“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.


4 Responses to “One Way Function: (Draft Preprint)”

  1. Alexandre Says:

    regarding your comments on the one-way functions in Lipton’s blog…you can email to me.

    Liked by 1 person

  2. rjlipton Says:

    I found this interesting. The issue of course is the use of real numbers rather than finite field elements. That is probably the main interest and possibly the main problem. We have little experience in how well real functions are to invert.

    Liked by 1 person

  3. Thank you for your comment Richard!
    It appears to boil down to properties of the exponent curve. Lower part of the curve compact for discretisation, upper curve has the number space for function interpolation. Never the twain shall meet. Asymptotic mapping boundaries between discrete approximation and error? Is this worth pursuing? I’ve heard of interest in the exigency of hashing using FPU. My thoughts have turned from cryptography to self-organising memory architecture…
    Much Appreciation,
    Phill. S


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