← Back to Chapter 10, Noise budget and symmetric representatives

Regev noise budget on Z_q

An honest Regev ciphertext is guaranteed to decode correctly while the parameters keep its noise inside the budget. Slide the error bound B and sample count m, scrub the noise inner product e⊤r, and toggle the modulus. The decoded points move along Z_q. While the chapter budget 2mB < ⌊q/2⌋ holds, no honest ciphertext can decode wrongly. Once it is violated the guarantee is gone, and a large enough realized e⊤r flips the bit, which the scrubber lets you find.