14 citations · 50 across the 57 of their papers we have counts for
70 papers
CHAMP: Cayley HAshing with Matrix Products
Alexander Demin, Alexey Ovchinnikov, Vladimir Shpilrain
Cayley hash functions hash binary strings by representing the bits of the message as elements of a semigroup and multiplying the corresponding elements. This gives Cayley hash func…
Redactable blockchains and polynomial equations
Alexander Demin, Alexey Ovchinnikov, Vladimir Shpilrain
We develop new tools for constructing redactable authenticated data structures with post-quantum security. In our construction, inverting the proposed one-way function means solvin…
Automorphic orbits in free groups: recent progress
Vladimir Shpilrain
In this survey, we describe recent progress on asymptotic properties of various automorphic orbits in free groups. In particular, we address the problem of counting potentially pos…
Easy estimates of Lyapunov exponents for random products of matrices
Nadya Nabahi, Vladimir Shpilrain
The problems that we consider in this paper are as follows. Let be square matrices (over reals). Let be a random product of matrices.…
Knot invariants from representations of braids by automorphisms of a free group
Vladimir Shpilrain
We describe an alternative way of computing Alexander polynomials of knots/links, based on the Artin representation of the corresponding braids by automorphisms of a free group. Th…
Orbit-blocking words in free groups
Lucy Koch-Hyde, Siobhan O'Connor, Eamonn Olive +1
By strengthening known results about primitivity-blocking words in free groups, we prove that for any nontrivial element w of a free group of finite rank, there are words that cann…