New Technique Improves Decoding Failure Rate Estimates for Post‑Quantum Cryptosystems

Global: New Technique Improves Decoding Failure Rate Estimates for Post‑Quantum Cryptosystems

A team of cryptography researchers has introduced a closed‑form method for estimating the decoding failure rate (DFR) of a two‑iteration parallel bit‑flipping decoder, a component increasingly used in post‑quantum key‑encapsulation mechanisms. The approach delivers estimates that satisfy security thresholds of DFR ≤ 2^{-128} without relying on extensive Monte Carlo simulations.

Background

Iterative decoders for low‑ and moderate‑density binary parity‑check codes are central to several lattice‑based and code‑based cryptosystems. Achieving DFRs at or below 2^{-128} is a prerequisite for 128‑bit security claims, yet traditional simulation methods become infeasible at such low error probabilities.

Proposed Estimation Method

The authors model the bit‑flipping probabilities at the second iteration and derive the syndrome‑weight distribution both before and after the first iteration as explicit functions of code parameters and error weight. By analytically tracking these distributions, the technique predicts the DFR after two iterations across both the waterfall and error‑floor regimes.

Validation and Results

Numerical experiments compare the analytically modelled syndrome weights, the distribution of incorrectly guessed error bits after the first iteration, and the resulting DFR against simulated outcomes. The findings show close alignment in both regimes, confirming the model’s accuracy.

Impact on LEDAcrypt

Applying the method to the LEDAcrypt key‑encapsulation system, the researchers report an improvement factor exceeding 2^{70} over prior estimation techniques for configurations targeting 128‑bit security. This enhancement translates into a 20 % reduction in public‑key and ciphertext sizes without compromising security.

Potential for BIKE

The paper notes that the same analytical framework can be adapted to the Bit Flipping Key Encapsulation (BIKE) scheme by replacing the existing “BIKE‑flip decoder” with the two‑iteration decoder. Such a substitution would grant BIKE provable indistinguishability under adaptive chosen‑ciphertext attack (IND‑CCA2).

Future Directions

The authors suggest that the closed‑form estimates could be extended to higher‑iteration decoders and other code families, potentially streamlining security assessments for a broader class of post‑quantum protocols.

This report is based on information from arXiv, licensed under See original source. Source attribution required.