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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