In this note we show a consequence of the recent observation that narrow-pipe hash designs manifest an abberation from ideal random functions for finding collisions for those functions with complexities much lower than the so called generic birthday paradox lower bound. The problem is generic for narrow-pipe designs including classic Merkle-Damg̊ard designs but also recent narrow-pipe SHA-3 cand...

The inverse Gröbner basis problem is to find the ideals that have a given monomial ideal as its initial ideal. We consider the problem of finding when the given monomial ideal is the initial ideal of a prime ideal. Kalkbrenner and Sturmfels (1995), in Theorem 1, prove that the radical of the initial ideal of a prime ideal is equi-dimensional and connected in codimension one or equivalently, the...

We give a classification of generic coadjoint orbits for the groups of symplectomorphisms and Hamiltonian diffeomorphisms of closed symplectic surfaces. We also classify simple Morse functions on symplectic surfaces with respect to actions of those groups. This gives an answer to V.Arnold’s problem on invariants of generic isovorticed fields for 2D ideal fluids.

Given a simplicial complex, it is easy to construct a generic deformation of its Stanley-Reisner ideal. The main question under investigation in this paper is how to characterize the simplicial complexes such that their Stanley-Reisner ideals have Cohen-Macaulay generic deformations. Algorithms are presented to construct such deformations for matroid complexes, shifted complexes, and tree compl...

Utilizing smart antennas in multi-hop wireless networks can boost their performance. However, most of the work done in the context of wireless adhoc and sensor networking assume ideal or over-simplistic antenna patterns that overrate the performance benefits. In this paper, we compute the optimal throughput of multi-hop wireless networks with realistic smart antenna model. Our goal is to evalua...

We propose and analyze the Lizard-construction, a way to construct keystream generator (KSG) based stream ciphers with provable 2 3 n-security with respect to generic time-memory-data tradeoff attacks. Note that for the vast majority of known practical KSG-based stream ciphers such attacks reduce the effective key length to the birthday bound n/2, where n denotes the inner state length of the u...

In [3], the authors proved a number of results regarding Gröbner bases and initial ideals of those ideals J , in the free associative algebra K 〈X1, . . . , Xn〉, which contain the commutator ideal. We prove similar results for ideals which contains the anti-commutator ideal (the defining ideal of the exterior algebra). We define one notion of generic initial ideals in K 〈X1, . . . , Xn〉, and sh...

We study phase retrieval from rank-one magnitude and more general linear magnitude measurements of an unknown signal as an algebraic estimation problem. It is verified that a certain number of generic rank-one or generic linear measurements are sufficient to enable signal reconstruction for generic signals, and slightly more generic measurements yield reconstructability for all signals. Our res...