## IACR News item: 23 January 2023

We give constructions of this primitive from a common template, which can be instantiated under either the LPN (with non-negligible correctness error) or the LWE (with negligible correctness error) assumptions. Our construction uses a novel twist on the standard non-interactive key exchange based on the Alekhnovich cryptosystem, which upgrades it to a non-interactive inner product protocol almost for free. In addition to being non-interactive, our constructions have linear communication (with constants smaller than all known alternatives) and small computation: using LPN or LWE with quasi-cyclic codes, we estimate that encoding a length-$2^{20}$ vector over a 32-bit field takes less that 2s on a standard laptop; decoding amounts to a single cheap inner-product.