Equality Operators for Constant-weight Codewords with Applications in (Keyword) PIR

Abstract

Homomorphic encryption allows computation to be performed on data while in encrypted form. However, the computational overhead of a circuit that is run using homomorphic encryption depends on the number of multiplications and multiplicative depth. For example, equality checks which are a common step in many tasks, have a multiplicative depth that depends on the bit-length of the numbers. In this work, we propose constant-weight equality operators, which compare constant-weight codewords using a circuit that has a multiplicative depth that depends solely on the Hamming weight of the constant-weight code, not the size of the operands.

Private Information Retrieval (PIR) is one task where equality operations are a solution. In a PIR protocol, a user wishes to query a database without revealing which element is queried to the server. In this thesis, we also detail an architecture for PIR which was previously assumed to be impractical. At the heart of this architecture is the constant-weight equality operator.

Our experiments show how constant-weight equality operators outperform existing equality operators and can be used for practical purposes. We also conduct experiments to show the practicality of PIR using our approach and our results show how constant-weight PIR outperforms existing work in aspects of scale such as large domain sizes and large responses.