Who Is 1011011111\(\ldots \)1110110010? Automated Cryptanalysis of Bloom Filter Encryptions of Databases with Several Personal Identifiers
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We provide the first efficient cryptanalysis of Bloom filter encryptions of a database containing more than one personal identifier. The cryptanalysis is fully automated and shows several drawbacks of existing encryption methods based on Bloom filters. In particular, the special representation of the hash functions as linear combinations of two hash functions f and g is exploited in order to detect Bloom filter encryptions of single bigrams (so-called atoms). The assignment of atoms to bigrams is obtained via a modification of an algorithm which was originally proposed for the automated cryptanalysis of simple substitution ciphers. Using our approach, we were able to reconstruct 77.7 % of the identifier values correctly. We point to further improvements of the basic Bloom filter approach that are worth being investigated with respect to their privacy guarantees in future work.
KeywordsBloom filter Privacy-preserving record linkage Anonymity Hash function Cryptographic attack
Research of both authors was supported by the research grant SCHN 586/19-1 of the German Research Foundation (DFG) awarded to the head of the Research Methodology Group, Rainer Schnell. We thank him and the three anonymous reviewers for their helpful comments.
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