Figure 1.
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.
Figure 3.
PSO pseudocode.
Figure 4.
PSO based threshold selection flowchart.
Table 1.
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 |
Table 2.
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] |
Figure 5.
Syndrome weight progression across iterations
Table 3.
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] |
Figure 6.
Total number of bits flipped over iterations
Figure 7.
Cumulative percentage of corrected bits over iterations.