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

Abdellatif Kichna

Abdellatif Kichna

LIMATI Laboratory, Polydisciplinary Faculty, Sultan Moulay Slimane UniversityBeni Mellal, Morocco
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Kichna, Abdellatif
, 
Abderrazak Farchane

Abderrazak Farchane

LIMATI Laboratory, Polydisciplinary Faculty, Sultan Moulay Slimane UniversityBeni Mellal, Morocco
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Farchane, Abderrazak
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Said Hakimi

Said Hakimi

LIMATI Laboratory, Polydisciplinary Faculty, Sultan Moulay Slimane UniversityBeni Mellal, Morocco
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Hakimi, Said
  
12. Sept. 2025
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Online veröffentlicht: 12. Sept. 2025
Seitenbereich: 58 - 73
DOI: https://doi.org/10.2478/ias-2025-0004
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© 2025 Abdellatif Kichna et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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 level n0 n r ω t
80 2 9602 4801 90 84

Parameters of the Particle Swarm Optimization used in this study

Parameter Value
Number of particles (swarm size) 20
Maximum number of iterations 50
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

Method Mean iterations 95% Confidence Interval
Miscozki et al. 5.36 [5.3132, 5.4068]
Our work 3.01 [3.0047, 3.0193]
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