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**2017/964**

**Title:**

Recursive ORAMs with Practical Constructions

**Authors:**
Sarvar Patel, Giuseppe Persiano, Kevin Yeo

**Abstract:**

We present Recursive Square Root ORAM (R-SQRT), a simple and flexible ORAM that can be instantiated for different client storage requirements. R-SQRT requires significantly less bandwidth than Ring and Partition ORAM, the previous two best practical constructions in their respective classes of ORAM according to client storage requirements. Specifically, R-SQRT is a 4x improvement in amortized bandwidth over Ring ORAM for similar server storage. R-SQRT is also a 1.33-1.5x improvement over Partition ORAM under the same memory restrictions. R-SQRT-AHE, a variant of R-SQRT, is a 1.67- 1.75x improvement over the reported Partition ORAM results in the same settings. All the while, R-SQRT maintains a single data roundtrip per query. We emphasize the simplicity of R-SQRT which uses straightforward security and performance proofs. Additionally, we present Twice-Recursive Square Root ORAM (TR-SQRT) with smaller client stor- age requirements. Due to its flexibility, we construct several instantiations under different memory requirements. TR-SQRT is asymptotically competitive with previous results, yet remarkably simple.

**ePrint:**
https://eprint.iacr.org/2017/964

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