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Algebraic Aspects of the Advanced Encryption Standard
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.
Lie Algebras and Algebraic Groups
The theory of Lie algebras and algebraic groups has been an area of active research in the last 50 years. It intervenes in many different areas of mathematics : for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory so as to present the foundation of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the last chapters. All the prerequisites on commutative algebra and algebraic geometry are included.
