## CryptoDB

### Paper: Obfuscated Fuzzy Hamming Distance and Conjunctions from Subset Product Problems

Authors: Steven D. Galbraith Lukas Zobernig DOI: 10.1007/978-3-030-36030-6_4 Search ePrint Search Google We consider the problem of obfuscating programs for fuzzy matching (in other words, testing whether the Hamming distance between an n-bit input and a fixed n-bit target vector is smaller than some predetermined threshold). This problem arises in biometric matching and other contexts. We present a virtual-black-box (VBB) secure and input-hiding obfuscator for fuzzy matching for Hamming distance, based on certain natural number-theoretic computational assumptions. In contrast to schemes based on coding theory, our obfuscator is based on computational hardness rather than information-theoretic hardness, and can be implemented for a much wider range of parameters. The Hamming distance obfuscator can also be applied to obfuscation of matching under the $\ell _1$ norm on $\mathbb {Z}^n$.We also consider obfuscating conjunctions. Conjunctions are equivalent to pattern matching with wildcards, which can be reduced in some cases to fuzzy matching. Our approach does not cover as general a range of parameters as other solutions, but it is much more compact. We study the relation between our obfuscation schemes and other obfuscators and give some advantages of our solution.
##### BibTeX
@article{tcc-2019-29968,
title={Obfuscated Fuzzy Hamming Distance and Conjunctions from Subset Product Problems},
booktitle={Theory of Cryptography},
series={Lecture Notes in Computer Science},
publisher={Springer},
volume={11891},
pages={81-110},
doi={10.1007/978-3-030-36030-6_4},
author={Steven D. Galbraith and Lukas Zobernig},
year=2019
}