The Doghouse: Crown Sterling

A decade ago, the Doghouse was a regular feature in both my email newsletter Crypto-Gram and my blog. In it, I would call out particularly egregious -- and amusing -- examples of cryptographic "snake oil."

I dropped it both because it stopped being fun and because almost everyone converged on standard cryptographic libraries, which meant standard non-snake-oil cryptography. But every so often, a new company comes along that is so ridiculous, so nonsensical, so bizarre, that there is nothing to do but call it out.

Crown Sterling is complete and utter snake oil. The company sells "TIME AI," "the world's first dynamic 'non-factor' based quantum AI encryption software," "utilizing multi-dimensional encryption technology, including time, music's infinite variability, artificial intelligence, and most notably mathematical constancies to generate entangled key pairs." Those sentence fragments tick three of my snake-oil warning signs -- from 1999! -- right there: pseudo-math gobbledygook (warning sign #1), new mathematics (warning sign #2), and extreme cluelessness (warning sign #4).

More: "In March of 2019, Grant identified the first Infinite Prime Number prediction pattern, where the discovery was published on Cornell University's www.arXiv.org titled: 'Accurate and Infinite Prime Number Prediction from Novel Quasi-Prime Analytical Methodology.' The paper was co-authored by Physicist and Number Theorist Talal Ghannam PhD. The discovery challenges today's current encryption framework by enabling the accurate prediction of prime numbers." Note the attempt to leverage Cornell's reputation, even though the preprint server is not peer-reviewed and allows anyone to upload anything. (That should be another warning sign: undeserved appeals to authority.) PhD student Mark Carney took the time to refute it. Most of it is wrong, and what's right isn't new.

I first encountered the company earlier this year. In January, Tom Yemington from the company emailed me, asking to talk. "The founder and CEO, Robert Grant is a successful healthcare CEO and amateur mathematician that has discovered a method for cracking asymmetric encryption methods that are based on the difficulty of finding the prime factors of a large quasi-prime numbers. Thankfully the newly discovered math also provides us with much a stronger approach to encryption based on entangled-pairs of keys." Sounds like complete snake-oil, right? I responded as I usually do when companies contact me, which is to tell them that I'm too busy.

In April, a colleague at IBM suggested I talk with the company. I poked around at the website, and sent back: "That screams 'snake oil.' Bet you a gazillion dollars they have absolutely nothing of value -- and that none of their tech people have any cryptography expertise." But I thought this might be an amusing conversation to have. I wrote back to Yemington. I never heard back -- LinkedIn suggests he left in April -- and forgot about the company completely until it surfaced at Black Hat this year.

Robert Grant, president of Crown Sterling, gave a sponsored talk: "The 2019 Discovery of Quasi-Prime Numbers: What Does This Mean For Encryption?" I didn't see it, but it was widely criticized and heckled. Black Hat was so embarrassed that it removed the presentation from the conference website. (Parts of it remain on the Internet. Here's a short video from the company, if you want to laugh along with everyone else at terms like "infinite wave conjugations" and "quantum AI encryption." Or you can read the company's press release about what happened at Black Hat, or Grant's Twitter feed.)

Grant has no cryptographic credentials. His bio -- on the website of something called the "Resonance Science Foundation" -- is all over the place: "He holds several patents in the fields of photonics, electromagnetism, genetic combinatorics, DNA and phenotypic expression, and cybernetic implant technologies. Mr. Grant published and confirmed the existence of quasi-prime numbers (a new classification of prime numbers) and their infinite pattern inherent to icositetragonal geometry."

Grant's bio on the Crown Sterling website contains this sentence, absolutely beautiful in its nonsensical use of mathematical terms: "He has multiple publications in unified mathematics and physics related to his discoveries of quasi-prime numbers (a new classification for prime numbers), the world's first predictive algorithm determining infinite prime numbers, and a unification wave-based theory connecting and correlating fundamental mathematical constants such as Pi, Euler, Alpha, Gamma and Phi." (Quasi-primes are real, and they're not new. They're numbers with only large prime factors, like RSA moduli.)

Near as I can tell, Grant's coauthor is the mathematician of the company: "Talal Ghannam -- a physicist who has self-published a book called The Mystery of Numbers: Revealed through their Digital Root as well as a comic book called The Chronicles of Maroof the Knight: The Byzantine." Nothing about cryptography.

There seems to be another technical person. Ars Technica writes: "Alan Green (who, according to the Resonance Foundation website, is a research team member and adjunct faculty for the Resonance Academy) is a consultant to the Crown Sterling team, according to a company spokesperson. Until earlier this month, Green -- a musician who was 'musical director for Davy Jones of The Monkees' -- was listed on the Crown Sterling website as Director of Cryptography. Green has written books and a musical about hidden codes in the sonnets of William Shakespeare."

None of these people have demonstrated any cryptographic credentials. No papers, no research, no nothing. (And, no, self-publishing doesn't count.)

After the Black Hat talk, Grant -- and maybe some of those others -- sat down with Ars Technica and spun more snake oil. They claimed that the patterns they found in prime numbers allows them to break RSA. They're not publishing their results "because Crown Sterling's team felt it would be irresponsible to disclose discoveries that would break encryption." (Snake-oil warning sign #7: unsubstantiated claims.) They also claim to have "some very, very strong advisors to the company" who are "experts in the field of cryptography, truly experts." The only one they name is Larry Ponemon, who is a privacy researcher and not a cryptographer at all.

Enough of this. All of us can create ciphers that we cannot break ourselves, which means that amateur cryptographers regularly produce amateur cryptography. These guys are amateurs. Their math is amateurish. Their claims are nonsensical. Run away. Run, far, far, away.

But be careful how loudly you laugh when you do. Not only is the company ridiculous, it's litigious as well. It has sued ten unnamed "John Doe" defendants for booing the Black Hat talk. (It also sued Black Hat, which may have more merit. The company paid $115K to have its talk presented amongst actual peer-reviewed talks. For Black Hat to remove its nonsense may very well be a breach of contract.)

Maybe Crown Sterling can file a meritless lawsuit against me instead for this post. I'm sure it would think it'd result in all sorts of positive press coverage. (Although any press is good press, so maybe it's right.) But if I can prevent others from getting taken in by this stuff, it would be a good thing.

Posted on September 5, 2019 at 5:58 AM • 76 Comments

Comments

Ismar September 5, 2019 6:41 AM

Not very smart of them to present this at Back Hat as they may have had more success selling their oil somewhere else - say to some of the despotic countries which have proven very good customers for a range of similar value products .

Clive RobinsonSeptember 5, 2019 7:19 AM

@ All,

One of the problems with "snake oil" is all to often it's not to easy to tell if you are dealing with those who "don't understand" or "understand only to well".

That is people who for various reasons actually believe in what they are saying, as opposed to those who want you to believe in what they are saying so that they can get you to buy into the launch phase of their "fly by night" operation to "take the money and run".

