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 numbergeneration 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.

The book in front of you contains the proceedings of SAC 2008, the 15th - nual Workshop on Selected Areas in Cryptography. SAC 2008 took place during August 14-15 at Mount Allison University, Sackville, New Brunswick, Canada. This was the ?rst time that SAC was hosted in New Brunswick, and the second time in an Atlantic Canadian province. Previous SAC workshops were held at Queen's University in Kingston (1994, 1996, 1998, 1999, and 2005), at Carleton University in Ottawa (1995, 1997, 2003), at the University of Waterloo (2000, 2004), at the Fields Institute in Toronto (2001), at Memorial University of N- foundland at St. John's (2002), at Concordia University in Montreal (2006) and at the University of Ottawa (2007). The intent ofthe workshopseriesis to provide a relaxedatmospherein which researchers in cryptography can present and discuss new work on selected areas of current interest. The SAC workshop series has ?rmly established itself as an international forum for intellectual exchange in cryptological research. Theresponsibilityforchoosingthe venueofeachSACworkshopandappoi- ingtheCo-chairslieswiththeSACOrganizingBoard.TheCo-chairsthenchoose the Program Committee in consultation with the Board. Hence, we would like to expressour gratitudeto the SAC OrganizingBoardfor giving usthe mandate to organize SAC 2008, and for their invaluable feedback while assembling the Program Committee.

This book contains revised selected papers from the 23rd International Conference on Selected Areas in Cryptography, SAC 2016, held in St. John's, NL, Canada in August 2016. The 28 full papers and 2 invited papers presented in this volume were carefully reviewed and selected from 100 submissions. They are organized in the following topical sections: side channels and fault attacks; design and implementation of symmetric cryptography; efficient symmetric primitives; cryptanalysis of symmetric primitives; MACs and PRNGs; lattice-based cryptography; and cryptanalysis of asymmetric primitives.