# A Finite Regime Analysis of Information Set Decoding Algorithms
## 3 A Finite Regime Analysis of Information Set Decoding Techniques
### Lee-Brickell
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Problem**} & \multicolumn{3}{c}{**Category 1–Security Level Equivalent to Break AES-120 on a Classical Machine**} \\ \hline \multirow{2}{*}{**Problem**} & \multirow{2}{*}{**Cipher**} & **Variant** & **Pr** & **LB** & **Le** & **St** & **FS** & **MMT** & **BJMM** & **Q-LB** & **Q-St** & \(\mathbf{-\log_{2}(1-\frac{k}{g})



\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Category 3–Security Level Equivalent to Break AES-192 on a Classical Machine**} \\
**Problem** & **Cipher** & **Variant** & **Pr** & **LB** & **Le** & **St** & **FS** & **MMT** & **BIMM** & **Q-LB** & **Q-St** & \(\mathbf{-log_{2}(1-\frac{k}{2})\,t}\) \\ \hline \multirow{9}{*}{Syndrome Decoding Problem (SDP)} & Classic McEliece & & 214.70 & 203.45 & 203.36 & 194.36 & 194.32 & 155.09 & 190.53 & 118.71 & 120.18 & 180.91 \\  & NTS-KEM & & 224.34 & 260.40 & 259.95 & 248.01 & 247.91 & 190.18 & 240.63 & 147.85 & 148.46 & 238.21 \\  & BIKE-2 & CPA & 229.50 & 217.61 & 215.82 & 205.99 & 205.98 & 178.12 & 210.87 & 127.49 & 128.89 & 195.12 \\  & CCA & 234.01 & 222.09 & 220.17 & 210.33 & 210.32 & 182.57 & 215.95 & 130.11 & 131.51 & 199.00 \\  & & \(n_{0}=2\) & 234.14 & 222.22 & 220.26 & 210.43 & 201.42 & 182.79 & 216.33 & 130.23 & 131.63 & 199.00 \\  & & \(n_{0}=3\) & 253.23 & 223.84 & 220.82 & 211.91 & 211.90 & 180.13 & 217.56 & 130.67 & 132.07 & 201.29 \\  & LEDAcrypt & \(n_{0}=4\) & 235.98 & 224.66 & 220.97 & 212.39 & 212.39 & 177.94 & 218.56 & 131.26 & 132.66 & 202.00 \\  & & LT, \(n_{0}=2\) & 236.74 & 248.23 & 222.67 & 213.20 & 213.20 & 187.02 & 222.64 & 133.01 & 134.41 & 199.00 \\  & & \(\chi\), \(n_{0}=2\) & 283.67 & 226.57 & 224.33 & 214.80 & 214.80 & 189.40 & 225.67 & 134.79 & 136.19 & 199.00 \\ \hline \multirow{9}{*}{Codeword Finding Problem (CFP)} & \multicolumn{4}{c}{**Category 5–Security Level Equivalent to Break AES-256 on a Classical Machine**} \\
**Problem** & **Cipher** & **Variant** & **Pr** & **LB** & **Le** & **St** & **FS** & **MMT** & **BIMM** & **Q-LB** & **Q-St** & \(\mathbf{-log_{2}(1-\frac{k}{2})\,t}\) \\ \cline{2-10}  & BIKE-2 & CPA & 302.77 & 289.92 & 288.03 & 276.41 & 276.40 & 2439.96 & 281.57 & 160.7 & 162.18 & 274.00 \\  & & CCA & 303.239 & 290.38 & 288.41 & 267.63 & 276.43 & 241.65 & 282.72 & 161.3 & 162.72 & 274.00 \\  & & \(n_{0}=2\) & 315.08 & 302.11 & 300.19 & 288.35 & 288.34 & 250.97 & 293.22 & 167.0 & 168.44 & 286.00 \\  & & \(n_{0}=3\) & 205.305 & 306.39 & 304.48 & 292.78 & 292.77 & 257.64 & 297.70 & 170.3 & 171.71 & 289.56 \\  & LEDAcrypt & \(n_{0}=4\) & 312.68 & 298.84 & 295.66 & 284.59 & 284.58 & 250.96 & 289.06 & 166.82 & 280.57 \\  & & LT, \(n_{0}=2\) & 317.16 & 304.20 & 302.03 & 290.38 & 290.37 & 257.62 & 299.52 & 169.3 & 170.76 & 286.00 \\  & & \(\chi\), \(n_{0}=2\) & 318.57 & 305.61 & 303.37 & 291.83 & 291.83 & 261.01 & 302.47 & 170.8 & 172.24 & 286.00 \\ \hline \multirow{9}{*}{Syndrome Decoding Problem (SDP)} & Classic McEliece & \(n=6688\) & 293.55 & 281.32 & 281.17 & 20.46 & 270.42 & 219.80 & 263.74 & 158.38 & 159.84 & 256.89 \\  & Classic McEliece & \(n=6904\) & 294.49 & 282.29 & 282.05 & 211.88 & 271.13 & 218.79 & 264.39 & 158.87 & 1603.32 & 258.18 \\  & Classic McEliece & \(n=8192\) & 331.64 & 319.30 & 318.37 & 306.63 & 306.54 & 249.74 & 299.98 & 177.55 & 179.01 & 294.34 \\  & NTS-KEM & & 338.58 & 325.94 & 325.68 & 313.52 & 313.44 & 256.88 & 306.72 & 181.02 & 182.48 & 300.85 \\  & CPA & 300.21 & 287.47 & 285.56 & 274.15 & 274.15 & 239.12 & 279.52 & 163.30 & 164.70 & 264.00 \\  & CCA & 300.38 & 288.10 & 266.11 & 274.75 & 274.74 & 240.81 & 280.84 & 164.00 & 165.40 & 264.00 \\  & & \(n_{0}=2\) & 303.56 & 290.79 & 288.84 & 277.40 & 277.39 & 242.63 &