Which is the case with this collection of people I'll leave to orhers to decide, but when it comes to taking the money and running, I'm guessing they prefer the bluster hard and fast then jump to the excercise option when the inevitably comes down hill in their direction...

xoaSeptember 5, 2019 7:32 AM

After the Black Hat talk, Grant -- and maybe some of those others -- sat down with Ars Technica and spun more snake oil. They claimed that the patterns they found in prime numbers allows them to break RSA. They're not publishing their results "because Crown Sterling's team felt it would be irresponsible to disclose discoveries that would break encryption." (Snake-oil warning sign #7: unsubstantiated claims.)
This should actually arguably be Snake-oil Warning Sign #1 shouldn't it? At least it should be when they're actually foolish enough to make such a claim. From rough recollection of previous incidents it's more common to have a bunch of wishy-washy nonsense like the rest of their stuff that can't really be nailed down to anything definitive, just "more research required" (aka, "we want someone to give us more money"). That's classic snake-oil behavior, the snake-oil peddler is trying to peddle something so definitive binary claims are to be avoided as long as possible. Ambiguity/deniability is the scammer's friend. Even if it all collapses a few years later, they can always claim "well we thought it was very promising" or "sometimes even the best fail!" and a lot of people won't be able to tell it was wrong from the start.


But claiming to break RSA, or for that matter not even breaking but "merely" greatly speeding up, is a completely quantifiable/provable assertion, and it doesn't involve any disclosure requirements even. Given the nature of cryptography it's perfectly feasible to demonstrate as a black box, they could ask anyone to use public key crypto to encrypt their own arbitrary message and upload the public key and ciphertext to their site (or send it to them any other method), and then reply with the plaintext. Done. If they were claiming a lesser speed up they could request it the exact number of bits required to show that, ie., I believe so far the largest factored one remains RSA-768? And it took a few years. So even if they could not handle 2048/4096, they could still prove they had a better then-brute-force attack by requesting a shorter one not in use and handling it faster then any known method would. (let's ignore in all this that if they could crack RSA they could sell it to the NSA tomorrow for $[MANYMANY] billions)

I think that's basically all that's needed, it's an easy lazy method to look at this sort of thing. "Are they claiming to actually have done something, yes/no? If yes, do they show it? If they don't then into the trash it goes."

RPSeptember 5, 2019 7:59 AM

To answer Ismar, the presentation at Black Hat may well have been an other attempt at "undeserved appeal to authority" -> "Featured at the Black Hat convention".

Jakub NarębskiSeptember 5, 2019 8:31 AM

It is very easy to verify if TIME AI can break RSA in reasonable time: send encrypted message (and perhaps also its hash for verification; certainly publish a hash or two), ask for decrypted plain text.

TimHSeptember 5, 2019 8:49 AM

People, including me, so much want these sort of SiFi discoveries to be true. I've debunked some perpetual motion demos to friends that I'd expect to be more analytical. There's always a hidden something, or a small battery "to power the measuring equipment".

TatütataSeptember 5, 2019 8:54 AM

"Crown Sterling Corporation" was registered in Delaware under the number 7379065 on 17 April 2019 (trying to find any more concrete information in DE is generally pointless), and filed a Foreign Corporation declaration with the California corporate registry on 6 May 2019. The events at Black Hat occurred between 3 and 8 August 2019. The New York lawsuit was filed 22 August 2019.

1) They don't lose any time;
2) They either have a load of cash on hand, or patient and/or generous legal counsels.

According to reports, CS paid 115k$ for its "sponsored session" at Black Hat. The lawsuit really sounds like if they expected that their money entitled them to a "safe space" including a goon squad to shield them from any criticism. So very 2019 USA...

If demonstrated, what they claim is so valuable that the entire world would already be crawling at their doorstep.

There is no mention of any patents or pending applications on the web site (regardless of what you may think of them), and I couldn't find any. If they have any money to file a lawsuit, then they must have enough to pay a patent attorney. As a rule, new applications are published 18 months after the earliest priority filing, unless it was filed in the US and a declaration was made that it wouldn't be filed in any other country, so there might still be something out there. Or not. Had they been slapped with a secrecy order at the USPTO (37 CFR 5.2), they wouldn't be babbling in a conference...

In April, a colleague at IBM suggested I talk with the company.

Sigh.

Incidentally, Mr. Schneier left IBM in June...

What's the heraldic Bohemian forked tail lion, like is found on the Czech coat of arms? The people listed on the "Management team" page seem to be real (at least in the Gugl universe; the mugshots apparently aren't stock photos), and mostly associated with entities including "Strathspey Crown" in their name, which indicates a place of business at the same address as CS, but one floor below (suite 210 instead of 310, but they don't seem to be listed in the CA registry). BTW, they use the same overgrown kitten as a corporate logo. Just a coincidence?

Most of it is wrong, and what's right isn't new.

I usually read it formulated like this: The good part isn't original, and the original part isn't good.

I watched the promo video. Here's the Youtube automated transcript. Most of the words are there, I tried adding some punctuation, but I gave up half way through. Even with commas, capitals, periods, etc., the whole thing still reads like surrealist poetry, only less serious.

You are unlike any other a beautifully unique human being with integral patterns patterns that become data, data that mirrors who you are, making its ownership and privacy essential to your individuality. In addition to all of your transactions messages and financial account data, today your private in-home interactions, geolocation and even your own DNA are protected only by a single static encryption algorithm now recognized by the world's experts as obsolete. The Fibonacci sequence repeats every cycles when viewed using digital route analysis a pattern that can be represented with an Akasa (?) Tetragon spiral. By positioning integers in positions for every degrees Crown Stirling solved one of the greatest mathematical mysteries of all time: identifying for the first time an infinitely predictable prime number pattern. These patterns also revealed an entirely new classification of non prime numbers called quasi primes, as well as a new understanding of how mathematical constants interact with primes, and quasi prime's to propagate and mirror reflect in infinite wave conjugations. Academic researchers believe this discovery may be the key to unlocking a new unified physics cosmology, a theory of everything. This new discovery enables large prime factorization using standard computers, thus rendering obsolete all static factorizing encryptions presently used in public key crytography. More than ever before now is the time for a new adaptive encryption granting you security and full control of your digital individuality. A new paradigm of data sovereignty made possible only with time AI as an entirely new classification in data privacy called quantum encryption an impenetrable system utilizing five dimensions of encryption technology rather than depending on prime numbers and only a two-dimensional static matrix time AI introduces time and high-speed oscillations of infinite wave values of irrational numbers as its encryption modality using the infinite variations within music compose real time by artificial intelligence time AI generates quantum encryption keys as unique as your own iris each quantum public key is paired with two quantum private keys that are entangled through mirror symmetry mathematics in value time exposure and oscillation speed these quantum keys change at the nano scale of time directed by state-of-the-art AI technology harnessing times entanglement one key from the past and one key from the future changing the number series billion times per second with no pattern the speed of the AI oscillations allow years of oscillations in a single second of data authentication to unlock the future and the past must converge perfectly in a split second unpredictable by any non intelligence in the universe and if ever attacked time AI learns and unfolding its defenses through incalculable infinite variations. Time AI is a simple elegant software solution that drops easily into any computer or IOT mobile device with standard memory and storage capacities it is so adaptive so impenetrable and so unique to each user even its own architects cannot break quantum leap in data privacy is the work of Crown Sterling, a team whose mission is to reshape the foundation of encryption providing total data sovereignty for all information privacy is the new frontier of freedom and time is your shield

