“This paper presents a potential ‘one way’ mathematical function mediated through iterative forward-coding of two scaled, fractional variables. These variables are derived from the quantized step-error of the inverse function. The equation’s modulated output constitutes a binary walk through an information space, maintaining discrete parameterizations which enable the enfolding conservation of a single ‘bit’ of information in addition to the function product. As the delta of the function and it’s inverse describe a ternary probability inheritance tree, it is shown that such a function cannot be self-contained in terms of total entropy production when the ‘spare bit’ is used to operate upon a separate data set and as such, necessitates a ‘trap-door’ table to preserve an additional single ‘bit’ of information required to correctly derive the inverse function.
Furthermore, such a trap-door table represents an essential index in order for the equation to operate as a collision free hash function. The splitting of the equation’s output between a cumulative, discretely iterated, binary hash function and a separate binary trapdoor table means that without benefit of access to both information sources, the inverse function is consequently encrypted in exponential time.” Cont; see link.
Draft Preprint: One Way Function with Trapdoor.
“A novel cryptographic primitive (ATYP) is presented in form of a symmetric stream cipher derived from an iterated, fractal, trapdoor permutation with polynomial pre-image span (PPS) and input obfuscation (iO). The described fractal transform outputs a Real numbered hash function which maintains an enfolding, parameterized, information conserving Boolean identity. Binary modulation of the hash identity is mediated via forward-feed of an inverse-error dependent, deterministic variable. The forward-feed operating as an avalanche secure pseudo-random generator (PRG), consequent to the inverse function’s ternary, step-wise, floating point error and the concurrent, ternary-permissive, binary integration of plain-text. Taken together, the enfolding hash identity and its associated trapdoor allow an invertible bijection. Somewhat counter-intuitively, the hash function’s pre image correlation is shown to enhance key strength in the setting of PPS.” Cont; see link.
Second Draft Preprint: Real Permutations yield Sticky Predicates with Input Obfuscation & Poly Pre-Image Span.