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Bleichenbacher CCA, proof of termination

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I am currently thinking about how to prove that the algorithm presented in Bleichenbacher's paper (http://archiv.infsec.ethz.ch/education/fs08/secsem/bleichenbacher98.pdf) actually terminates.

I know that in each round the intervals in $M_i$ become smaller as we increase $s_i$, and that $m$ must be contained in exactly one interval from $M_i$. Since the intervals are intersected, it follows that the interval in which $m$ actually lies can be decreased in each round. But why can't there be intervals left in which $m$ does not lie?

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