Roger A. GrimesSeptember 5, 2019 9:10 AM

In the Ars Technica article, Grant says all prime numbers squared beyond 3 end up being evenly divisible by 24 plus 1. Anyone know if this is true? I tried out a few small primes (like 9539 and 8887) and it did hold true for them. Anyone know if this is true for all prime numbers? If so, that is interesting. I'm not buying into any of the other stuff...but this does seem interesting. And if it's true doesn't it allow very quick prime creation and verification (at least as compared to the other shortcut methods I'm aware of)?

sitaramSeptember 5, 2019 9:23 AM

that video that Bruce linked to... the music track, especially toward the end, sounds very much like Hans Zimmer... wonder if someone who is more "music" minded can confirm/reject this guess.

yes, completely off topic for security, I know, but then their time AI uses music also so we can call it "on topic" :)

TatütataSeptember 5, 2019 9:30 AM

"Strathspey Crown" is listed as the assignee in 16 patent families, of which 12 include one Robert Edward Grant among the inventors, none of them relating to cryptography.

I like US10398908B2 (yes, it was issued) for its remarkable gobbledegook factor:

A system and method for using a sonic wave to influence material in a target structure requires using a confined plasma antenna to generate an electromagnetic carrier wave, λ. The confined plasma antenna also pulses the carrier wave at a sonic frequency, f, to create a sonic wave. In detail, pulsing the carrier wave results in a sequential plurality of solitons which are separated from each other by a periodicity p, wherein λ<<p. For the present invention, f is selected to resonate with a material (e.g. a cellular structure) in a target structure (e.g. a patient).

Re: In the Ars Technica article, Grant says all prime numbers squared beyond 3 end up being evenly divisible by 24 plus 1. Anyone know if this is true?

I saw that a long time ago; if I'm not blithering, this is an immediate consequence of prime numbers >3 not being divisible by either 2 or 3. See here. Not sure whether this is a very interesting property.

Erdem MemisyaziciSeptember 5, 2019 10:19 AM

Why are so many rich people dumb as hell? Because they dare do things like this. They have no idea what they are doing. They think scientists are just gutless nerds who are dime a dozen and they think purchasing a gold sponsorship package means no scrutiny from the public. Not only that but they decide to do this in Black Hat, people who are mainly there to call out bullshit. I assume they thought the crowd were actors hired by Black Hat ordered to clap and go home? How are you going to make encryption work without mathematical accuracy? "We bought the gold package." *sigh*

h2odragonSeptember 5, 2019 10:29 AM

@Tatütata: Thanks for the transcript, poetry indeed. The patent application sounds like the "candle flame as a speaker" trick but with therapeutic claims for sound waves so generated? Perhaps just the foundation for later such claims?

Clive RobinsonSeptember 5, 2019 11:08 AM

@ Tatütata,

With regards the "script" the first paragraph or two even though flowery hyper-bollocks in language usage is just an expression of a well known problem.

Thus the first thing that you can actually say is compleate nonsense is,

    ... identifying for the first time an infinitely predictable prime number pattern.

A "predictable" "patten" without limits expressed would hold to atleast infinity (beyond that you'ld have to be a follower of Cantor and successors) therefore the "infinitely" is at best superfluous / redundant.

As for "identifying for the first time" there are several algorithms that produce predictable patterns in which prime numbers fall.

For instance we know that each number has a successor, that is where each number has another one following it which Peano's Axioms clarify. That it is stated that a successor of a number is not the number itself or zero, therefore must be a new unique number.

Or Peano's fifth axiom the "induction axiom" states,

    If a set S of numbers contains zero and also the successor of every number in S, then every number is in S.

This in effect gives a set of natural positive numbers when ordered from zero upwards gives the set N+. A simple manipulation extends the set to give all natural numbers both positive and negative. Or under set theory there is Zermelo-Fraenkel axiom which likewise asserts the existence of a set containing all the natural numbers.

From this we can futher show that not just all natural numbers are in the set but all their addatives as well, and more fun their respective multiples. Which means that all Factorials and Primes are in there as well.

But also of interest the numbers that appear each side of the factorials represent a large number of "twin Primes". From this it can be seen that these primes have a definate underlying pattern... I worked this out several decades ago whilst a quite young teenager, and I suspect I am not alone in seeing this harmonic relationship in the location of primes.

Ross SniderSeptember 5, 2019 11:11 AM

@ Ismar

It was smart. The whole point was so that they could also add "Presented at Black Hat" to their ridiculous claims.

"Published on Cornell's website, and presented at Black Hat. New classical computer quantum TIME AI music cryptography!"

TatütataSeptember 5, 2019 11:38 AM

More on the alleged sequence of events:

In March of 2019, Grant identified the first Infinite Prime Number prediction pattern, where the discovery was published on Cornell University's www.arXiv.org titled: 'Accurate and Infinite Prime Number Prediction from Novel Quasi-Prime Analytical Methodology.' The paper was co-authored by Physicist and Number Theorist Talal Ghannam PhD.

"Crown Sterling Corp." was registered in Delaware just a few weeks later. They were very swift.

In fact, they even travelled back in time. The domain name was registered in late 2018 according to whois information, before the "capital discovery" was made:

Domain Name: CROWNSTERLING.IO
Registry Domain ID: D503300000209269605-LRMS
Updated Date: 2019-06-15T01:27:56Z
Creation Date: 2018-10-08T21:45:28Z
Registry Expiry Date: 2019-10-08T21:45:28Z
Registrar: GoDaddy.com, LLC

Talal Ghannam doesn't seem to have much of an internet footprint. A person of that name self-published in 2011/2012 a book on numerology [sic], with the title "The Mystery of Numbers".

The Amazon blurb states "His research spans many disciplines including: alchemy, alternative or spiritual science, sacred numbers and geometry, numerology, among many others." Further down the page, it is stated that "Talal is currently residing with his family in Canada."

A search in patents with that name currently yields 3 families. These are physics related and originate from an university in Saudi Arabia. However, the most recent US application publications list an address in Mississauga Ontario for the named inventor, which suggests that this may be the same person.

I note that these applications relate to laser technology, like some of the early applications by said Robert Edward Grant of Laguna Beach CA (not filed by "Strathspey Crown"), which suggests another connection.

The buyer's comment by "Avid Reader" also suggests a relationship: This is an entire book written about the "mystery" surrounding the fact that when 10 is divided by 3 there is a remainder of 1. That jibes with the "24" prime divisibility test.

@Clive:

I occasionally deal professionally with nonsense, and it proves every single time a frustrating experience.

