OrBIT-KDF: A Chirikov–Julia Chaotic Key Derivation Function

We introduce OrBIT-KDF, an experimental key derivation function that composes two clas-
sical chaotic systems—the Chirikov standard map on the two-dimensional torus and a quadratic
Julia iteration on the complex plane—with a modern cryptographic hash.The construction takes
a username and password, interprets the username as a seed for the Chirikov map, uses the
resulting orbit to define a Julia parameter, and interprets the password as an initial condition for
the Julia system.The coupled Chirikov–Julia trajectory is sampled as a finite sequence of points
in [0, 1)3, encoded as IEEE-754 64-bit floats, concatenated into a byte string, and compressed
by SHA-512 to a 512-bit key, as specified in the public prototype repository.[Haa26]We give a
complete mathematical specification of OrBIT-KDF, analyze the dynamical systems used (orbits,
attractors, and sensitivity), discuss security considerations, and report empirical measurements
of output distribution, avalanche behavior, and collision search over restricted input spaces.Our
conclusion is that OrBIT-KDF behaves like a SHA-512-based password KDF augmented with a
highly structured chaotic pre-processing layer, suitable as a chaos-cryptography laboratory but not
as a replacement for standard, memory-hard KDFs in high-assurance applications.[oST12, Nor25]