Monday, June 22, 2020 ... Deutsch/Español/Related posts from blogosphere

Why I don't believe that a Bitcoin puzzle was honestly solved

...And why you need to assume that everyone in the cryptoworld is lying to your eyes unless you have a rigorous proof indicating otherwise...

Especially a month ago or so, I spent roughly "a dozen of hours" or perhaps "dozens of hours" by the "Bitcoin halving puzzle". If you successfully extracted 12 words (in the right order, each from the list of 2048 English BIP39 words), you could unlock a Bitcoin (basic Segwit, 84/0/0/...) wallet and send a modest amount of money, around $500, to your Bitcoin wallet. Recall that in the cryptocurrency world, knowing the private key is equivalent to "possessing the funds" because the private key is necessary and sufficient to sign messages "I want to send BTC XY from that wallet to some particular other wallet".

I previously wrote three blog posts and up to yesterday, I didn't know the central question "whether there was a chance for me or a typical 'you' to solve it". The puzzle was announced as solved yesterday and the money was taken by an alleged Pogo or Elron V. Hubbard who wrote a perfectionist solution. It was the last day before the contest would be ended, and a few hours after some nontrivial but not decisive final hints were posted by the author of the puzzle, Logic Beach (allegedly astrophysicist Herman Falker).

Now I feel almost certain that I couldn't have solved it even after years (good that I completely stopped "working" on it a few weeks ago, and advised the same to E.T.) – and while I am less certain about the following claim, I also think that no other person on Earth except for the creator could have solved it "completely".

OK, the previous blog posts were the following: On May 12th, I learned about the puzzle and liked the pictures in the spectrograms of the songs which is why I promoted the contest. On May 14th, I wrote a text about contrived hypotheses which was both about contrived theories in physics as well as contrived puzzles, and this blog post is a "remake" of that older text of mine. And on May 18th, I suggested a very low-entropy seed with the word "tree" repeated many times. That solution – or even a vague idea what the solution could look like – had absolutely nothing to do with the right seed.

OK, playing with the spectrograms and a few other things was fun and I learned to use some new software (Sonic Visualizer and perhaps Audacity) a little bit. Those were very sensibly invested "several hours". But the subsequent hours would only be meaningfully invested "if one had a big chance to solve the damn puzzle". So all this extra work was clearly justified by the assumption "yes, there was a chance". For this chance to be nonzero, the puzzle had to be "much more organized or constrained" than the worst case scenario. And the worst case scenario was the following "Ansatz" for the seed:

  • Pick twelve BIP39 words
  • Store them to nine songs (nine 35-megabyte long WAV files) using 9 basically completely different contrived techniques
  • Permute the order of the 9 songs or 12 keywords by a permutation of numbers 1-9 or 1-11 or 1-12 that is stored in a random song in another contrived way
Well, this "Ansatz" was sufficiently well-defined and right now it seems obvious that it was correct. The puzzle did fit into this "Ansatz" and because the techniques to get the order and especially many words were extremely contrived, I do think that the puzzle was unsolvable.

OK, my alternative "Ansatz" that made me invest the additional "dozen(s) of hours" of my time, and many hours of E.T., was based on the assumption that the order is actually a rather special and also constrains the right words. It seemed that the author of the puzzle was a big fan of chaos theory. He said to be an astrophysicist so chaos theory isn't "quite his field". So he probably knows much about chaos theory from a popular book. I was led to James Gleick's "Chaos" which happens to have 11 chapters; the creator had to be obsessed with that book, I thought (lots of the songs and their titles refer to rather obscure stories and explanations in that book). And a great new "Ansatz" was that the words 1-11 were chosen from chapters of that book (there are 11 of them) as representative words of those chapters. And it really looks like good enough words overlapping with the hints may be found in good enough chapters of the book etc.

Only yesterday, when the full solution was posted, I could see that this assumption was wrong, all the evidence that this is what Logic Beach did was an illusion or noise, and there were uncountably many possibilities for you to pick another nice enough organizing principle and "rationalize it". All such work could have swallowed an unlimited amount of time of many people (with very different ideas) and it would only lead to noise.