The best approach is IMO avoidance, but that's not always a practical option.

An in-law of mine is dabbling in "free energy" and "new physics" stuff, and is trying to enlist my help in pursuing an enterprise of his. I have several times attempted a reasoned discussion, but to no avail. So every time he brings up the topic, I smile kindly and try to steer the conversation in any other direction. Where is the boundary between self-delusion and fraud?

Clive RobinsonSeptember 5, 2019 11:41 AM

@ h2odragon, Tatütata,

The patent application sounds like the "candle flame as a speaker" trick

A flame is a plasma, which has charged particles, likewise electric arcs and lightning etc.

Particles that are charged can be attracted and repulsed by electromagnetic E fields and likewise H fields. But as with motors and generators if you can somehow move the charged particles in a field you can generate EM signals proportional to the rate of change. Thus if you have a charged "pith ball" on a thin cotton thread which you spin around you will generate radio signals, all be it of incredibly low frequency, and great inefficiency.

@ ALL,

The thing about patents is they are in effect of no scientific value what so ever. All a patent clark who assesses the patent is that the idea is not already a patent or sufficiently the same as an existing patent.

Thus you can get a patent on a perpetual motion machine if you word it right...

TatütataSeptember 5, 2019 11:58 AM

The thing about patents is they are in effect of no scientific value what so ever.

I would qualify this statement. There is a tremendous amount of valid technical information in patents, but it is buried in an even more tremendous amount of chaff, i.e., verbose boiler plate legalese, plain obfuscation, endless generalisations, speculative daydreaming, covetous claiming, and just plain nonsense.

All a patent clark who assesses the patent is that the idea is not already a patent or sufficiently the same as an existing patent.

In fact, against the entire prior art in general, not just existing patents. But if you actually get that from the authority, you're in luck. :-(

Thus you can get a patent on a perpetual motion machine if you word it right...

Or a plasma-antenna plasmonic whatever...

But you can also get a patent on genuinely and LITERALLY earth-changing inventions. I.e., tetraethyl lead and freon (both from the same bloke), or ammonia production. Or a steam engine. All of these had a direct impact and lasting on the biosphere...

Jamie BaxterSeptember 5, 2019 12:11 PM

There was a reddit thread discussing Sterling's presentation and claims. I found the final paragraph on the original post to be pretty on the nose:

There is a mountain of bad-{math, phys, phil, bio} to be ruthlessly mined here. The CEO has ten other publications and several companies. Think Time Cube meets Silicon Valley, or Theranos on math.

TomSeptember 5, 2019 12:55 PM

From the Strathspey Crown website, we learn of their very serious mission:
"We fearlessly innovate, incubate, and invest in disruptive technologies that transform conventional paradigms of scarcity and impossibility, into abundance and advantage."

How many red flags in one sentence can there be?

They go on:
"We focus on the industries with the highest barrier to entry and greatest complexity, and disrupt them through innovative thinking, creating new business models and leveraging technologies to deliver simplicity within challenging markets."

Recently The New Yorker ran an article about Esalen Institute, subtitled "Where big tech goes to ask deep questions." At, they could have added, the font of New Age Philosophies. No surprise really that when the time is ripe to appeal to chumps, err investors, for money, the talk turns vacuous and vague hand waving occurs.

"The Mystery of Numbers" indeed.

It's worth following the link embedded by @Bruce in the OP to a twitter thread:
https://twitter.com/ncweaver/status/1160225585051783170?ref_src=twsrc%5Etfw
As in so many such threads, the wish is finally expressed that, realizing the untenable situation, the conversation might be made to vanish.

@Tatütata Thanks for your digging into things here.

Alyer Babtu September 5, 2019 12:55 PM

The paper seems to deal with prime nunber sieves, see Wikipedia several articles [1], which started with Eratosthenes. The basic idea is very simple, just list all the numbers and start crossing out every 2nd, every 3rd, etc., whatever’s left is prime; but getting it to work efficiently brings in subtler ideas.

Primes seem to still elude understanding, and what seems at first glance unrelated continuous rather than discrete integer mathematics enters, e.g. as in [2].

Perhaps part of the problem is that primes are more or less defined by negation (have *no* non-trivial factors), rather than by a commensurate positive property. Things become simple once the right definitions and objects are found.

For example, the result p^2-1 =~ 0 mod 24 for p prime is mysterious. But the mystery goes away when one sees the theorem is really that for numbers q not divisible by 2 or 3, q^2 -1 =~ 0 mod 24. The statement about primes is just an ad hoc special case, and in a way not really a “theorem”, i.e. scientific.

[1]
https://en.m.wikipedia.org/wiki/Generation_of_primes
https://en.m.wikipedia.org/wiki/Sieve_of_Atkin
https://en.m.wikipedia.org/wiki/Wheel_factorization

[2]
https://en.m.wikipedia.org/wiki/Dirichlet%27s_theorem_on_arithmetic_progressions

KeithBSeptember 5, 2019 1:48 PM

You forgot to mention the other indication of snake oil, though this usually applies to medical snake oil:
Gratuitous appeal to Quantum Mechanics.

AsaSeptember 5, 2019 2:46 PM

If I could break RSA what I would do is I would publicly ask for an encrypted message to break, then I would crack it as proof. Then the entire world would move away from it after you did that a few times.

Another way to do it would be to send a researcher $1000 and ask them to send you an encrypted message to crack. They'd suspect you compromised their machine but that would get their attention and they would run another test.

Frank DanaSeptember 5, 2019 3:21 PM

@Tatütata

An in-law of mine is dabbling in "free energy" and "new physics" stuff, and is trying to enlist my help in pursuing an enterprise of his. I have several times attempted a reasoned discussion, but to no avail.

"Reasoning will never make a Man correct an ill Opinion, which by Reasoning he never acquired"

–Jonathan Swift, "A Letter to a Young Gentleman, Lately Enter’d Into Holy Orders by a Person of Quality" 1721 (letter dated January 9, 1720) Printed for J. Roberts at the Oxford Arms in Warwick Lane, London.

HumdeeSeptember 5, 2019 5:21 PM

@ Tatütata

The scariest part of this entire episode is that there were able to get someone at IBM (!!) to needle @Bruce about it. It is difficult for me to imagine that any "colleague" of Bruce's at IBM would be so stupid as to fall for this, so someone how they got pressure there. Scary.

Impossibly StupidSeptember 5, 2019 6:23 PM

@Clive Robinson

One of the problems with "snake oil" is all to often it's not to easy to tell if you are dealing with those who "don't understand" or "understand only to well".

It's pretty easy in my experience. Like legitimate scientists, the ones who are fooling themselves still do try to explain what they're doing so that others can comprehend their "breakthrough". The intentional scammers are all smoke and mirrors, because any solid grounding in reality is going to expose the fraud. This company appears to be the latter case.

@xoa

But claiming to break RSA, or for that matter not even breaking but "merely" greatly speeding up, is a completely quantifiable/provable assertion, and it doesn't involve any disclosure requirements even.

