How to Encrypt with the LPN Problem

We present a probabilistic private-key encryption scheme named LPN-C whose security can be reduced to the hardness of the Learning from Parity with Noise (LPN) problem. The proposed protocol involves only basic operations in GF(2) and an error-correcting code. We show that it achieves indistinguishability under adaptive chosen plaintext attacks (IND-P2-C0). Appending a secure MAC renders the scheme secure under adaptive chosen ciphertext attacks. This scheme enriches the range of available cryptographic primitives whose security relies on the hardness of the LPN problem.