Ido Shahaf

Searchable symmetric encryption: optimal locality in linear space via two-dimensional balanced allocations

Searchable symmetric encryption (SSE) enables a client to store a database on an untrusted server while supporting keyword search in a secure manner. Despite the rapidly increasing interest in SSE technology, experiments indicate that the performance of the known schemes scales badly to large databases. Somewhat surprisingly, this is not due to their usage of cryptographic tools, but rather due to their poor locality (where locality is defined as the number of non-contiguous memory locations the server accesses with each query). The only known schemes that do not suffer from poor locality suffer either from an impractical space overhead or from an impractical read efficiency (where read efficiency is defined as the ratio between the number of bits the server reads with each query and the actual size of the answer). We construct the first SSE schemes that simultaneously enjoy optimal locality, optimal space overhead, and nearly-optimal read efficiency. Specifically, for a database of size N, under the modest assumption that no keyword appears in more than N1 − 1/loglogN documents, we construct a scheme with read efficiency Õ(loglogN). This essentially matches the lower bound of Cash and Tessaro (EUROCRYPT ’14) showing that any SSE scheme must be sub-optimal in either its locality, its space overhead, or its read efficiency. In addition, even without making any assumptions on the structure of the database, we construct a scheme with read efficiency Õ(logN). Our schemes are obtained via a two-dimensional generalization of the classic balanced allocations (“balls and bins”) problem that we put forward. We construct nearly-optimal two-dimensional balanced allocation schemes, and then combine their algorithmic structure with subtle cryptographic techniques.

Can PPAD Hardness be Based on Standard Cryptographic Assumptions

We consider the question of whether PPAD hardness can be based on standard cryptographic assumptions, such as the existence of one-way functions or public-key encryption. This question is particularly well-motivated in light of new devastating attacks on obfuscation candidates and their underlying building blocks, which are currently the only known source for PPAD hardness.

Tight Tradeoffs in Searchable Symmetric Encryption

A searchable symmetric encryption (SSE) scheme enables a client to store data on an untrusted server while supporting keyword searches in a secure manner. Recent experiments have indicated that the practical relevance of such schemes heavily relies on the tradeoff between their space overhead, locality (the number of non-contiguous memory locations that the server accesses with each query), and read efficiency (the ratio between the number of bits the server reads with each query and the actual size of the answer). These experiments motivated Cash and Tessaro (EUROCRYPT ’14) and Asharov et al. (STOC ’16) to construct SSE schemes offering various such tradeoffs, and to prove lower bounds for natural SSE frameworks. Unfortunately, the best-possible tradeoff has not been identified, and there are substantial gaps between the existing schemes and lower bounds, indicating that a better understanding of SSE is needed.

Strengthening the Security of Encrypted Databases: Non-transitive JOINs

Database management systems that operate over encrypted data are gaining significant commercial interest. CryptDB is one such notable system supporting a variety SQL queries over encrypted data (Popa et al., SOSP ’11). It is a practical system obtained by utilizing a number of encryption schemes, together with a new cryptographic primitive for supporting SQL’s join operator.