IndisputableMonolith.Cryptography.KeyLengthFromPhiLadder
This module defines cryptographic key lengths derived from the phi-ladder in Recognition Science, with security levels spaced by phi to the power 1/2 on the log base 2 scale. It supplies concrete values for 80-bit, 128-bit, and 256-bit security along with a doubling property and a certification structure. Applied cryptographers or RS modelers would cite these definitions when mapping fundamental constants to practical key sizes. The module is built from definitions and elementary lemmas with no complex proofs.
claimThe security level ratio equals $sqrt(phi)$, where $phi$ is the self-similar fixed point. Key lengths satisfy keyLength80, keyLength128, keyLength256 with the doubling relation keyLength_doubling, and the whole construction is certified by KeyLengthCert.
background
Recognition Science obtains phi as the self-similar fixed point forced by J-uniqueness in the T5-T6 steps of the unified forcing chain. The module imports the RS time quantum tau_0 = 1 tick from Constants and the J-cost machinery from Cost. It places security levels on a log_2 key-length ladder whose spacing is fixed at phi^{1/2}, consistent with the eight-tick octave periodicity.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the cryptographic layer that converts the phi-ladder into discrete security parameters. It supports downstream use of the RCL and the D=3 spatial structure by furnishing ready-to-apply key lengths. No theorems yet depend on it, but it closes the interface between abstract RS constants and applied security.
scope and limits
- Does not derive key lengths from quantum algorithms or attack models.
- Does not prove concrete security reductions.
- Does not address implementation or side-channel issues.
- Does not link key lengths to the mass formula or particle spectrum.