Bit-flipping Decoder Failure Rate Estimation for (v,w)-regular Codes
CoRR(2024)
摘要
Providing closed form estimates of the decoding failure rate of iterative
decoder for low- and moderate-density parity check codes has attracted
significant interest in the research community over the years. This interest
has raised recently due to the use of iterative decoders in post-quantum
cryptosystems, where the desired decoding failure rates are impossible to
estimate via Monte Carlo simulations. In this work, we propose a new technique
to provide accurate estimates of the DFR of a two-iterations (parallel) bit
flipping decoder, which is also employable for cryptographic purposes. In doing
so, we successfully tackle the estimation of the bit flipping probabilities at
the second decoder iteration, and provide a fitting estimate for the syndrome
weight distribution at the first iteration. We numerically validate our
results, providing comparisons of the modeled and simulated weight of the
syndrome, incorrectly-guessed error bit distribution at the end of the first
iteration, and two-iteration Decoding Failure Rates (DFR), both in the floor
and waterfall regime for simulatable codes. Finally, we apply our method to
estimate the DFR of LEDAcrypt parameters, showing improvements by factors
larger than 2^70 (for NIST category 1) with respect to the previous
estimation techniques. This allows for a ≈ 20
and ciphertext sizes, at no security loss, making the smallest ciphertext for
NIST category 1 only 6
analyzed two-iterations decoder is applicable in BIKE, where swapping it with
the current black-gray decoder (and adjusting the parameters) would provide
strong IND-CCA2 guarantees.
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