This paper presents OnionPIR and stateful OnionPIR, two single-server PIR schemes that significantly improve the response size and computation cost over state-of-the-art schemes. OnionPIR scheme utilizes recent advances in somewhat homomorphic encryption (SHE) and carefully composes two lattice-based SHE schemes and homomorphic operations to control the noise growth and response size. Stateful OnionPIR uses a technique based on the homomorphic evaluation of copy networks. OnionPIR achieves a response overhead of just 4.2x over the insecure baseline, in contrast to the 100x response overhead of state-of-the-art schemes. Our stateful OnionPIR scheme improves upon the recent stateful PIR framework of Patel et al. and drastically reduces its response overhead by avoiding downloading the entire database in the offline stage. Compared to stateless OnionPIR, Stateful OnionPIR reduces the computation cost by 1.8~x for different database sizes.

Oblivious RAM (ORAM) is a cryptographic primitive that allows a client to hide access pattern to its data encrypted and stored at a remote server. Traditionally, ORAM algorithms assume the server acts purely as a storage device. Under this assumption, ORAM has at least log(N) bandwidth blowup for N data entries. After three decades of improvements, ORAM algorithms have reached the optimal logarithmic bandwidth blowup. Nonetheless, in many practical use-cases a constant bandwidth overhead is desirable. To this purpose, Devadas et al. (TCC 2016) formalized the server computation model for ORAM and proposed Onion ORAM which relies on homomorphic computation to achieve constant worst-case bandwidth blowup. This line of work is generally believed to be purely theoretical, due to the large overheads of homomorphic computation. In this paper, we present Onion Ring ORAM, the first efficient constant bandwidth ORAM scheme in the single server model, based on the Onion ORAM construction and the leveled version of the TFHE scheme by Chillotti et al.. We propose a series of improvements, most notably including a more efficient homomorphic permutation protocol. We implement Onion Ring ORAM and show that it can outperform state-of-the-art logarithmic-bandwidth ORAM like Path ORAMs and Ring ORAM when the network throughput is limited. Under one setting, our construction reduces monetary cost per access by 40% and end-to-end latency by 35% over Ring ORAM.

Homomorphic Encryption (HE) is a cryptosystem which supports computation on encrypted data. Ló pez-Alt et al. (STOC 2012) proposed a generalized notion of HE, called Multi-Key Homomorphic Encryption (MKHE), which is capable of performing arithmetic operations on ciphertexts encrypted under different keys. In this paper, we present multi-key variants of two HE schemes with packed ciphertexts. We present new relinearization algorithms which are simpler and faster than previous method by Chen et al. (TCC 2017). We then generalize the bootstrapping techniques for HE to obtain multi-key fully homomorphic encryption schemes. We provide a proof-of-concept implementation of both MKHE schemes using Microsoft SEAL. For example, when the dimension of base ring is 8192, homomorphic multiplication between multi-key BFV (resp. CKKS) ciphertexts associated with four parties followed by a relinearization takes about 116 (resp. 67) milliseconds. Our MKHE schemes have a wide range of applications in secure computation between multiple data providers. As a benchmark, we homomorphically classify an image using a pre-trained neural network model, where input data and model are encrypted under different keys. Our implementation takes about 1.8 seconds to evaluate one convolutional layer followed by two fully connected layers on an encrypted image from the MNIST dataset.

Fully Homomorphic Encryption (FHE) refers to a set of encryption schemes that allow computations on encrypted data without requiring a secret key. Recent cryptographic advances have pushed FHE into the realm of practical applications. However, programming these applications remains a huge challenge, as it requires cryptographic domain expertise to ensure correctness, security, and performance.

Private Set Intersection (PSI) allows two parties, the sender and the receiver, to compute the intersection of their private sets without revealing extra information to each other. We are interested in the unbalanced PSI setting, where (1) the receiver's set is significantly smaller than the sender's, and (2) the receiver (with the smaller set) has a low-power device. Also, in a Labeled PSI setting, the sender holds a label per each item in its set, and the receiver obtains the labels from the items in the intersection. We build upon the unbalanced PSI protocol of Chen, Laine, and Rindal (CCS~2017) in several ways: we add efficient support for arbitrary length items, we construct and implement an unbalanced Labeled PSI protocol with small communication complexity, and also strengthen the security model using Oblivious Pseudo-Random Function (OPRF) in a pre-processing phase. Our protocols outperform previous ones: for an intersection of 220 and $512$ size sets of arbitrary length items our protocol has a total online running time of just $1$~second (single thread), and a total communication cost of 4 MB. For a larger example, an intersection of 228 and 1024 size sets of arbitrary length items has an online running time of $12$ seconds (multi-threaded), with less than 18 MB of total communication.

Private information retrieval (PIR) is a key building block in many privacy-preserving systems. Unfortunately, existing constructions remain very expensive. This paper introduces two techniques that make the computational variant of PIR (CPIR) more efficient in practice. The first technique targets a recent class of CPU-efficient CPIR protocols where the query sent by the client contains a number of ciphertexts proportional to the size of the database. We show how to compresses this query, achieving size reductions of up to 274X. The second technique is a new data encoding called probabilistic batch codes (PBCs). We use PBCs to build a multi query PIR scheme that allows the server to amortize its computational cost when processing a batch of requests from the same client. This technique achieves up to 40× speedup over processing queries one at a time, and is significantly more efficient than related encodings. We apply our techniques to the Pung private communication system, which relies on a custom multi-query CPIR protocol for its privacy guarantees. By porting our techniques to Pung, we find that we can simultaneously reduce network costs by 36× and increase throughput by 3X.

Private Set Intersection (PSI) is a cryptographic technique that allows two parties to compute the intersection of their sets without revealing anything except the intersection. We use fully homomorphic encryption to construct a fast PSI protocol with a small communication overhead that works particularly well when one of the two sets is much smaller than the other, and is secure against semi-honest adversaries.