Statistical Decoding 2.0: Reducing Decoding to LPN

The security of code-based cryptography relies primarily on the hardness generic decoding with linear codes. best algorithms are all improvements an old algorithm due to Prange: they known under name information set decoders (ISD). A while ago, a which does not belong this family was proposed: statistical decoding. It is randomized that requires computation large parity-checks moderate weight, and uses some kind majority voting these equations recover error. This long forgotten because even variants it performed poorly when compared simplest ISD algorithm. We revisit by using parity-check in more general way. Here used get LPN samples secret part error noise related weight we produce. corresponding problem then solved standard Fourier techniques. By properly choosing method producing low size problem, able outperform way significantly at code rates smaller than 0.3. gives for first time after 60 years, better significant range family.