OK, my best candidates for a seed looked like this (with lots of minor localized variations):

west perfect silver mountain cat tree age cabbage radio rhythm ladder future

The words West-to-ladder are chosen from Chapters 1-11 of Gleick's book where they play a prominent role, the 12th word doesn't have to be from any chapter but it is still one of the hints from the 9 songs (Song 10 was announced not to store any word). The seed that unlocks the wallet is

love sound electric bomb quantum radio silver mountain tree west solve sad

There are some words that agree, largely those that were known, the order is very different (note that radio+tree are on positions 6,9 or 9,6 in both, my solution and the "right" one, I was trying both possibilities, a fact that I consider a complete coincidence now), and there are 5 words that I or we (with E.T.) didn't even consider, namely love, sound, electric, solve, sad. On top of that, bomb was considered but I wasn't personally persuaded that it was the right word from Song 2, E.T. was right. And both of us preferred "cat" over "quantum" as the word from the song whose spectrogram included Schrödinger's equation. Effectively, about 6 words were unknown to us, along with the right order.

The order – an extra permutation that had to be applied to the songs – was hidden in a very particular way in Song 2 (it could have been hidden in 8-9 other songs and in billions other ways). The Feigenbaum constant (the upper value) was being read in English (it was very hard to understand it!) and you had to write down all the digits and verify dozens of digits of this constant.
Real value:   4.669201609102990671853203820466201617258185577475
From track 2: 4.669201609102990671853203820642231917278885517575 
                                           642 3 9 7 8 1 5
Great. So the voice doesn't quite read the correct constant even though the first 20+ digits are OK. If you list the digits that were replaced with some wrong ones (at the same location), you get 642397815 as the wrong digits (there was another choice, you could also try to write down the correct digits instead, or you could invert the permutation that you get in this way, and so on and so on). That is the desired extra permutation of Songs 1-9 that you have to apply to get the right order of the 12 words hiding in these 9 songs. It obviously sounds simple enough when I say in this way. But there were millions of other ways to extract a permutation of 9 or 10 or 11 or 12 numbers out of the correct digits of this constant, another constant anywhere, or any function of the bits in the 300+ megabytes of WAV files. ;-) Also, I think that this relatively contrived method to hide the permutation contradicts Logic Beach's assurances that the "permutation is not even hidden or encoded" because the verbs "hide" or "encode" don't properly describe how clearly visible the permutation is in the albus. Sorry, it is in no way "clearly visible".

Great, what about the individual words? Look at the solution for details.

As the permutation above indicates, the first two words (we were told that three particular 5,6,7 songs would contribute 2 words) were taken from Song 6. It started with a Bitcoin chart in the spectrogram so almost all the contestants were using words such as "satoshi price", "price future", we had "future perfect" (because that's what's heard in the audio) or "pitch fork" (because pitch forks also appear in the spectrogram and Gleick's book, and the words start with the same PF), the number of possibilities is almost unlimited. However, we're told that the Bitcoin chart was (a red herring, like almost everything) meant to tell you that it's some "thunder" and you should speed up the song 50 times, do many other operations to remove some kind of noise, and when you do such things, you barely hear the words "love sound". I've done many comparable operations using Audacity and this one looks even more contrived than everything I did before. So I didn't even try to reproduce the operations that were said to produce "love sound"; I believe that you may get it if you follow the instructions.

Do I believe that both Logic_Beach, the author of the puzzle, and Pogo, the alleged solver, did the exact same thing to get "love sound"? And that Pogo could have feel certain that he could have discarded "satoshi price" and "perfect future" and "pitch fork" or any other candidates that are really at least equally justified? Not really. Storing something in a song that needs to be accelerated by a factor of 50 is an extremely rare idiosyncrasy. Why would another person think that this is a natural thing to do with a 30 MB WAV file? Fine. I think that the person who would get this "love sound" from that "satoshi price" song would have to be as fanatical a user of the Audacity software as the author but even that wouldn't be enough. He would have to like the same awkward and impractical operations with the software and with sound files. Speedup by a factor of 50, removals of noise, decibels here, decibels there, and he would still have to be convinced that this sequence of operations is more natural than any interpretation of the spectrograms, melody, title name, or anything else that is hiding in the song; and that there isn't any "even more sophisticated" method to extract even fancier words. Unlikely. Also, it's strange that the author of the puzzle didn't offer any improvement how to hear the words "love sad" more clearly or how to improve the Audacity operations that were described by Pogo. Are we supposed to believe that these two men independently did the same sequence of operations with the speedup and filtering?

