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.


Originally published in; Frankfurter Allgemeine; Feuilleton

Governmental control is nothing compared to what Google is up to. The company is creating a wholly new genus of capitalism, a systemic coherent new logic of accumulation we should call surveillance capitalism. Is there nothing we can do?surveillance capitalism

Google surpassed Apple as the world’s most highly valued company in January for the first time since 2010.  (Back then each company was worth less than 200 billion. Now each is valued at well over 500 billion.)  WhileGoogle’s new lead lasted only a few days, the company’s success has implications for everyone who lives within the reach of the Internet. Why? Because Google is ground zero for a wholly new subspecies of capitalism in which profits derive from the unilateral surveillance and modification of human behavior.  This is a new surveillance capitalism that is unimaginable outside the inscrutable high velocity circuits of Google’s digital universe, whose signature feature is the Internet and its successors.  While the world is riveted by the showdown between Apple and the FBI, the real truth is that the surveillance capabilities being developed by surveillance capitalists are the envy of every state security agency.  What are the secrets of this new capitalism, how do they produce such staggering wealth, and how can we protect ourselves from its invasive power?

Read full story…

Shoshana Zuboff is the Charles Edward Wilson Professor, Emerita, Harvard Business School. This essay was written for a 2016 address at Green Templeton College, Oxford. Her forthcoming book is Master or Slave: The Fight for the Soul of Our Information Civilization, to be published by Eichborn in Germany and Public Affairs in the U.S.

A short note by way of raising discussion on some ‘key’differences between the involution logic of the Alex DeCastro work presented here and the PRG, temporal error feed-forward of my algorithm.

Alex’s work, consisting of an one-way (permutation) involution over GF2, is presumably best suited to construction of asymmetric, public key encryption schemes. I note that he has published a version of the protocol here, with application to private information retrieval.
I’m not sure if his method can be extended to private key exchange, excuse my ignorance?
As far as I can make out, this would involve a lot of polling back-and-forth between Bob & Alice. There is a name for this class of public key extension? I came across it recently and can’t remember the reference. My understanding is that all asymmetric key protocols are susceptible to man-in-middle attacks anyhow & so, extended polling may not be an issue within this framework?

I.M.H.O, the greatest potential for my algorithm, other than it’s yet to be formally qualified security strength,  lies with construction of symmetric, synchronous, user-sided, key exchange & certification protocols. (Apple take note!) More about that perhaps at a later date…

Phill. S

Tangled up in Blue

February 14, 2016

spunwebOut of frustration at my limitations & lack of progress I’ve posted a second, premature draft.
I fear it’s just getting worse? Unfinished, unsure of the validity of definitions, way out of my depth. It’s a mess but my lack of skill knows little shame so here ’tis anyhow, a work in progress… comment welcome.

Real Permutations yield Sticky Predicates with Input Obfuscation & Poly Pre-Image Span

“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.”

So now I’m going back again
I got to get her somehow
All the people we used to know
They’re an illusion to me now
Some are mathematicians
Some are carpenter’s wives
Don’t know how it all got started
I don’t what they do with their lives
But me, I’m still on the road
Heading for another joint
We always did feel the same
We just saw it from a different point of view
Tangled up in blue

Bob Dylan

A Tangled Web

February 6, 2016

Charlottes-Webb-TerrificA nice pigeon-pair of posts from George Danezis, Reader in Security and Privacy Engineering (A.P) at University College, London. Well worth reading in tandem. The first being a bit of a ‘you are here’, overview of the state-of-art in cryptography and the security assumptions thereof.


The second post looks into the implications behind a recently published Snowden-GCHQ document from 2011 which goes to the nitty-gritty of the (then) data-mining capabilities of GCHQ. Danezis hints at the likelihood national agencies now posses the ability to trace ‘Tor’ type anonymizing sources. Of interest from my viewpoint, it also provides a rare glimpse into the vertical integration extant between academia & national security. Something worth keeping in mind when there’s a crescendo of governmental voices clamouring for default crypto-backdoors. 😉



As promised back in July, Alexandre De Castro’s exploration of involutionary logic negation as applied to Russell’s paradox, has been published as a letter-to-editor in the Journal of the Association for Information Science and Technology; Vol 66, Issue 10.


D-Wave Systems chip with purported quantum properties.

From arstechnica;
“The National Security Agency is advising US agencies and businesses to prepare for a time in the not-too-distant future when the cryptography protecting virtually all e-mail, medical and financial records, and online transactions is rendered obsolete by quantum computing.

Quantum computers have capabilities that can lay to ruin all of the public-key cryptographic systems currently in use. These capabilities, which aren’t known to be present in the classical computers of today, include the ability to almost instantly find the prime factors of extremely large numbers, using a method called Shor’s algorithm. Quantum computing is also believed to be capable of tackling other mathematical problems classical computers can’t solve quickly, including computing discrete logarithm mod primes and discrete logs over elliptic curves.

The difficulty of factoring and computing discrete log primes and elliptic curve discrete logs play an essential role in cryptographers’ confidence in RSA, elliptic curve cryptography, and other public-key crypto systems. When implemented correctly, most scientists and cryptographers believe that the crypto can’t be defeated with today’s computers before the end of the universe.”


from projectbullrun.org;

Abstract. Dual EC is an algorithm to compute pseudorandom numbers starting from some random input. Dual EC was standardized by NIST, ANSI, and ISO among other algorithms to generate pseudorandom numbers. For a long time this algorithm was considered suspicious – the entity designing the algorithm could have easily chosen the parameters in such a way that it can predict all outputs – and on top of that it is much slower than the alternatives and the numbers it provides are more biased, i.e., not random.

