A structural analysis of the A5/1 state transition graph

We describe efficient algorithms to analyze the cycle structure of the graph induced by the state transition function of the A5/1 stream cipher used in GSM mobile phones and report on the results of the implementation. The analysis is performed in five steps utilizing HPC clusters, GPGPU and external memory computation. A great reduction of this huge state transition graph of 2^64 nodes is achieved by focusing on special nodes in the first step and removing leaf nodes that can be detected with limited effort in the second step. This step does not break the overall structure of the graph and keeps at least one node on every cycle. In the third step the nodes of the reduced graph are connected by weighted edges. Since the number of nodes is still huge an efficient bitslice approach is presented that is implemented with NVIDIA's CUDA framework and executed on several GPUs concurrently. An external memory algorithm based on the STXXL library and its parallel pipelining feature further reduces the graph in the fourth step. The result is a graph containing only cycles that can be further analyzed in internal memory to count the number and size of the cycles. This full analysis which previously would take months can now be completed within a few days and allows to present structural results for the full graph for the first time. The structure of the A5/1 graph deviates notably from the theoretical results for random mappings.Comment: In Proceedings GRAPHITE 2012, arXiv:1210.611

Explain3D: Explaining Disagreements in Disjoint Datasets

Data plays an important role in applications, analytic processes, and many aspects of human activity. As data grows in size and complexity, we are met with an imperative need for tools that promote understanding and explanations over data-related operations. Data management research on explanations has focused on the assumption that data resides in a single dataset, under one common schema. But the reality of today's data is that it is frequently un-integrated, coming from different sources with different schemas. When different datasets provide different answers to semantically similar questions, understanding the reasons for the discrepancies is challenging and cannot be handled by the existing single-dataset solutions. In this paper, we propose Explain3D, a framework for explaining the disagreements across disjoint datasets (3D). Explain3D focuses on identifying the reasons for the differences in the results of two semantically similar queries operating on two datasets with potentially different schemas. Our framework leverages the queries to perform a semantic mapping across the relevant parts of their provenance; discrepancies in this mapping point to causes of the queries' differences. Exploiting the queries gives Explain3D an edge over traditional schema matching and record linkage techniques, which are query-agnostic. Our work makes the following contributions: (1) We formalize the problem of deriving optimal explanations for the differences of the results of semantically similar queries over disjoint datasets. (2) We design a 3-stage framework for solving the optimal explanation problem. (3) We develop a smart-partitioning optimizer that improves the efficiency of the framework by orders of magnitude. (4)~We experiment with real-world and synthetic data to demonstrate that Explain3D can derive precise explanations efficiently

The convergence to equilibrium of neutral genetic models

This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree based representation of stationary populations that holds both for finite and infinite types (or alleles) models. We then analyze the decays to the equilibrium of finite populations in terms of the convergence to stationarity of their first common ancestor. We estimate the Lyapunov exponent of the distribution flows with respect to the total variation norm. We give bounds on these exponents only depending on the stability with respect to mutation of a single individual; they are inversely proportional to the population size parameter