Non-Abelian Analogs of Lattice Rounding

Lattice rounding in Euclidean space can be viewed as finding the nearest point in the orbit of an action by a discrete group, relative to the norm inherited from the ambient space. Using this point of view, we initiate the study of non-abelian analogs of lattice rounding involving matrix groups. In one direction, we give an algorithm for solving a normed word problem when the inputs are random products over a basis set, and give theoretical justification for its success. In another direction, we prove a general inapproximability result which essentially rules out strong approximation algorithms (i.e., whose approximation factors depend only on dimension) analogous to LLL in the general case.Comment: 30 page

Balancing sums of random vectors

We study a higher-dimensional 'balls-into-bins' problem. An infinite sequence of i.i.d. random vectors is revealed to us one vector at a time, and we are required to partition these vectors into a fixed number of bins in such a way as to keep the sums of the vectors in the different bins close together; how close can we keep these sums almost surely? This question, our primary focus in this paper, is closely related to the classical problem of partitioning a sequence of vectors into balanced subsequences, in addition to having applications to some problems in computer science.Comment: 17 pages, Discrete Analysi

Runtime protection via dataflow flattening

Software running on an open architecture, such as the PC, is vulnerable to inspection and modification. Since software may process valuable or sensitive information, many defenses against data analysis and modification have been proposed. This paper complements existing work and focuses on hiding data location throughout program execution. To achieve this, we combine three techniques: (i) periodic reordering of the heap, (ii) migrating local variables from the stack to the heap and (iii) pointer scrambling. By essentialy flattening the dataflow graph of the program, the techniques serve to complicate static dataflow analysis and dynamic data tracking. Our methodology can be viewed as a data-oriented analogue of control-flow flattening techniques. Dataflow flattening is useful in practical scenarios like DRM, information-flow protection, and exploit resistance. Our prototype implementation compiles C programs into a binary for which every access to the heap is redirected through a memory management unit. Stack-based variables may be migrated to the heap, while pointer accesses and arithmetic may be scrambled and redirected. We evaluate our approach experimentally on the SPEC CPU2006 benchmark suit

Quantifying Trust

Trust is a central concept in public-key cryptography infrastruc- ture and in security in general. We study its initial quantification and its spread patterns. There is empirical evidence that in trust-based reputation model for virtual communities, it pays to restrict the clusters of agents to small sets with high mutual trust. We propose and motivate a mathematical model, where this phenomenon emerges naturally. In our model, we separate trust values from their weights. We motivate this separation using real examples, and show that in this model, trust converges to the extremes, agreeing with and accentuating the observed phenomenon. Specifically, in our model, cliques of agents of maximal mutual trust are formed, and the trust between any two agents that do not maximally trust each other, converges to zero. We offer initial practical relaxations to the model that preserve some of the theoretical flavor