Defined model
Guess an Enigma M3 configuration after Banburismus clues
- Probability:
- 1.89 × 10⁻¹⁸%
- Odds:
- 1 to (5.3 × 10¹⁹)
- dBan
- −197.2 dBan
In Tony Sale’s Banburismus example, clues cut the possible rotor orders from 336 to about 20. The starting positions and plugboard still leave a formidable field for one guess.
Calculation
N = [26! / (6! × 10! × 2¹⁰)] × 20 × 26³ = 52,987,518,405,942,120,000. p = 1/N. Shift from all 336 orders = 10 log₁₀[(890,190,309,219,827,616,000 − 1) / (52,987,518,405,942,120,000 − 1)] ≈ +12.3 dBan
Assumptions
The reflector, wiring, and ring settings are known. The correct order is assumed to remain among 20 equally likely rotor orders. Each rotor has 26 possible starting positions. Exactly 10 plugboard cables pair 20 letters, leaving six unplugged. The reduction to 20 is illustrative and varies by intercept. Effective cryptographic strength also depended on attack methods and message context.