Rungs + curves
A rung is the key size in bits. Each rung has its own toy curve whose base point has order exactly 2N. The key k is published: it is a toy, the point is chip versus coin.
| rung | curve | G | n | k | Q = kG | qubits |
|---|---|---|---|---|---|---|
| 4-BIT | y² = x³ + 2x + 1 over F₁₁ | (0, 1) | 16 | 11 (1011) | (6, 8) | 12 |
| 5-BIT | y² = x³ + x + 10 over F₂₃ | (5, 5) | 32 | 19 (10011) | (20, 16) | 15 |
| 6-BIT | y² = x³ + x + 6 over F₅₃ | (0, 18) | 64 | 43 (101011) | (29, 37) | 18 |
| 7-BIT | y² = x³ + 11x + 11 over F₁₁₃ | (2, 43) | 128 | 89 (1011001) | (100, 65) | 21 |
| 8-BIT | y² = x³ + x + 7 over F₂₂₇ | (0, 37) | 256 | 173 (10101101) | (176, 10) | 24 |
Circuit builder: qcrack-shor-ecdlp-draper/1. Every attempt's params.json carries its curve verbatim.