The Snowden revelations, and in particular reports on Project Bullrun and the SIGINT Enabling Project, have indicated that Dual EC was part of a systematic effort by NSA to subvert standards.

This paper traces the history of Dual EC including some suspicious changes to the standard, explains how the back door works in real-life applications, and explores the standardization and patent ecosystem in which the standardized back door stayed under the radar.” IMG_0071-0


image; © Rachael Parsons. The BackDoor Gallery @ Room 60 QLD

A Transfinite Shave

July 11, 2015

A version of this post has been accepted into the Journal of the Association for Information Science and Technology as a letter-to-editor. Congratulations Alex DeCastro!

Tambo University

barberpoleRussell’s Barber: paradox or (else) pseudoparadox?

Some axioms can be “unprovable truths” of Godel’s incompleteness theorem. Today, we show that Godel’s theorem can be easy to understand in general terms, but hard to understand beyond a typical contradiction, as per Russell’s barber (pseudo) paradox.

Consider the classical Russell’s gedankenexperiment wherein, all the men that live in a village are cleanly shaven. They either shave themselves or they do not. If they do not shave themselves, the village’s only barber must shave them.

Hence there exist two sets: the set of all men who shave themselves and the set of all men who have the barber do it for them.

But, who shaves the barber?

Let us analyze this problem based on Zermelo-Fraenkel’s set theory and Cantor’s set theory.

Zermelo-Fraenkel’s set theory

Take a male barber that lives in the village. He is clean-shaven. Then, either he shaves himself or else he…

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2015 marks the 80th. anniversary of the EPR paradox.

“One can give good reasons why reality cannot at all be represented by a continuous field. From the quantum phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seem to be in accordance with a continuum theory and must lead to an attempt to find a purely algebraic theory for the representation of reality. But nobody knows how to find the basis for such a theory.” A. Einstein; Appendix 2: The Meaning of Relativity, 1935

albert-einsteinIn 1935 Albert Einstein, along with two colleagues, Boris Podolsky and Nathan Rosen, published a work known as the EPR paper, challenging the foundations of quantum mechanics. The three scientists argued that extra pieces of information – hidden variables – were necessary to perform the unitary evolution of the wave function and make quantum mechanics a complete theory. In the following, we show that the idea of hidden variables can be understood from the measurement-based implementation of a controlled-NOT (CNOT) quantum gate.

In quantum mechanics, the EPR paradox is a thought experiment which challenges long-held ideas about the completeness of quantum theory. The core of the EPR paradox is that quantum mechanics cannot be both consistent and complete unless hidden variables exist.

The EPR paradox has been strongly debated over for eighty years and almost all of the arguments, including the work of John Bell, have refuted the hidden variables theory. Here we show in a fairly simple way, how the concept of hidden variables advocated by Einstein, Podolsky and Rosen can be understood with the aid of a most common quantum device: the controlled-NOT gate.

The controlled-NOT gate (CNOT) is used to entangle and disentangle EPR states. Its unitary U_{CNOT} operator  can be written on two-bits operationally, |a\rangle  and |b\rangle \in GF_{2} , where the former is the control bit, the latter is the target bit, and GF_{2}  is the Galois field of two elements F_{2}= \{0,1\} :

U_{CNOT} (|a\rangle \otimes |b\rangle) = |a\rangle \otimes |a \oplus b\rangle where, a \oplus b = (a + b)mod2

The matrix U_{CNOT}  for this operation is:

|0,0\rangle |0,1\rangle |1,0\rangle |1,1\rangle
|0,0\rangle 1 0 0 0
|0,1\rangle 0 1 0 0
|1,0\rangle 0 0 0 1
|1,1\rangle 0 0 1 0

Now, note that the state transformation |1,0\rangle = |1,1\rangle can be replaced with |1,b\rangle = |1,NOT(b)\oplus b\rangle , where b=0 .
In GF_{2} , the inverter gate corresponds to the polynomial representation NOT(b) = b \oplus 1 , and every element b satisfies the property b = b^2 .
Hence, the logical negation can also be represented by the polynomial NOT(b)=b^2 \oplus 1 .

The exclusive disjunction NOT(b)\oplus b corresponds to the field’s addition (mod2) operation in Galois field of two elements, therefore, NOT(b) \oplus b = b^2 \oplus b \oplus 1 .
It follows that the mapping |1,b\rangle = |1,NOT(b)\oplus b becomes |1,b\rangle = |1,b^2\oplus b \oplus 1\rangle for b = 0 .

As quantum logic gates are reversible, the action of a CNOT gate must be undone when/if a second CNOT is applied. Hence, the transformation |1,b\rangle = |1,b^2\oplus b \oplus 1\rangle  must be a bijective map that is its own inverse, so that there exits the involution CNOT|1,0\rangle \rightleftharpoons |1,1\rangle for b = \left\{0,1\right\} .

But, the polynomial in one variable P=b^2\oplus b\oplus 1  is irreducible over GF_{2} , namely, it always outputs 1 for b equal to 0 or 1. Therefore, P  requires some hidden variable for the state transformation |1,b\rangle = |1,b^2\oplus b \oplus 1\rangle  to be two-way.

This is exactly the core of the EPR paradox advocated by Einstein, Podolsky and Rosen, because, if a unitary operation needs one extra piece of information outside the reach of the binary system, then the quantum theory cannot be complete.

A. DeCastro