Rotating Constant Method (RCM)
An allocation pattern where each change key shares one position at TMK depth — the constant — and the constant rotates across keys, reducing phantom count.
The Rotating Constant Method (RCM) is a TMK allocation pattern that reduces phantom key generation in master key systems. Each change key shares exactly one cut position with the TMK — that position is at TMK depth (the constant) — and the constant rotates across keys.
For a 6-pin system with three change keys:
- Change key A’s constant is at position 1 (positions 2–6 differ from TMK).
- Change key B’s constant is at position 2 (positions 1, 3–6 differ).
- Change key C’s constant is at position 3 (positions 1, 2, 4–6 differ).
The chamber that has the constant doesn’t get a master pin — it accepts only the TMK depth, since the change key cuts at TMK depth in that position too. The other five chambers do get master pins.
Why RCM reduces phantoms
In a chamber with no master pin, only one cut depth opens the cylinder. In a chamber with a master pin, two cut depths do. Phantom enumeration walks every combination of valid cut depths per chamber against the access matrix.
A 6-pin system using Total Position Progression (TPP — every position differs from TMK) gets 2⁶ = 64 valid keys per cylinder. A 6-pin system using RCM gets 2⁵ = 32 valid keys per cylinder, because one chamber has only one valid depth. Half the phantom search space, instantly.
For deep hierarchies with many master keys per cylinder, the reduction compounds. A system with TMK + 2 master groups using RCM-style allocation typically generates 30–50% fewer phantoms than the same system using TPP.
When RCM doesn’t help
RCM doesn’t eliminate phantoms — that’s structurally impossible for any non-trivial master keyed system — and it imposes its own constraint: every change key has at least one position at TMK depth, which can produce predictable patterns if not paired with strong allocation in the remaining positions.
Keyzee’s optimiser uses RCM as the seeding pass and then anneals the remaining positions to maximise distance from the TMK and from sibling change keys.
Related
→ TMK — the apex key RCM allocates around → Change key — the keys that get RCM constants → Phantom key — what RCM is designed to reduce → Master pin — the mechanism RCM avoids in constant chambers