Yeah, whether you're a scientist or a businessman, if you actually had the goods (even if you were just deluded), you'd be bending over backwards to demonstrate you can pass this basic test. Even the perpetual motion goons know that much. These guys are more like psychics who say they can predict the future, but never win the lottery or clean up in the stock market (or do anything else that is objectively valuable).

@Humdee

It is difficult for me to imagine that any "colleague" of Bruce's at IBM would be so stupid as to fall for this

Then you clearly haven't dealt with IBM's hiring process. I once dealt with an IBM "professional services partner" to go in as a consultant, and they were laughably incompetent. Many companies are similarly clueless when it comes to the HR process. The reputation of IBM went down the tubes decades ago. Time to update your imagination.

Ross SniderSeptember 5, 2019 9:49 PM

They can easily prove their claim that they can factor RSA without revealing the method. Some notable cryptographer (Bruce Schneier for example) can post a 2048 bit key, and they can factor it and release it as a zero knowledge proof.

They should be formally challenged with that.

bad JimSeptember 6, 2019 1:14 AM

About this finding that the square of a prime, minus one, is divisible by 24. It's blindingly simple. x2-1=(x+1)*(x-1). Since x is odd, both x+1 and x-1 are even, and since every other even number is a multiple of 4, their product is a multiple of 8. By hypothesis, x is not divisible by 3, so either x-1 or x+1 is.

I'm dull, so sometimes it amuses me to belabor the obvious.

WeatherSeptember 6, 2019 4:55 AM

Bad Jim, that's just plus one decimal place times minus one,using a centre points, . But yeah on the face of it, I wouldn't have anything to do with it, I skipped half of arstechnia page.

Petre Peter September 6, 2019 6:45 AM

I would think that there is a template for companies like these.I am wondering if there is another company that became successful which inspired them.

Clive RobinsonSeptember 6, 2019 7:40 AM

@ Weather,

Bad Jim, that's just plus one decimal place times minus one,using a centre points,

You could be fancy and call it,

    A sequential ordered tripple

But there are other "sequential ordered trippls that have interesting properties.

Take the tripple,

    p!-1,p!,p!+1

Where p! is "primorial"(factorial of the prime sequence[1]) thus is always even. The odds are quite high that p!-1 and p!+1 are both primes, thus form a twin prime.

There is also a reflective property around p! That is for every p!-n (where n is a simple interger) that is prime, there is a high probability that p!+n is also prime. Further if you look at the preceading primorial in the sequence it's reflections go up around the integer multiples untill you get to p!. The exceptions are when p!+n is equall to a multiple of a smaller prime.

[1] The name primorial and it's definition are down to Harvey Dubner, which happened in the era of PCs sufficiently advanced to be able to develop and test new sieves,

https://en.m.wikipedia.org/wiki/Primorial

This naming was a decade or so after I noticed the reflection possibilities for making a sieve when I was a young teenager, and might account for why I had difficulty explaining the idea to people such as teachers, who at the end of the day are generally not "mathematicians" so actually could not help with my question of how to move forward to an equation that would only give "twin primes".

Löwenbräu September 6, 2019 2:07 PM

The crown sterling company lion is not the one from the Czech coats and Arms lion. It is copied from the German brewery Löwenbräu/Späten (Part of AnheuserBush/InBev) and slightly photoshopped.

https://upload.wikimedia.org/wikipedia/commons/2/2e/Maly_statni_znak.PNG

https://upload.wikimedia.org/wikipedia/de/thumb/a/ad/Loewenbraeu_Bayern_Logo.svg/1200px-Loewenbraeu_Bayern_Logo.svg.png

http://timeai.io/wp-content/uploads/2019/03/Crown-Sterling-Logo-WhiteText-V2-AA.png

Keith DouglasSeptember 6, 2019 4:01 PM

I read about this via AT. I got about half way through the description before I gave up, laughing aloud at the obvious crap.

And I am not a number theorist, a cryptographer ... yet I can see through it. Sheesh.

My only question is - how does the Black Hat code of conduct play in here? I know that at these things one should be "respectful" of a speaker, but what exactly went down and should insisting that something that is obviously bullshit is such be regarded as rude?

I attended a nonsensical talk years ago at the Society for Exact Philosophy meeting (it was an abstract only session, so it was not surprising it made it through). In this case, I refrained from commenting since it seemed clear the presenter of the actual "contradictions in physics" was self-fooled, and the "interpreter" was a charlatan, but ...

SpaceLifeFormSeptember 6, 2019 4:39 PM

The mod 24 issue is seriously trivial.

Takes less than a minute.

All primes greater than 3 are of the form 6x+1 or 6x-1.

Use x being even or odd.

You have 4 cases.

Do the math. It really is that trivial.

maqpSeptember 6, 2019 6:19 PM

@Tatütata

Another aspect to the timeline:

At 4:14 of https://www.youtube.com/watch?v=MLb95ESwy60 the interviewer asks Grant what the implication of finding quasi primes is, to which Grant responds he does not know enough to know how profound the implication is. According to the video (3:53) it was filmed on March 19 (day before the paper was published arXiv). The Time AI marketing crap was uploaded on March 28.

So in just ten days Grant was able to figure out it meant he could break RSA, come up with the implementation, discover a quantum encryption algorithm to replace RSA, design and render the video, and push it for to the world to see.

In comparison, it took the Hold My Ark six days longer to cut and publish Grant's interview.

maqpSeptember 6, 2019 6:23 PM

@Tatütata

Whoops, I mean since the video says the paper was published "yesterday", the filming date was March 21, so he did all that in eight days.

TatütataSeptember 6, 2019 7:53 PM

Re: Talal Ghannam . I discover that what I wrote echoes what is in the post, but it seems to have evolved a bit. I found a LinkedIn page (no URL, as most of the time it lands you on an invitation to join) that confirms that this is indeed the same person.

I tried to get a copy of the pdf of the complaint, as the awful scribd also insists that you sign you for an account. (Why do people use scribd at all eludes me. Is web hosting so difficult to find?) I found one at ArsTechnica.

I bumped across a commercial site providing access to court dockets, and I noticed ">something curious in this case. Item 4 is a "Rule 7.1 Corporate Disclosure Statement", with an annotation "No Corporate Parent. Document filed by Crown Sterling Limited LLC.(Bressler, Joshua)". The information demanded by Rule 7.1 appears for presiding magistrates to decide whether they should recuse themselves.

I can't quite square the apparent statement with the existence of "Strathspey Crown", which lives at the same address, has the same logo, has phone and fax numbers differing only in the last digit from those of "Crown Sterling", and shares staff with, and the "No corporate parent" text. What would then the relationship between both entities?

I then remembered I had a Pacer account, and just wasted the last hour in trying to revive it in vain, and then in trying to register anew. I wanted to see the original of piece #4. There is also a "NOTICE TO ATTORNEY REGARDING DEFICIENT PLEADING" on the record which might make interesting reading.

