BF-Max: an Efficient Bit Flipping Decoder with Predictable Decoding Failure Rate

TL;DR

BF-Max is a novel bit-flipping decoder with predictable decoding failure rate, enabling reliable and efficient syndrome decoding in cryptographic applications, especially where security requires negligible failure probabilities.

Contribution

Introduces BF-Max, a bit-flipping decoder with a theoretical DFR model, low complexity, and constant-time implementation, improving predictability and reliability in cryptographic decoding.

Findings

DFR tightly matches theoretical predictions and simulations

BF-Max achieves lower DFR than previous approaches

Efficient, constant-time implementation suitable for cryptography

Abstract

The Bit-Flipping (BF) decoder, thanks to its very low computational complexity, is widely employed in post-quantum cryptographic schemes based on Moderate Density Parity Check codes in which, ultimately, decryption boils down to syndrome decoding. In such a setting, for security concerns, one must guarantee that the Decoding Failure Rate (DFR) is negligible. Such a condition, however, is very difficult to guarantee, because simulations are of little help and the decoder performance is difficult to model theoretically. In this paper, we introduce a new version of the BF decoder, that we call BF-Max, characterized by the fact that in each iteration only one bit (the least reliable) is flipped. When the number of iterations is equal to the number of errors to be corrected, we are able to develop a theoretical characterization of the DFR that tightly matches with numerical simulations. We also show how BF-Max can be implemented efficiently, achieving low complexity and making it inherently constant time. With our modeling, we are able to accurately predict values of DFR that are remarkably lower than those estimated by applying other approaches.