Partitioned Searchable Encryption

in Qiong, Huang; Yu, Yu (Eds.) Provable and Practical Security, 15th International Conference, ProvSec 2021, Guangzhou, November 5 – November 8, 2021, Proceedings (2021, November 02)

Symmetric searchable encryption (SSE) allows to outsource encrypted data to an untrusted server and retain searching capabilities. This is done without impacting the privacy of both the data and the ... [more ▼]

Symmetric searchable encryption (SSE) allows to outsource encrypted data to an untrusted server and retain searching capabilities. This is done without impacting the privacy of both the data and the search/update queries. In this work we put forth a new flavour of symmetric searchable encryption (SSE): Partitioned SSE is meant to capture the cases where the search rights must be partitioned among multiple individuals. We motivate through compelling examples the practical need for such a notion and discuss instantiations based on functional encryption and trapdoor permutations. First we leverage the power of functional encryption (FE). Our construction follows the general technique of encrypting the set of keywords and the presumably larger datafiles separately, a keyword acting as a ``pointer'' to datafiles it belongs to. To improve on the constraint factors (large ciphertext, slow encryption/decryption procedures) that are inherent in FE schemes, the keyword check is done with the help of a Bloom filter -- one per datafile: the crux idea is to split the filter into buckets, and encrypt each bucket separately under an FE scheme. Functional keys are given for binary \masks checking if relevant positions are set to 1 inside the underlying bit-vector of the Bloom filter. The second construction we present achieves forward security and stems from the scheme by Bost in CCS'16. We show that a simple tweak of the original construction gives rise to a scheme supporting updates in the partitioned setting. Moreover, the constructions take into account the possibility that some specific users are malicious while declaring their search results. [less ▲]

From Clustering Supersequences to Entropy Minimizing Subsequences for Single and Double Deletions

E-print/Working paper (2018)

A binary string transmitted via a memoryless i.i.d. deletion channel is received as a subsequence of the original input. From this, one obtains a posterior distribution on the channel input, corresponding ... [more ▼]

A binary string transmitted via a memoryless i.i.d. deletion channel is received as a subsequence of the original input. From this, one obtains a posterior distribution on the channel input, corresponding to a set of candidate supersequences weighted by the number of times the received subsequence can be embedded in them. In a previous work it is conjectured on the basis of experimental data that the entropy of the posterior is minimized and maximized by the constant and the alternating strings, respectively. In this work, in addition to revisiting the entropy minimization conjecture, we also address several related combinatorial problems. We present an algorithm for counting the number of subsequence embeddings using a run-length encoding of strings. We then describe methods for clustering the space of supersequences such that the cardinality of the resulting sets depends only on the length of the received subsequence and its Hamming weight, but not its exact form. Then, we consider supersequences that contain a single embedding of a fixed subsequence, referred to as singletons, and provide a closed form expression for enumerating them using the same run-length encoding. We prove an analogous result for the minimization and maximization of the number of singletons, by the alternating and the uniform strings, respectively. Next, we prove the original minimal entropy conjecture for the special cases of single and double deletions using similar clustering techniques and the same run-length encoding, which allow us to characterize the distribution of the number of subsequence embeddings in the space of compatible supersequences to demonstrate the effect of an entropy decreasing operation. [less ▲]