Details:
Title  Gr\"obner basis cryptosystems.  Author(s)  Peter Ackermann, Martin Kreuzer  Type  Article in Journal  Abstract  In the first sections we extend and generalize Gröbner basis theory to submodules of free right modules over monoid rings. Over free monoids, we adapt the known theory for right ideals and prove versions of Macaulay’s basis theorem, the Buchberger criterion, and the Buchberger algorithm. Over monoids presented by a finitely generated convergent string rewriting system we generalize Madlener’s Gröbner basis theory based on prefix reduction from right ideals to right modules. After showing how these Gröbner basis theories relate to classical grouptheoretic problems, we use them as a basis for a new class of cryptosystems that are generalizations of the cryptosystems described in Barkee et al. (J Symb Comput 18, 497–501, 1994) and Fellows and Koblitz (Contemp Math 168, 51–61, 1994). Well known cryptosystems such as RSA, ElGamal, Polly Cracker, Polly Two and a braid group cryptosystem are shown to be special cases. We also discuss issues related to the security of these Gröbner basis cryptosystems.  Keywords  Gröbner basis, Cryptosystem, Monoid ring  ISSN  09381279; 14320622/e 
URL 
http://link.springer.com/article/10.1007%2Fs0020000600020 
Language  English  Journal  Appl. Algebra Eng. Commun. Comput.  Volume  17  Number  34  Pages  173194  Publisher  Springer, Berlin/Heidelberg  Year  2006  Edition  0  Translation 
No  Refereed 
No 
