren

Roberto Avanzi

Tanja Lange

Gerhard Frey

Christophe Doche

The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications. The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the group operations and computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method and provides the algorithms in an explicit manner. It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves. For some special curves the discrete logarithm problem can be transferred to an easier one; the consequences are explained and suggestions for good choices are given. The authors present applications to protocols for discrete-logarithm-based systems (including bilinear structures) and explain the use of elliptic and hyperelliptic curves in factorization and primality proving. Two chapters explore their design and efficient implementations in smart cards. Practical and theoretical aspects of side-channel attacks and countermeasures and a chapter devoted to (pseudo-)random number generation round off the exposition. The broad coverage of all- important areas makes this book a complete handbook of elliptic and hyperelliptic curve cryptography and an invaluable reference to anyone interested in this exciting field.

Handbook of Elliptic and Hyperelliptic Curve Cryptography

Bart Preneel

This book constitutes the refereed proceedings of the 16th International Conference on on Applied Cryptography and Network Security, ACNS 2018, held in Leuven, Belgium, in July 2018. The 36 revised full papers presented were carefully reviewed and selected from 173 submissions. The papers were organized in topical sections named: Cryptographic Protocols; Side Channel Attacks and Tamper Resistance; Digital Signatures; Privacy Preserving Computation; Multi-party Computation; Symmetric Key Primitives; Symmetric Key Primitives; Symmetric Key Cryptanalysis; Public Key Encryption; Authentication and Biometrics; Cloud and Peer-to-peer Security.

16th International Conference, ACNS 2018, Leuven, Belgium, July 2-4, 2018, Proceedings

Applied Cryptography and Network Security

Frederik Vercauteren

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