Topic: URGENT: please peer review a possible back door in Bitcoin? (Read 2295 times)

They were temp banned for multiple postings in a row. Tptb additionaly posted the same over and over in a multitude of threads...

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Which similar reasons?

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FYI truce, I will cease & desist:

I asked you to not do what you just did above:

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The point is that with a supercomputer together with a new cryptoanalysis break, the two together might be required to accomplish the attack. I want you to know that if China's pools see nearly all the mining shares, then they are viewing about 2⁶⁸ of SHA-256 hashing power per annum which may or may not be fulcrum. Don't presume you know all the theoretical attacks that are possible.


You've made at least two mathematically illiterate errors in that quoted text:

1. Testing that double-hashing fulfills some criteria you have prechosen, says nothing about security against cryptoanalysis which your criteria has not considered.
2. Securing a password by iterated hashing (because it requires the dictionary attacker to perform the iteration cost on each dictionary trial) says nothing about the increased vulnerability of collision cryptanalysis. You are conflating two separate issues of security.  

I am done speaking to these amateurs. Waste of my time.

I'll interpret your reply as an ostensibly intentional veiled admission that you could not answer the question. So I will proceed to explain the sort of theoretical analysis that I was interested in discussing in the thread that the "forum-Hitler" Gmaxwell nuked.

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Tangentially note the disclaimer that I wrote in the OP of the thread which was nuked:


I had written in that nuked and vaporized thread a post (my last or nearly last post in that nuked thread) which explained that at the moment I wrote that quoted OP, I had been mislead by sloppy writing on the news sites (and also the linked sites of the protagonists) into thinking that the hash of the Sartre text was already confirmed. For example, I provided this quote:


Being at is was by that time late in the evening for my timezone and I had been awake roughly 18 hours already, and I was skimming in an attempt to make some quick feedback on this potentially important event, so I could return to my work asap. In the nuked thread, I quickly realized that the Sartre text hadn't been verified to match the hash, so I actually stopped posting in the nuked thread for a few hours. Then when I came back to thread, it didn't exist so I could no longer follow up or read what had been elucidated. Thus note my original focus was on how the hell could Craig have achieved that match, so he must have broken the hash. I had recalled that I had theoretically doubts about the double hashing which I had never bothered to discuss with anyone. It had been 2+ years since I did that research on cryptographic hash functions, so I had to decide if I was going to go dig back into that research or not. I figured I'd sleep on it and then be able to think with a clearer, rested mind about the implications of the revelation (to me) that the hash had not been verified to match the text because the portion of the text had not been sufficiently specified (again the "undisclosed" term didn't make sense to me in quick skimming because I had read on the blog that the Sartre text was referred to).

But instead of being able to sleep on it and then decide whether to let it go or dig back into my past research, my thread was nuked and I was under attack. Remember I don't back down from anyone when I think I am justified. When I think I am wrong, I mea culpa.

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So now back to the subject matter of whether double hashing could theoretically lead to any weakening of the second preimage and/or collision security of the SHA-256 cryptographic hash function.

Afaik, there is no research on this question. If anyone is aware of any, please kindly inform me.

First I will note the Merkle–Damgård construction (which SHA-256 employs) is subject to numerous generic attacks and even though afaik none of these are currently known to be a practical threat against a single hash of SHA-256, we can perhaps look to those generic attacks for potential clues as to what a double-hashing might enable which a single-hash application perhaps might not.

Note in the pseudo-code for SHA-256 that what distinguishes a double-hashing from doubling rounds (i.e. "Compression function main loop:") or repeating the input text in double the block chunks (i.e. "Process the message in successive 512-bit chunks:"), is that the h0 - h8 compression function state which is normally orthogonal to the input block chunks instead gets transmitted as input to a block chunk in the second hash application (i.e. "Produce the final hash value (big-endian):") after being added to the output of the compression function (i.e. "Add the compressed chunk to the current hash value:"). And the h0 - h8 compression function state is reset to a constant (i.e. "Initialize hash values:").

The reason I think this might be theoretically significant is because we should note that the way cryptographic hash functions are typically broken is by applying differential cryptanalysis. Differential cryptanalysis is attempting to find some occurrence of (even higher order) differences between inputs that occurs with more frequent probability than a perfectly uniform distribution. In essence, differential cryptanalysis is leveraging some recurrent structure of the confusion and diffusion and avalanche effect of the algorithm.

