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 tech­ niques. 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 cryptogra­ phers 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.

The Advanced Encryption Standard (AES) is the successor to the Data Encryption Standard, and is potentially the world's most important block cipher (a method for encrypting text). While existing analytical techniques for block ciphers have used a statistical approach, this book provides a comprehensive analysis of the application of algebraic techniques to the Advanced Encryption Standard (AES). These techniques may have a dramatic effect on the security of the AES.

to the AES.- Mathematical Background.- Description of the AES.- Algebraic Properties of the AES.- Equation Systems for the AES.- Analysis of AES Equation Systems.- Closing Remarks.