At least in the US there is excellent public access to court dockets (when it works), contrary to Europe. I recently had a lousy experience in obtaining in obtaining a final German decision (which are thoroughly scoured and anonymised), with some abusive nitwit clerk insisting I present a full justification as to why I should be entitled to read a public judgement rendered "Im Namen des Volkes".

OTOH, corporate information is incomparably better in Europe (I have experience with BE, NL, CH, UK, FR and DE) than in the US (e.g., the wretched Delaware registry). But I digress.

I watched the vertical videos of the presentation, and from the lawsuit I expected something bordering on the pugilistic. But no, it was rather civilised. They even got a dose of applause from the tamer nerds. I was harsher than these hecklers in the past, at conferences and film festivals.

RachelSeptember 6, 2019 10:50 PM

This is one of the more entertaining things I've read in a while, not least owing to stellar contributions by Tatütata. Thnaks for the laughs everyone! I read the twitter thread referenced, and while there was nothing I could see in the twitter about the author wishing they could delete the thread, as the poster suggested: it was obvious they had no idea you don't go toe to toe with Nicholas Weaver and except to walk away, unless you are legitimate! He clearly had no idea who he was!

WaelSeptember 6, 2019 11:51 PM

Excellent work! You people are way too harsh!

Robert Grant is a successful healthcare CEO and amateur mathematician

Mathematician, eh?

From the first few seconds of the link @maqp shared:

Well, I think as human beings, first of all, we have an inherent ability to recognize patterns!

That's right, dawg!

Clive RobinsonSeptember 7, 2019 4:27 AM

@ SpaceLifeForm,

The mod 24 issue is seriously trivial.

Yes and no. You first have to recognize that it would normally being used as an example of a "sieve" not a "generator" thus 24 is marginally better than 6.

When it comes to very large prime selection of the 1024byte size generation is usually done by random selection and sieve rather than by determanistic generation, so anything that makes a marked improvment as a sieve would be of interest the fact that 24 = 3 x 2 x 2 x 2 whilst 6 = 3 x 2 makes a difference when doing fast division tricks on very large integer numbers in binary form, especially on CPU's that might only have an eight bit data bus width.

SpaceLifeFormSeptember 7, 2019 3:59 PM

@Clive

I was not referring to any sieve aspects.

Trust me on this, I've investigated sieves for decades.

I was only noting that any prime greater than 3, when squared, is congruent to 1 mod 24.

Easily shown.

All primes greater than 3 are of the form 6x+1 or 6x-1.

And x can be even or odd.

Lets eliminate the easy two cases where x
is even.

When x is even (let x = 2y), we have

[ (6*(2y) + 1 ] squared or [ (6*(2y) - 1 ] squared

In the 6x+1 case, we get
36*4*y*y + 2*6*2y + 1

In the 6x-1 case, we get
36*4*y*y - 2*6*2y + 1

By obvious introspection, in the case of x being even, the prime greater than 3, when squared, must be congruent to 1 mod 24.

I'll do another post of the case where x is odd, because it is much longer.


Clive RobinsonSeptember 7, 2019 4:44 PM

@ SpaceLifeForm,

I'll do another post of the case where x is odd, because it is much longer.

Yup, it's one of those things they get you to do when you take an interest in maths at an early age (and you try to forget when physics feels more like fun ;-)

Trust me on this, I've investigated sieves for decades.

It's a branch of math that some would feel it does not get the love it deserves, others well they figure that there is no fame or fortune in it.

The big bug that the neigh says tend to drag up is the issue of division or factoring. Whilst their are some tricks with polynomials and bases, many think most sieves can never be efficient especially with very long integers.

SpaceLifeFormSeptember 7, 2019 5:16 PM

Now, we look at the case of a prime greater than 3, and of course, where the prime is of the form 6x+1 or 6x - 1.

And here, lets look at x being odd. I already covered the x being even case above.

We are looking at the prime squared being congruent to 1 mod 24.

So, two cases left, and let x=2z+1

So, we have either

[ 6*(2z+1) + 1 ] or [ 6*(2z+1) - 1 ]

In the first case, where the prime is right-handed,

[ 6*(2z+1) + 1 ] squared

[ 36*(4z*z + 4*z + 1) + 2*6*(2z+1) + 1 ]

[ 144*z*z + 144*z + 36 + 24*z + 12 + 1 ]

By introspection, the 36 + 12 gets you the mod 24.


In the left-handed case

[ 6*(2z+1) - 1 ] squared

[ 36*(4z*z - 4*z + 1) - 2*6*(2z+1) + 1 ]

[ 144*z*z - 144*z + 36 - 24z -12 + 1 ]

By introspection, the 36 - 12 gets you the mod 24.

In conclusion, any odd number that is not divisible by 3, when squared, must be congruent to 1 mod 24.

QED


SpaceLifeFormSeptember 7, 2019 5:46 PM

@Clive

"Whilst their are some tricks with polynomials and bases, many think most sieves can never be efficient especially with very long integers."

Unfortunately, I have doubts. I do not trust RSA.

The bigger the semiprime, the more the attack surface shrinks.

SpaceLifeFormSeptember 7, 2019 8:03 PM

In re N!-1 and N!+1 being twin primes.

It is a pet theory of mine, that not only are there infinite pairs of twin primes, but that there are infinite sets of quad primes.


I.E. there are infinite X (very few and very far between), where

X-1 is prime
X+1 is prime
X+5 is prime
X+7 is prime

tttSeptember 7, 2019 8:29 PM

Robert Grant owns this "scientific" company:

https://arkcrystals.com/lifestyles/science/

"Haramein’s patented Harmonic Flux Resonator replicates the magnetohydrodynamic behaviors which naturally occur in a variety of astrophysical objects and enables each ARK crystal to become a point of high coherence in the structure of space around it, providing great benefits to biological health."

Bruce SchneierSeptember 7, 2019 9:40 PM

@Humdee:

"The scariest part of this entire episode is that there were able to get someone at IBM (!!) to needle @Bruce about it. It is difficult for me to imagine that any "colleague" of Bruce's at IBM would be so stupid as to fall for this, so someone how they got pressure there. Scary."

It's really not scary. IBM -- like every tech company -- has non-technical employees. Someone tells someone that someone has a new startup and wants to talk to me. If that middle someone isn't technical, he's not going to vet the startup first.

TatütataSeptember 7, 2019 10:15 PM

@ttt: Robert Grant owns this "scientific" company

Granted, there is undoubtedly a connection [1, 2], but how did you establish ownership?

TVSeptember 8, 2019 11:14 AM

I started reading this and suddenly was reminded of an episode of Star Trek TNG where this guy (Kosinski) was allowed to install new warp technology onto the Enterprise, even though there were no engineers in Star Fleet (or aboard the ship) who could understand and explain how the algorithms worked or even if they did work. This seems exactly like that script. To find out how the ship actually traveled a billion light years in a few seconds, you have to watch the episode, google "Where No One Has Gone Before".

