On the Hardness of Learning With Errors with Binary Secrets

We give a simple proof that the decisional Learning With Errors (LWE) problem with binary secrets is at least as hard as the standard LWE problem (with unrestricted, uniformly random secrets). This proves that the binary-secret LWE distribution is pseudorandom, under standard worst-case complexity assumptions on lattice problems. Our results are similar to those proved by (Brakerski, Langlois, Peikert, Regev and Stehlé, STOC 2013), but provide a shorter, more direct proof, and a slight improvement in the noise growth of the reduction.