# Privacy-Preserving Plaintext-Equality of Low-Entropy Inputs

## Abstract

Confidentiality requires to keep information away from the eyes of non-legitimate users, while practicality necessitates to make information usable for authorized users. The former issue is addressed with cryptography, and encryption schemes. The combination of both has been shown to be possible with advanced techniques that permit to perform computations on encrypted data. Searchable encryption concentrates on the problem of extracting specific information from a ciphertext.

In this paper, we focus on a concrete use-case where sensitive tokens (medical records) allow third parties to find matching properties (compatible organ donor) without revealing more information than necessary (contact information).

We reduce such case to the plaintext-equality problem. But in our particular application, the message-space is of limited size or, equivalently, the entropy of the plaintexts is small: public-key existing solutions are not fully satisfactory. We then propose a suitable security model, and give an instantiation with an appropriate security analysis.

## Notes

### Acknowledgments

This work was supported in part by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement no. 339563 – CryptoCloud).

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