Alex De Castro recently posted this paper on arXiv. I suppose it represents a rigorous development of the work mentioned here & here previously, whilst also extending the scope, demonstrating quantum information theory equivalence.
“Our result demonstrates by well-known theorems that existence of one-way functions implies existence of a quantum one-way permutation.”
The introduction & outline are relatively easy to follow. The proofs, for me, more difficult.

Link; Quantum one-way permutation over the finite field of two elements


Hound in the Hunt

October 31, 2016

That Obscura Object of Desire; a Verisimilitude of Truth?

While working up my next post, thought I’d leave this article from the MONA blog. (It’s worth watching the documentary, ‘Tim’s Vermeer’ by way of background.) Putting aside David’s Walsh’s ego, the post covers a fascinating if meandering discussion between David, Tim Jenison and interviewer Elizabeth Pearce. It touches upon a range of subjects, which I posit as generally concerning the verisimilitude of truth in art, science & anthropology?

Mona Blog

In the gallery at Mona, there is an exhibition-experiment taking place, called Hound in the Hunt. Read more about it here, and also – for the enthusiastic – watch the documentary Tim’s Vermeer, and get your hands on our big, beautiful book as well (online, in our bookshop, or in the library, for free).

The following is a conversation between David Walsh and Tim Jenison about Vermeer, Viagra, and the nature of genius. (Interviewed by Elizabeth Pearce, with a cameo appearance by Mona curator Jarrod Rawlins.)

Hound in the Hunt Photo Credit: Mona/Rémi Chauvin Image Courtesy Mona, Museum of Old and New Art, Hobart, Tasmania, Australia Hound in the Hunt
Photo Credit: Mona/Rémi Chauvin
Image Courtesy Mona, Museum of Old and New Art, Hobart, Tasmania, Australia

Elizabeth Pearce: David, in the exhibition catalogue for Hound in the Hunt, you write that even if you don’t give a shit about art you should watch Tim’s Vermeer, because it will teach you how to learn. What did…

View original post 13,959 more words

Whorls of Attraction

October 1, 2016

I recently purchased this most excellent ‘Kickstarter’ project, vintage style Mandelbrot map. Lovingly created by Bill Tavishttp://www.mandelmap.com.
He even went to the trouble of including a couple of the intrinsic attractor mappings…

Serendipitously, we were having a domestic Spring clean of accumulated detritus and I found this page among my personal effects. It dates from around 25 years ago. Ignoring the naïveté of the notation, screen co-ordinates & all, I thought I’d just leave this old print-out here for posterity, before it  gets trashed. It shows a graphic representation of the fractal reflection-translation used in my algorithm.
The bulbar cardoid of the Madelbrot may be famously familiar but the actual attractor-escape mappings are not so commonly illustrated, or much commented upon…

The closer an iterated point is to the central cartesian symmetry points x(-1,1) y(0), then characteristically, the stronger is the attractor’s ‘gravity’and the lesser the number of spiral limbs. Iterating points closer to the set’s escape boundary results in more complex spirals & increasingly chaotic ‘fingerprints’. From memory, the two centre shapes illustrated below, resulted from points on or just within the bulb’s boundary.

So I’ve discarded one Mandelbrot picture only to frame another…
Haven’t fully decided what to do with the framed poster. If it looks too ‘school-roomish’ on my study wall, I may end up donating it to my kid’s school. Perhaps there, it might stimulate some errant student’s curiosity into discovering that mathematics holds deeper mystery and wonder than any dry school syllabus’ could ever convey?


Albert Wengcrackeder, venture capitalist at Union Square Ventures, puts forward compelling arguments for a decentralised internet protocol layer. An idea whose time has come?
His proposal; blockchain, blockchain, blockchain…
He envisions incentive for this tectonic tech shift arising via value from a reserved token portion of any distributed crypto protocol(s).

I can see the enourmous potential benefit in any decentralised IP protocol which enables semantic utility but there already exists, planetary scale inertia in capture of the status quo . And are there any better candidates than blockchain? That model has scaling issues, ledger overhead and even more importantly, arbitrary semantic structure. A replacement with the self-same attendant problems handicapping HTTP, plus even some new unforeseen ones?
Correlated hashing as per this site’s trapdoor scheme is my two-bobs worth… (this concept deserves its own explanatory post. I will see what I can do?)
Private crytpo contracts from correlated hashings constitute an evolutionary step higher up the disruption hierarchy than any block-headed legerdemain…
How to start the revolution?

tumblr post; Crypto Tokens and the Coming Age of Protocol Innovation
by Albert Wengler



‘Roll your own crypto’ is an oft & casually tossed IT security pejorative… with good reason. Cryptography is complex. The security assumptions implicit within individual mathematical facets can easily cancel one another out when wielded indiscriminately.
Stretching the analogy further, one might also surmise that the quality of the security ‘smoke’ is very much & mightily dependent upon the type of leaf you’re rolling!

