## State of the Art

### February 2, 2015

There was a small flurry of cryptography theory papers last year addressing inputs obfuscation of varying form & degree as it relates to poly-span pre-image, correlated inputs, auxiliary inputs and deterministic public key schemes.

Most notable from my reading were, On the Implausibility of Differing-Inputs Obfuscation and Extractable Witness Encryption with Auxiliary Input by Garg, Gentry et al., along with, Poly-Many Hardcore Bits for Any One-Way Function and a Framework for Differing-Inputs Obfuscation, published by Bellare et al in September.

Those two papers seem to reach opposing conclusions or at least disagree as to the degree of obfuscation possible under certain pre-image & auxiliary input assumptions. That’s my take anyhow, please feel free to add any clarification?

Getting into the ‘meat & potatoes’ section of my paper, I have to dissect this theory and decide where & how I fit in?

On a more practical but no less complex level, I’m trying to understand the relative logarithmic, cryptographic ‘hardness’ of correlated bits at differing decimal place of significance. This is related to the function’s relaxation time to a fixed attraction point, or when inverted, the number of iterations needed to go ‘out of range’ on any given error magnitude.

If anyone could point me to a relevant function condition formula, thanks!

February 2, 2015 at 3:14 am

I recall, but dimly, some papers on a generalization of functions called “reluctant functions” many years ago, but that’s all I remember at present.

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February 2, 2015 at 3:24 am

Thanks Jon, I’ll follow that up. Cheers!

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February 2, 2015 at 4:43 am

Gian-Carlo Rota is the man?

http://www.stat.ncsu.edu/information/library/mimeo.archive/ISMS_1970_600.24.pdf

Leads to considerations of Lah Numbers… rising factorials.

http://en.wikipedia.org/wiki/Lah_number

Is this what you had in mind Jon?

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February 2, 2015 at 6:17 am

Yes, I was thinking it might be Rota. That looks like an early version of the journal paper I read.

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