A Beautiful Equation

November 4, 2014

A bit of a light bulb moment for me with the understanding that trapdoor functions are essentially polynomial time reductions in decision problems… something at least that’s intuitively understandable.
In casting about the literature for related quadratic crypto primitives it’s bewildering to see the wide range of (barely comprehensible) schema. HFE, Elliptic Curves, Multivariate Equations etc. It’s also reassuring to see that there is little in the way of fractal error feedback algorithms outside the realm of say, signal processing or neural networks.
From what I can follow/understand of existing quadratic based cryptography, it’s generally ¬pretty!
There’s a certain, ‘Heath Robinsonian’, bolt-on arbitrariness to the various ‘multivariate/set extension’ methods given for introducing pseudo-randomness or ‘hard-to-invert-edness’.
One of the main reasons new cryptography primitives are worth examining is that they may present in unique form and combination of known cryptographic attributes.
The trapdoor permutation I’m advancing appears to be novel and satisfies a range of desired cryptographic characteristics. Including PRNG, satisfaction of avalanche criteria and collision resistance over its combined hashing/trapdoor output.
Most importantly of all, it has beauty.  There’s an aesthetic in its branching fractal symmetry, married with a perfect amount of embedded temporal randomness.

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