2 citations · 5 across the 10 of their papers we have counts for
12 papers · 1 filter
Densities in free groups and , Visible Points and Test Elements
Ilya Kapovich, Igor Rivin, Paul Schupp +1
In this article we relate two different densities. Let be the free group of finite rank and let be the abelianization map from onto . We pr…
Combinatorial group theory and public key cryptography
Vladimir Shpilrain, Gabriel Zapata
After some excitement generated by recently suggested public key exchange protocols due to Anshel-Anshel-Goldfeld and Ko-Lee et al., it is a prevalent opinion now that the conjugac…
Translation equivalence in free groups
Ilya Kapovich, Gilbert Levitt, Paul Schupp +1
Motivated by the work of Leininger on hyperbolic equivalence of homotopy classes of closed curves on surfaces, we investigate a similar phenomenon for free groups. Namely, we study…
On the palindromic and primitive widths of a free group
Valery Bardakov, Vladimir Shpilrain, Vladimir Tolstykh
Let G be a group and S a subset of G that generates G. For each x in G define the length l_S(x) of x relative to S to be the minimal k such that x is a product of k elements of S.…
Assessing security of some group based cryptosystems
Vladimir Shpilrain
One of the possible generalizations of the discrete logarithm problem to arbitrary groups is the so-called conjugacy search problem (sometimes erroneously called just the conjugacy…
Generic properties of Whitehead's Algorithm and isomorphism rigidity of random one-relator groups
Ilya Kapovich, Paul Schupp, Vladimir Shpilrain
We prove that Whitehead's algorithm for solving the automorphism problem in a fixed free group has strongly linear time generic-case complexity. This is done by showing that…