The Belgian block cipher Rijndael was chosen in 2000 by the U.S. government’s National Institute of Standards and Technology (NIST) to be the successor to the Data Encryption Standard. Rijndael was subsequently standardized as the Advanced Encryption Standard (AES), which is potentially the world’s most important block cipher. In 2002, some new analytical techniques were suggested that may have a dramatic effect on the security of the AES. Existing analytical techniques for block ciphers depend heavily on a statistical approach, whereas these new techniques are algebraic in nature.

Algebraic Aspects of the Advanced Encryption Standard, appearing five years after publication of the AES, presents the state of the art for the use of such algebraic techniques in analyzing the AES.

The primary audience for this work includes academic and industry researchers in cryptology; the book is also suitable for advanced-level students.

It is now more than five years since the Belgian block cipher Rijndael was chosen as the Advanced Encryption Standard {AES). Joan Daemen and Vincent Rijmcn used algebraic techniques to provide an unparalleled level of assurance against many standard statistical cryptanalytic techniques. The cipher is a fitting tribute to their distinctive approach to cipher design. Since the publication of the AES, however, the very same algebraic structures have been the subject of increasing cryptanalytic attention and this monograph has been written to summarise current research. We hope that this work will be of interest to both cryptographers and algebraists and will stimulate future research.

During the writing of this monograph we have found reasons to thank many people. We are especially grateful to the British Engineering and Physical Sciences Research Council (EPSRC) for their funding of the research project Security Analysis of the Advanced Encryption System (Grant GR/S42637), and to Susan Lagerstrom-Fifc and Sharon Palleschi at Springer. Wo would also hke to thank Glaus Diem, Maura Paterson, and Ludovic Perret for their valuable comments. Finally, the support of our families at home and our colleagues at work has been invaluable and particularly appreciated.