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A Novel Approach to Bit-Flipping Threshold Selection with Particle Swarm Optimization in the QC-MDPC-McEliece Cryptosystem Cover

A Novel Approach to Bit-Flipping Threshold Selection with Particle Swarm Optimization in the QC-MDPC-McEliece Cryptosystem

Journal of Information Assurance and Security
Volume 20 (2025): Issue 2 (September 2025)
By: Abdellatif Kichna,  Abderrazak Farchane and  Said Hakimi  
Open Access
|Sep 2025

Figures & Tables

Figure 1.

Encryption process. Plaintext m is encoded into codeword mG, combined with an error vector e to produce ciphertext c=mG+e.
Encryption process. Plaintext m is encoded into codeword mG, combined with an error vector e to produce ciphertext c=mG+e.

Figure 2.

Decryption process. Ciphertext c is decoded via bit-flipping decoder. Corrected codeword mG yields m from its first r bits, exploiting G's systematic structure.
Decryption process. Ciphertext c is decoded via bit-flipping decoder. Corrected codeword mG yields m from its first r bits, exploiting G's systematic structure.

Figure 3.

PSO pseudocode.
PSO pseudocode.

Figure 4.

PSO based threshold selection flowchart.
PSO based threshold selection flowchart.

Figure 5.

Syndrome weight progression across iterations
Syndrome weight progression across iterations

Figure 6.

Total number of bits flipped over iterations
Total number of bits flipped over iterations

Figure 7.

Cumulative percentage of corrected bits over iterations.
Cumulative percentage of corrected bits over iterations.

Recommended parameters for QC-MDPC McEliece cryptosystem by Misoczki et al_ (2013)

Security leveln0nrωt
802960248019084

Parameters of the Particle Swarm Optimization used in this study

ParameterValue
Number of particles (swarm size)20
Maximum number of iterations50
Cognitive constant (c1)2
Social constant (c2)2
Inertia weight (ω)0.4
Random values: r1, r2[0,1]

Mean Iterations and 95% Confidence Intervals for Misoczki et al_ and PSO Methods

MethodMean iterations95% Confidence Interval
Miscozki et al.5.36[5.3132, 5.4068]
Our work3.01[3.0047, 3.0193]
DOI: https://doi.org/10.2478/ias-2025-0004 | Journal eISSN: 1554-1029 | Journal ISSN: 1554-1010
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Language: English
Page range: 58 - 73
Published on: Sep 12, 2025
Published by: Cerebration Science Publishing Co., Limited
In partnership with: Paradigm Publishing Services
Publication frequency: 6 issues per year
Keywords:
bit flipping decoding,
Mceliece cryptosystem,
particle swarm optimization,
post-quantum cryptography,
QC-MDPC codes
Related subjects:
Computer sciences,
Fundamentals of computer sciences,
Theoretical computer sciences,
IT-security and cryptology

© 2025 Abdellatif Kichna, Abderrazak Farchane, Said Hakimi, published by Cerebration Science Publishing Co., Limited
This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License.

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