Applying SAT-Solvers to Extension Fields of Low Degree

  • Gregory V. Bard


In this book we have been discussing polynomial equations over finite fields of characteristic two for quite some time. However, the finite field in question has almost always been \(\mathbb{G}\mathbb{F}\)(2). In cryptanalysis, this is usually the field of interest, with notable exceptions, including several ciphers: Rijndael [89] which later become the Advanced Encryption Standard (AES), which uses \(\mathbb{G}\mathbb{F}\)(256); the cryptosystem called TTM [127], over the same field; the Courtois Toy Cipher (CTC) [14] [73], can be modeled over \(\mathbb{G}\mathbb{F}\)(8) for certain settings. The stream cipher family QUAD [42] can operate over any finite field, but finite fields of characteristic two would be the natural setting (see Section 5.2 on Page 66).


Advance Encryption Standard Polynomial System Product Formula Triple Product Irreducible Polynomial 
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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Department of MathematicsFordham UniversityBronxUSA

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