Presently, we find ourselves in the midsts of an undeclared ‘Crypto-War 2.0’. The first casualty of war being truth etc., then perhaps the bona-fides of the various legitimate actors are also worthy of examination? There is much misdirection & misinformation…
The major players occupy two corners of a supposedly three-cornered conflict. In one corner, the ‘Kong’ like proportions of the government-security State. In the other, the corporate Godzillas that are the trans-national entities such as Google, Facebook & Apple. Privacy & civil liberty interests are two chihuahuas called ‘EFF’ & ‘ACLU’, on leashes in the far corner .

A large amount of analysis has been written on the tensions at stake between State-sponsored issues over surveillance & privacy. Little attention to date, has focused upon the corporate world’s vectors of self-interest. Shoshana Zuboff’s excellent article; ‘The Secrets of Surveillance Capitalism‘, highlighted the conflicted posturing that underscores much collective corporate proselytizing upon privacy matters.

Recently, fresh evidence emerged of the vertical integration between State & academia in support of surveillance, (not that that should be surprising from an historical ‘spying’ perspective.) See: Carnegie-Mellon re; TOR de-anonymization.)
Perhaps what is surprising though, is the State’s co-option of research into weaponised-math, when it is so tightly tied up in support of an unparalleled expansion of dragnet scale surveillance? This state of affairs prompted Phillip Rogaway of UCLA to publish a missive plea for academic efforts towards protection of privacy last December in; ‘The Moral Character of Cryptographic Work‘.

And then, there was the NSA’s ill-considered sabotage of the NIST standard for Dual-EC cryptography.

At this years RSA Conference, Prof. Adi Shamir intimated at the dissonance between the supposed practical state of Quantum Computing and the NSA/NIST policy advice on the imperative for migration towards post-quantum cryptography standards. He conjectured that the NSA has likely made some advance (non quantum hardware related) in breaking elliptic curve cyptography.
Well worth watching; his views on quantum crypto & the move away from ECC @ 30:00.

And so it goes…

On that note, I’d like to largely close out my interest in, and promotion of cryptography on these pages. The efforts of this blog have been those of an honest (amateur) broker, the worth of the method(s) put forward remain for others to assess. I can state with certainty, that no ‘Elliptic Flake’ was used in their manufacture!

As cryptography and complexity essentially represent two-sides of the same coin, I perhaps would like, in the future, to make one or two very general posts about complexity issues as they relate to ‘free-lunch’ theorems and matters P & NP, as they apply to neuroscience. Beyond that, my work here is probably done.

Thankyou for your interest!

NB; I’ve been pondering this post for some time, & ended up knocking it out in short order. Edits may appear subsequent.

Ancillary Diagram.

May 24, 2016


The following ‘circuit’ diagram might be helpful in following the logic flow of my algorithm.
An unbroken blue line shows the path of inheritance, dotted line demonstrates the active node’s interrogation of the preceding node, in order to determine the error locus relative to the default median inversion of blunt-precision regression. Grey line, excluded path.
Essentially, a 1-in-3 tree?
The designation of the interrogating node as x’ might be a little confusing in terms of order, (should be x ?) but I wanted to avoid clutter with the base level labels…


Constituting a ternary tree, two bits are required to encode the a-priori, inherited state.
One (control?) bit is assigned to indicate if the tree is of median or lateral inheritance.
The other (target?) bit receives its value according to the L-R lateral branch to be encoded.
In the case of the ‘median’ case inheritance, the target-bit is ‘free’ to encode on some external data set, as the discriminant of the lateral inheritance case is superfluous in this instance.

One final technical point. The computationally intensive nature of my algorithm is in contrast to the intrinsic Boolan-algebraic efficiency of the method proposed by Alex DeCastro. Perhaps my work is better considered on its merits as a PRG?

Quiz; Perhaps someone would like to explain how the cumulative probability of the two lateral legs converges to 0.625?

Suggestions welcome, as always…


Spreadsheet Note

March 23, 2016

Will be out of the office over Easter so, the following brief note;

As a few visitors of late have taken the effort of viewing the Excel spreadsheet, I thought I’d point out the following (obvious) point to save any confusion. The message ‘coding’ that occurs in the spreadsheet is just pseudo-random.

Laziness on my behalf, perhaps some of you drive-by comp.sci whiz’s would like to help out with a working demo?

Meantime, I hope to get some substance  & life resurrected into this blog post Easter break, in time for its second anniversary…

Safe travels, catch you on the flip side.