Low Noise LPN: Key dependent message secure public key encryption an sample amplification

Abstract

Cryptographic schemes based on the learning parity with noise (LPN) problem have several very desirable aspects: low computational overhead, simple implementation and conjectured post-quantum hardness. Choosing the LPN noise parameter sufficiently low allows for public key cryptography. In this study, the authors construct the first standard model public key encryption scheme with key dependent message security based solely on the low-noise LPN problem. Additionally, they establish a new connection between LPN with a bounded number of samples and LPN with an unbounded number of samples. In essence, they show that if LPN with a small error and a small number of samples is hard, then LPN with a slightly larger error and an unbounded number of samples is also hard. The key technical ingredient to establish both results is a variant of the LPN problem called the extended LPN problem.