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.

From the reviews: "This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. [...] Overall, this is an excellent expository text, and will be very useful to both the student and researcher." Mathematical Reviews

This book constítutes the thoroughly refereed postproceedings of the 4th International Conference on the Advanced Encryption Standard, AES 2004, held in Bonn, Germany in May 2004. The 10 revised full papers presented together with an introductory survey and 4 invited papers by leading researchers were carefully selected during two rounds of reviewing and improvement. The papers are organized in topical sections on cryptanalytic attacks and related topics, algebraic attacks and related results, hardware implementations, and other topics. All in all, the papers constitute a most up-to-date assessment of the state of the art of data encryption using the Advanced Encryption Standard AES, the de facto world standard for data encryption.

This thesis examines the vulnerability of the Advanced Encryption Standard (AES) to algebraic attacks. It will explore how strong the Rijndael algorithm must be in order to secure important federal information. There are several algebraic methods of attack that can be used to break a specific cipher, such as Buchburger's and Faugere's F4 and F5 methods. The method to be used and evaluated in this thesis is the Multiple Right Hand Sides (MRHS) Linear Equations. MRHS is a new method that allows computations to be more efficient and the equations to be more compact in comparison with the previously referred methods. Because of the high complexity of the Rijndael algorithm, the purpose of this thesis is to investigate the results of an MRHS attack in a small-scale variant of the AES, since it is impossible to break the actual algorithm by using only the existent knowledge. Instead of the original ten rounds of AES algorithm, variants of up to four rounds were used. Simple examples of deciphering some ciphertexts are presented for different variants of the AES, and the new attack method of MRHS linear equations is compared with the other older methods. This method is more effective timewise than the other older methods, but, in some cases, some systems cannot be uniquely solved.

This textbook provides an introduction to the mathematics on which modern cryptology is based. It covers not only public key cryptography, the glamorous component of modern cryptology, but also pays considerable attention to secret key cryptography, its workhorse in practice. Modern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for achieving these aims. In both theory and practice it requires notions and constructions from three major disciplines: computer science, electronic engineering and mathematics. Within mathematics, group theory, the theory of finite fields, and elementary number theory as well as some topics not normally covered in courses in algebra, such as the theory of Boolean functions and Shannon theory, are involved. Although essentially self-contained, a degree of mathematical maturity on the part of the reader is assumed, corresponding to his or her background in computer science or engineering. Algebra for Cryptologists is a textbook for an introductory course in cryptography or an upper undergraduate course in algebra, or for self-study in preparation for postgraduate study in cryptology.

An authoritative and comprehensive guide to the Rijndael algorithm and Advanced Encryption Standard (AES). AES is expected to gradually replace the present Data Encryption Standard (DES) as the most widely applied data encryption technology. This book, written by the designers of the block cipher, presents Rijndael from scratch. The underlying mathematics and the wide trail strategy as the basic design idea are explained in detail and the basics of differential and linear cryptanalysis are reworked. Subsequent chapters review all known attacks against the Rijndael structure and deal with implementation and optimization issues. Finally, other ciphers related to Rijndael are presented.

Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.

This book constitutes the thoroughly refereed post-proceedings of the 12th International Workshop on Fast Software Encryption, FSE 2005, held in Paris, France in February 2005. The 29 revised full papers presented were carefully reviewed and selected from 96 submissions. The papers address all current aspects of fast primitives for symmetric cryptology, including the design, cryptanalysis, and implementation of block ciphers, stream ciphers, hash functions, and message authentication codes.

This book constitutes the refereed proceedings of the 10th IMA International Conference on Cryptography and Coding, held in Cirencester, UK, in December 2005. The 26 revised full papers presented together with 4 invited contributions were carefully reviewed and selected from 94 submissions. The papers are organized in topical sections on coding theory, signatures and signcryption, symmetric cryptography, side channels, algebraic cryptanalysis, information theoretic applications, number theoretic foundations, and public key and ID-based encryption schemes.

The book starts with a history of Cryptography from antiquity to present day. It then continues with Public Key Cryptography, extensively treating the security of Advanced Encryption Standard (AES) at the state of the art level. An overview of main Public Key cryptosystems is given in Chapter 3. Among other covered topics are the Diffie-Hellman and ElGamal protocols and various digital signature algorithms. Chapter 4 treats the use of systems of polynomials both in cryptography and cryptanalysis. Some of the material is frequently cited original research. The book is meant as a textbook at undergraduate and graduate level and for independent study.