Abstract
The Oblivious Cross-Tags (OXT) protocol due to Cash et al. (CRYPTO’13) is a highly scalable searchable symmetric encryption (SSE) scheme that allows fast processing of conjunctive and more general Boolean queries over encrypted relational databases. A longstanding open question has been to extend OXT to also support queries over joins of tables without pre-computing the joins. In this paper, we solve this open question without compromising on the nice properties of OXT with respect to both security and efficiency. We propose Join Cross-Tags (JXT) - a purely symmetric-key solution that supports efficient conjunctive queries over (equi-) joins of encrypted tables without any pre-computation at setup. The JXT scheme is fully compatible with OXT, and can be used in conjunction with OXT to support a wide class of SQL queries directly over encrypted relational databases. JXT incurs a storage cost (over OXT) of a factor equal to the number of potential join-attributes in a table, which is usually compensated by the fact that JXT is a fully symmetric-key solution (as opposed to OXT which relies on discrete-log hard groups). We prove the (adaptive) simulation-based security of JXT with respect to a rigorously defined leakage profile.
S. Patranabis—Most of the work was done while the author was affiliated with ETH Zürich, Switzerland and Visa Research USA.
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Notes
- 1.
The actual protocol is slightly more complicated to be fully secure and provably secure under DDH, but the above description gives the main gist of OXT.
- 2.
Throughout this paper, when we refer to joins, we mean equi joins.
- 3.
By high entropy attribute we mean the information-theoretic entropy of the column corresponding to the attribute. For example, the attribute gender has low entropy, whereas the attribute name can have high entropy in a table.
- 4.
By configuration we mean the (pre-) computation of the encrypted table. We remind the reader that this pre-computation does not involve join pre-computation, as each table is encrypted independently.
- 5.
We remark here that the transactions database is encrypted for post-transactional audit, fraud detection, money-laundering detection, machine learning etc. The real-time transactions database is usually updated and used without encryption, as it runs in a secure domain. It is later encrypted on a periodic basis for above additional functionalities.
- 6.
Note that we have \(\textsc {t}\) different \(\textsf{XSet}\)s, but their total size is same as the single \(\textsf{XSet}\) of OXT.
- 7.
Note that a function \(f:\mathbb {N}\rightarrow \mathbb {N}\) is said to be negligible in \(\lambda \) if for every positive polynomial p, \(f(\lambda )<1/p(\lambda )\) when \(\lambda \) is sufficiently large.
- 8.
Note that a multi-set additionally reveals the frequency of each entry.
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Acknowledgments
We thank the anonymous reviewers of IACR ASIACRYPT 2022 for their helpful comments and suggestions.
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Jutla, C., Patranabis, S. (2022). Efficient Searchable Symmetric Encryption for Join Queries. In: Agrawal, S., Lin, D. (eds) Advances in Cryptology – ASIACRYPT 2022. ASIACRYPT 2022. Lecture Notes in Computer Science, vol 13793. Springer, Cham. https://doi.org/10.1007/978-3-031-22969-5_11
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