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The cipher AES (»Advanced Encryption Standard«) is the successor of the obsolete DES. It was adopted after a thorough competitive selection procedure in 2001. The winner of the competiton was the Belgian algorithm Rijndael, henceforth called AES, sparing English speaking people the plight of correct pronunciation, and neglecting a small difference in the specifications: Rijndael contains some extended parameter options that are not standardized for AES.
AES is a multiple cipher with several rounds but not a Feistel cipher, not even an SP-network in the proper sense. The kernel map is based on an S-box that essentially is the multiplicative inversion in the finite field F256. For a comprehensive analysis of the nonlinear properties of this S-box see Appendix D.
In this text we only give an introduction into the overall scheme and the kernel map. The inventors Joan Daemen and Vincent Rijmen themselves published a book that provides a very comprehensive und comprehensible description of the method:
Joan Daemen, Vincent Rijmen, The Design of Rijndael. AES – The Advanced Encryption Standard. Springer-Verlag, Berlin 2002. ISBN 3-540-42580-2.(Note that Joan is a Flemish version of John.) Another good reference is the Wikipedia entry and the further references given there.