After Song 6, we have Song 4 (see the permutation above). That's even crazier, I think. Again, I haven't even tried to reproduce it. Around 2:52 of that song, you see some innocent vertical lines in the spectrogram. For some reason, both the creator of the puzzle and the allegedly independent winner recognized that this particular pattern in the spectrogram was Robot 36, a variety of SSTV, a method to encode static images in sound, and you need to take the software called MMSSTV and decode this pattern into an image. To make things worse, the MMSSTV application doesn't allow you to insert sound files so you really need to play it to a speaker, and make the application listen to a microphone! ;-) When you decode the random piece of the 30-minute-long album of electronic music, you get a somewhat blurry image with the letters saying "you clever bitch electric", and determine that the right word from Song 4 is "electric".

Again, there is no law of physics that would prevent two people on Earth from doing the same thing. But do I really believe it happened twice? Not really. The very idea that aside from Audacity, a solver of a puzzle – which only gives you $500 – is this big a fan of the MMSSTV software (I am sure that there aren't many among some "hundreds of" people who were exposed to the puzzle!) and that he finds the right place in the 30 minutes of spectrograms where it should be applied... it seems far-fetched to me. Again, even knowing how to use MMSSTV and how to determine that you need the Robot 36 subvariety etc. etc. aren't sufficient conditions to get "electric". Even a posteriori, if you know the exact operations, it's nontrivial to validate the claims. And you need to know that this MMSSTV trumps many other methods to extract a word from that song. That song contains a "ladder" in the spectrogram (a word in the afterword of Gleick's book, a check) and many other things. Quite generally, most words proposed by random commenters looked "clearly wrong" and "stupid" but some didn't. Some were real promising candidates.

The permutation 642... tells us that the next song should be 2. It was more or less publicly announced that the audio should store the right word in the Morse code and my collaborator "clearly heard" BOMB in the Morse code at some place. I can hear it as well, it is a very fast Morse code that really resembles the rate by which the Morse code is often broadcast. So it was surely possible (and, at some moment, publicly leaked secret) to extract the word "bomb" from that song but the degree of certainty that it was the right word from Song 2 couldn't have been too high.

6423... The next song that contributes is Song 3, the vertical deflection coil. The spectrogram includes Schrödinger's equation. We were told by the creator of the puzzle that you need a leap, he also said "nyet koshka" at some moment (which is Einstein's description of telegraphy: a telegraph is a long cat that you tickle in New York and it miaows in London, except that there is "no cat" in between, "nyet koshka" is a piecewise translation of "no cat" to Russian). We always did consider "quantum" as a very possible word from Song 3 but we considered "cat" to be somewhat more likely for various reasons.

62439... Now Song 9. This became publicly known. You had to find just two frames in the video where a robot plays with a radio (and tape player) in a car (towncar in a forest), and something blinks on the display of the cartoon radio. I subtracted two images because the noisy picture looked utterly unreadable to me and I obtained "rAd10" in digital calculator's letters. Many people got "radio" for free because it was "leaked". But of course, without these leaks, the probability that one would extract the word "radio" as the right keyword from that song wasn't much higher than 1/2048 (random word from BIP39).

Now the track 7. It contributed the words "silver" and "mountain" – which were mostly leaked – because the spectrogram includes overlapping sequences of letters "Ag" and "Mtn". So most people who read the publicly known information did consider "silver mountain" to be the most likely words. However, you can't really be sure that this is the right way to divide the letters. It could also be "Mg" and "Atn" or "Mgn" and "At" or "Agn" and "Mt" etc. These other combinations lead to various interpretations, you can do other things, you may speculate that the creator confused gold and silver (because the creator didn't want to confirm silver), and so on. But because of the leaks, it's at least right that most people did consider "silver mountain" to be by far the most likely words from Song 7.

Song 8, the word "tree" blinks in the robot's eye at 24:07 in the video in one frame, it's unreadable, so the creator had to leak that it was the right word from that song. Without that hint, it would be very far to guess the word even if YouTube didn't make that tiny word unreadable. That word appears exactly when Frank Zappa sings "mind" as the answer to the question "what is the ugliest part of your body" which is the title of that song (the original whose remake was recorded by Logic Beach). But the claim that the word "tree" almost uniquely follows from that song seems indefensible. It could have been the forest, mind, or (almost?) 2048 other words that may be connected to something in that song with a robot walking through a forest while listening to a Zappa song with lots of other words in it.

