Algebra seminar abstracts

"Removing commutativity from the classical cryptography: a combinatorial group theoretic approach."
Delaram Kahrobaei (St Andrews)
 
I am presenting a joint work with B.Eick. The idea I am discussing in this talk, is removing commutativity from the classical cryptology schemes (which uses finite fields (special cyclic groups)); initiated by Anshel-Anshel-Goldfeld in 1999, they particularly chose Braid groups. We introduce polycyclic groups as the best new platform for cryptology and also non-commutative Diffie-Helman key-exchange problem. The novelty of our approach is that polycyclic groups are a natural generalization of cyclic groups with much more complex algorithmic structures this promises to be a more substantial and secure platform than the existing cryptosystems. Note that nilpotent groups (they have polynomial growth) could be regarded as an example of polycyclic groups and the non-polycyclic soluble groups are not appropriate (indeed the word problem is in NP for any finitely generated metabelian groups). In this talk I will explain particularly Eick-Kahrobaei cryptosystem. Especially I will discuss how combinatorial group theoretic properties of polycyclic groups play a crucial role in this cryptosystem. Perhaps if time allows I will talk about possible quantum algorithmic attacks to this cryptosystem and the interesting future work.
 
Wednesday 16th February 2005 - 4.00 PM
 
Mathematics Building, room 214

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