MarkHSeptember 8, 2019 3:09 PM

I didn't look in on the site for a few days, so I'm late to this banquet ...

Before I read the blog post, the headline jumped out at me: the very name "Crown Sterling" tripped my grifter alarm.

Life experience has exposed me to enough fraudsters and compulsive liars, that there's a sort of aura I immediately recognize.

"Crown Sterling" is obviously grandiose, but more subtly has the effect of "confidence hijacking." In my opinion, it invites mental associations with "pound sterling," without doing this so bluntly that folks will necessarily be aware that this has happened.

The pound sterling is the oldest currency still in use; its use has never been interrupted; and it has held its value remarkably well across centuries of British economic boom and bust.

What better way to imply, "we're rock-solid and you can depend on us absolutely."

I don't know whether this was done consciously, but it's classic con-man.

MarkHSeptember 8, 2019 8:14 PM

@Clive, Impossibly Stupid:

The domains of those who know they're peddling garbage, and those who don't, are not exclusive.

American physicist Robert L Park has been an energetic teacher to the general public concerning pseudoscience.

His entertaining book Voodoo Science presents his thesis -- with abundant examples -- that the usual path begins with sincere belief in the false claim ... but over time, having been confronted with strong refutation, the would-be scientists cross the line from honest ignorance to the knowing perpetration of fraud.

WeatherSeptember 9, 2019 12:37 AM

Alyer Babtu
If 1 then its 1=1 but anything height is different, don't unstand mod in English,I've got a thersore;)

Wesley ParishSeptember 9, 2019 4:15 AM

@TimH

In my younger days, I had an idea that I thought would make a perpetual motion machine. I put a bit of thought into it, and proved to myself that it was nothing of the sort; taught me a lot about thermodynamics in the process.

For the sincerely self-deluded, it's a matter of getting them to ask (and answer) the questions they haven't thought of yet; for those intent on deluding others, one must aim at helping the intended victims.

InsertSomeCleverNameHereSeptember 9, 2019 10:15 AM

Asa writes:
>If I could break RSA what I would do is...

There's already an "RSA Challenge" with a long list of RSA numbers, the number of decimal digits, the number of binary digits and the (former) cash prize amounts that would have been awarded if somebody factored the number.

If you find a way to factor a large product of two primes, then just take this list of RSA numbers, factor the ones that haven't been factored yet, and publish the two factors of each number. The factors are not known to anyone, not even the people at RSA, but the factors are easily verified with "bc" or some other such calculator program so that anyone can verify for themselves that you have factored the RSA numbers correctly. See

h t t p s://en.wikipedia.org/wiki/RSA_Factoring_Challenge

Publishing a list of factored RSA primes would probably prove that you've really got the factoring algorithm that nobody else has and that it isn't snake oil.

Just thinking out loud...

Impossibly StupidSeptember 9, 2019 12:37 PM

@MarkH

The domains of those who know they're peddling garbage, and those who don't, are not exclusive.

No, they pretty much are. There may be some fuzzy thinking in the middle, but there is a stark difference between "I believe this to be true" and "I don't believe this to be true, but I'm going to pretend it is because it is to my advantage to do so". Just because people may shift from one to the other over time doesn't mean they overlap. The intent to defraud is a major difference and, like I said, that usually reveals itself in the way the person discusses the topic.

For example, I'd say a good 95% of flat-Earthers are just trying to gaslight people. There are just too many ways that a modern human can test that sort of hypothesis. If they choose to be willfully ignorant by not investigating the available facts, that defines their intention to deceive. It's a very small percentage who are looking at all the arguments for and against and still convincing themselves that living on a pancake makes the most sense.

MarkHSeptember 9, 2019 3:52 PM

@Impossibly Stupid:

Let's agree to disagree.

The relationships between knowledge, belief, and what is knowable by concrete experience are the subjects of a vast literature.

My conclusion is that in the average of humanity, what people "know" about the world is based on psychological comfort far more than any rational processes of evidence and analysis.

To dislodge a comfortable idea by essentially scientific means requires heavy rigor, discipline, and intellectual labor.

This is often demonstrated in comments on this blog, where technologists extraordinaires spout nonsense that couldn't survive 3 minutes of rational interrogation: even those expert in empiricism can't muster the resources to apply it uniformly.

Maybe you don't know many people who adhere to traditional religions, but I surely do. They hold as absolute fact claims which are readily disproved. If they were told that this established their "intention to deceive," I imagine they'd be astonished.

Impossibly StupidSeptember 10, 2019 11:11 PM

@MarkH

Let's agree to disagree.

No. If I am wrong, I want to find my error and correct it. If you are wrong and are willfully choosing not to fix your thinking, that puts you in the same mindset as the self-aware scammers.

To dislodge a comfortable idea by essentially scientific means requires heavy rigor, discipline, and intellectual labor.

This is not about changing anyone's mind, it's simply about classifying the error. A comfortable lie is still a lie. If someone spreads something they know to be a lie, that's a malicious action that falls far, far outside the bounds of simply fooling themselves.

Maybe you don't know many people who adhere to traditional religions, but I surely do. They hold as absolute fact claims which are readily disproved. If they were told that this established their "intention to deceive," I imagine they'd be astonished.

Their astonishment doesn't change the truth of it.

Alyer Babtu September 11, 2019 7:34 AM

@Weather

mod

Mod can be your friend in some cases, depending on what is being done. E.g. if the modulus is prime, arithmetic mod N is simpler than regular arithmetic on range -N to N: no special significance to positive/negative, every number is invertible etc. Of course there is the slight issue of getting back to regular numbers after doing something in the mod system.

PhilSeptember 12, 2019 2:52 AM

As soon as I read "infinite pattern inherent to icositetragonal geometry" It clicked in my mind. 24, they must have seen the Numberphile video about p^2-1=24 that was published in November ( https://www.youtube.com/watch?v=ZMkIiFs35HQ ).
Quantum computing, AI and huge amounts of PR resources. All that power and time wasted to confirm that all primes greater than 3 are neither divisible by 3 nor by 2. sad.

My true issue with this story is that I had the idea that Black Hat had some minimal requirements for soundness before accepting presentations. I would be interested in knowing how this one got through.

TRXSeptember 12, 2019 10:39 AM

> The company paid $115K to have its talk presented amongst actual peer-reviewed talks. For Black Hat to remove its nonsense may very well be a breach of contract.)
---
Sssoooo... does Black Hat normally charge presenters for "talks", and are they normally peer-reviewed?

Were the attendees aware that they were viewing a paid "product placement" ad instead of a "peer-reviewed presentation"?

While Black Hat may have been entirely on the up-and-up, the whole situation has a whiff of skeezy about it.


As to "breach of contract"... it sounds like they made their presentation despite hecklers. So unless the contract stipulates "and we will put a video of the presentation on our web site for some specified period of time" I don't see that argument going very far in court.