Song 1, West. The first spectrogram that most people discovered was the compass with "cardinal directions". After some time, some of us could see that there is "West" written in the Morse code next to this "compass". So the keyword was "West" and it was pretty much leaked. I think that this was the only word where the keyword "almost uniquely" followed from the song.

Finally, Song 5 produces the final two words which happen to be "solve" and "sad". The name of the song is the speed of light. I thought that you needed to accelerate the sampling frequency from 41,000 Hz to 300,000 Hz (to emulate the speed of light's numerical value). Then you would move all the tones by 3 octaves minus 3 semitones towards the high pitch, and you may get pieces of the melody that are very close to AGE and CABBAGE or CAGE and CABBAGE, words that may be found in the book. Instead, the words that are needed to unlock the wallets are "solve" and "sad" and they are written in the hexadecimal reader of the WAV file. But you must look near 0x493e0 which is the hexadecimal value of 300,000 (to look at the hexadecimal 300,000 would still be more natural, I think). You have to read the file as "16 bytes per line" and then you may see something like "solve#sad" in a column where "#" is some rubbish character.

This is another damn 30 megabytes or so long file. You can find lots of word-like sequences in such a long file. Impartially, I think it would be right to consider the sequences "solve" and "sad" that are found somewhere to be just noise, even if it is close to the "remarkable" place 0x493e0. ;-) Note that the speed of light in km/s isn't even 300,000. It is 299,792.458. So the message should have appeared 208 bytes earlier if the speed of light were quantified properly. Also, "solve" and "sad" have nothing to do with chaos theory, so they arguably violate the assertions that the keywords have something to do with this general topic.

Combining the low probabilities into one overall probability

Now, take all these things together. Pogo wrote a solution that indicates that he got every single thing out of these things correctly, the ordering that no one else seemed to have, plus the 5-6 words that no one has publicized (not even 1 of them), and he didn't need any brute force to find some of the 12 words (which would mean that he has no explanation for this word or words). Do I believe that he really got the complete flawless solution? Not really. It is a combination of too many extremely unlikely events.

On top of that, Pogo – which seems like a rather anonymous person – seems to have a Medium page with lots of other crypto puzzles. It looks like an industrial company to allow creators of the puzzle to pretend that their puzzles were solvable. Pogo's experience may also be said to make it more likely to solve similar puzzles. But what I find more important is that with this experience, Pogo almost certainly can run BtcRecover-like code to try many combinations of the words (many seeds). With this ability, it seems almost certain that he would have found the seed by testing all 2048 or 20482 or 20483 possibilities with 1,2,3 words replaced by a wild card. It's just vastly easier to run the BtcRecover software and check 2 thousand combinations than to decode the word "electric" by the contrived method above (or even "bomb"); or run BtcRecover to check 4 million words (still at most minutes) than to find "love sound" or "solve sad" somewhere.

Because Pogo could suddenly write the correct solution with the apparently right explanation for every single word (and the permutation), after some 6 weeks, in which he couldn't unlock the wallet even with the likely access to the BtcRecover brute force, I just find it unnatural, unlikely, implausible (especially because there's no hint of previous "mistakes" or "ambiguities" that he would have to encounter if the process of solution were natural). I don't have a rigorous proof that Pogo had to share information with Logic Beach (as far as I can say, they may be the very same person and maybe even the alleged collaborator of Pogo's is still the same person – keeping everything obscure and cryptic is a way to mask these basic statements and I think that it must mean a rational person skeptical about all the claims – without any enforcement of the transparency, lies are bound to be omnipresent). But the data that I see make this outcome immensely likely in my eyes; Pogo was just ~6 words plus the order ahead of everyone else. One has to make conclusions even if the available information is noisy and incomplete and this is the conclusion that I make. Even if my huge distance from the right solution were due to my low intelligence relatively to the allegedly real Pogo, it doesn't change anything about the following decision and it is: Never spend dozens of hours with cryptocurrency puzzles posted by anonymous parties again. ;-)

There were many clever aspects of the puzzle but I think that it was an unsolvable puzzle, it wasn't honestly solved, and this conclusion only strengthens the general thesis that pretty much everything in the cryptocurrency world is rigged, designed to push an overwhelming majority of the users and contestants to wrong conclusions about the questions that really matter. The anonymous character of "everything" in the cryptoworld is nothing else than a powerful tool to make lies and deception omnipresent and unaccountable.

And that's the memo.

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