TRXSeptember 12, 2019 10:55 AM

> Someone tells someone that someone has a new startup and wants to talk to me. If that middle someone isn't technical, he's not going to vet the startup first.
---
"I have no expertise to be able to tell is this is BS. But it *might* be important. It would take me roughly forever to research enough to make an informed decision on something that would take Bruce maybe thirty seconds; which is the most effective use of employee time for the company?"

maqpSeptember 14, 2019 2:10 PM

I've been looking into the Crown Sterling stuff a bit and one of the more interesting parts IMO is Grant's Instagram account: https://www.instagram.com/robertedwardgrant/

From what I've gathered, there seems to be three things Crown Sterling is currently working on

1. The 24-sided dart board with spooky remainders of primes mod 24 -- that when finding new primes, allows reducing the search space by two thirds (the effect is so insignificant, such speedups are ignored in the Big O notation). The most interesting part here is IMO that apparently the Knight's Templar have predicted primes with the help of tomatoes.

2. Breaking of the RSA.

3. Developing their Time AI public key encryption algorithm.

The section 1 has been hashed over and over, and section 3 has nothing published on it yet (I doubt there ever will be). But 3 isn't important until they show they can break RSA (section 2) so it's this one I want to draw attention to.

For some reason Grant is more open about his research on Instagram (might be because it doesn't intersect with the infosec bubble calling out his bullshit, and because his fanbase likes to look at his wanna-be da Vinci doodles).

One specific post I want to highlight is this one:

New Mathematical Discovery: The exact factors (5987 x 6323) of this Bi-prime 37,855,801 appear contiguously and perfectly within its 1/x reciprocal value (1/37,855,801) string. Since realizing the above, our research team has tested many Biprimes to see whether their factors appear in their respective 1/x reciprocal values and also how they may relate to the “period” (repetition) of those values (in repeating rationals).

For non-Unique (have period lengths that no other prime possesses) and non “Period” Primes where their period is substantially less than the scale of the number) it appears that their two prime factors, regardless of length appear inside their reciprocal decimal extensions! As the period for these numbers is generally quite large, one must extend the length of these decimal extensions at least long enough to surpass their first Period cycle.

Paradoxically, the longer the BiPrime you desire to factor, the easier to locate the long consecutive prime string embedded within its 1/x reciprocal value. I believe that this realization will have major ramifications in many fields of science and cryptography. It also says that numbers could never have been invented by Mankind, the degree of sophistication and analysis necessary to accomplish this is so far beyond even the world’s current understanding and comprehension of the language we call Mathematics.

This is fascinating work as we believe it says something very fundamental about the “Source Code” of numbers in general, and implies a deeper numerical meaning within nature’s elegant complexity, yet beautiful simplicity. These decimal extensions also appear to possess Wave characteristics (similar to constants) both in their period values as well as the distance between factors and how this also relates to periodicity. Perhaps the 1/x value is a veritable DNA 🧬 for numbers themselves. It’s a brave new world. Feels like we are on the verge of something really big that will unpack the nature of DNA and our awareness (and purpose) of numbers generally.


There's two aspects to this

1. It doesn't hold true for all primes. I wrote a tiny program that shows this: https://pastebin.com/uua5Jnxx Grant and his team acknowledge this in one of the Instagram posts but it doesn't stop them from fear mongering.

2. The efficiency of the algorithm ("search for prime factors in the recurring decimal of the reciprocal of the semi-prime") is ridiculously slow and requires ridiculous TMTO.

You first need to find the period of the semi-prime. It might be trivially doable with 2-6 digit semi-primes, but even the trivial RSA-100, broken in 1991, has 100 digits:

n = 15226050279225333605356183781326374297180681149613
80688657908494580122963258952897654000350692006139

a) Assuming n is not relatively prime to 10, determining the period with brute force takes too long. I'd appreciate if someone did the math.

b) Even if the period could be determined, to avoid having to calculate the decimal expansion again every time, it needs to be stored on memory. The period length is at worst n-1 so writing down the entire period takes at worst n-1 bytes, or 10^83 petabytes (there are only 10^82 atoms in the observable universe).

c) My conjecture is, it is actually quite likely the prime factors (37975227936943673922808872755445627854565536638199, 40094690950920881030683735292761468389214899724061) would be found on memory where every atom of our universe has been manipulated to contain petabytes of decimals.

The problem is, even with the TMTO, you still need to check practically every offset of that memory to see if what you tested is indeed a factor of the semi-prime. This takes in the order of n operations, and is thus completely infeasible.

In his post Grant says "I believe that this realization will have major ramifications in many fields of science and cryptography." The ramifications can be evaluated by considering Grant's "discovery" takes forever to run even with smallest numbers, and by considering the GNFS algorithm can factor RSA-100 in seconds on modern HW.

So, if RSA-100 is too slow, what chance does Crown Sterling have against the RSA-2048 challenge, where the semi-prime is

RSA-2048 = 2519590847565789349402718324004839857142928212620403202777713783604366202070
7595556264018525880784406918290641249515082189298559149176184502808489120072
8449926873928072877767359714183472702618963750149718246911650776133798590957
0009733045974880842840179742910064245869181719511874612151517265463228221686
9987549182422433637259085141865462043576798423387184774447920739934236584823
8242811981638150106748104516603773060562016196762561338441436038339044149526
3443219011465754445417842402092461651572335077870774981712577246796292638635
6373289912154831438167899885040445364023527381951378636564391212010397122822
120720357

Now, Crown Sterling would obviously say that this isn't how they broke RSA which begs the question -- if they already have factoring algorithm that runs in polynomial time, why waste time on "new discoveries" such as this, that don't offer any speedup at all?

But surely there's something else going on because as per this post's reasoning it's obvious they couldn't use this method to win the challenge they threw at JP Aumasson about factoring a 512-bit semi-prime. (Apparently they were thin-skinned enough to convince some random youtuber, which I find hilarious). So assuming the comment wasn't staged, how did they do it?

My guess is they did what Theranos did and tried to convince people they have something by running existing technology: e.g. GNFS on AWS.

But what about the discovery? I think it's possible that if they did what Theranos did, this was created to please the investors: another spooky phenomenon that is easy to follow, appears to offer big results, and that requires a course on algorithm design to determine it's useless on big numbers.

---

More and more I think the fraud here seems to be misleading the audience and especially the investors by showing patterns that leads to them drawing bad conclusions.

E.g. one of the questions the Instagram post has, is

Does this mean the end of public-key encryption based on prime factorization?

to which Grant replies

I have already stated publicly that all factor based encryptions are now, in my opinion, highly vulnerable. and this statement stands independent of size of the public key.

He doesn't claims this discovery will break RSA, but implies that by presenting the two next to each other. There's room for deniability too: he could later say "I was only answering a question and it had nothing to do with curious properties of decimal expansions the image was about!".

Another example is his youtube interview where he says

When I realized my discovery might have a significant impact on the way encryption is done--

He is not saying his discovery has an impact on the security of RSA, but "how encryption is done", i.e. what he can make people use, i.e. what he can sell to you. It's just the listener's mind that makes these conclusions from the context.

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