Not only does the double-hashing introduce a constant  h0 - h8 midstream thus introducing a known recurrent structure into the middle of the unified algorithm of a double-hashing, but it shifts the normally orthogonal compression function state to the input that it is designed supposed to be orthogonal to. On top of that, the additions of the h0 - h8 state at the midpoint, can possibly mean the starting state of the midpoint is known to have a higher probability of zeros in the least significant bits (LSBs). This last sentence observation comes from some research I did when I created a much higher bandwidth design variant of Berstein's ChaCha by fully exploiting AVX2 SIMD, that was for a specific purpose of creating a faster memory hard proof-of-work function. In that research, I had noted the following quote of an excerpt in my unfinished, rough draft, unpublished white paper written in late 2013 or early 2014 (and kindly note that the following might have errors because it was not reviewed for publishing and was merely notes for myself on my research understanding at that time 2+ years ago):


So now put those aforementioned insights about potential recurrent structure at the midpoint of the double-hashing, together with the reality that a Boomerang attack is a differential cryptoanalysis that employs a midpoint in a cipher to form new attacks that weren't plausible on the full cipher. Bingo!

I'll refrain from providing my further insights on specifics beyond this initial sharing. Why? Because I've been treated like shit by Gmaxwell and you all here grant him too much Hitler-esque control over the Bitcoin Technical Discussion subforum where these sort of discussions are supposed to occur, so I will take my toys else where. Enjoy your echo chamber.

Do I have an attack against Bitcoin's double-hashing? I leave that for you to ponder.

Just to be clear, for practical purposes what knightdk says is true. But from a cryptoanalysis point of view, it's slightly more likely to have a collision.

Another idea: if the NSA has a backdoor for sha256, then it is possible that backdoor doesn't work for double sha256.

This is not exactly true, the collision resistance is weaker than the weakest.

Hashing many times protects from some preimage attacks. It's sometimes used to make the hashing slower on purpose (like in WPA, in order to make cracking slower and more expensive). Doing it twice for mining makes sense because it prevents some mining algorithm optimizations and also because ASICs for sha256 existed before bitcoin, but not ASICS for double sha256. So hashing  twice may have been a way to prevent those ASICS from working.

Hashing more than once does increase the probability of collisions, however that increase is negligible. Consider the case of double sha256:
output = sha256(sha256(input))

If one of the two sha256 have a collision, then the double sha will have a collision too. So it's weaker: at least one of the two hashes is required sufficient for the double sha to collide. That probability of having one of two hashes collide is certainly higher than having only one hash collide.

However, consider that if double sha256 has a collision it is because at least one of the two iterations of sha256 did collide. So you see, it is still very unlikely because it still requires a collision in sha256. And as someone mentioned, a collision in sha256 is in itself more important news than having found Satoshi.

I consider it safe to assume that CSW didn't find a collision in sha256.

Other than the OP

How is any of this "Meta"?


~BCX~

TPTB_need_war, you cannot prove nor disprove that the Sartre text Craig Wright supposedly hashed is a collision for SHA256. The hash that he published is the exact hash that is signed by the signature that spent the Block 9 coinbase. Because calculating that hash is trivial and the signature is already public, it is reasonable and safe to assume that Craig Wright simply took that hash and claimed that it was the hash of the sartre text.

You also pointed out that he supposedly has access to a supercomputer. Even with access to a supercomputer, he would not be able to find a collision as other researchers have already tried. Simply having a lot of computing power does not mean that he can find a collision.

Alternatively, Craig could have found a vulnerability in sha256, in which case a lot more things than just Bitcoin is screwed. If Craig did not responsibly disclose such a vulnerability and instead exploited it, this would be incredibly sketchy and dishonest behavior.

The theory that the sha256 double hash is weaker than sha256 is false. It has been proven that performing multiple iterations of a hash is more secure than just one iteration. Specifically, many websites will store users passwords in the form of a multiple iteration hash. This is significantly more secure than a single iteration hash. The resulting hash of a multihash function (including multiple iterations) has the same collision resistance as the collision resistance of the weakest hash. This means that sha256d has the same collision resistance as sha256. What multiple hashes protect against is a preimage attack.

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It isn't really, it started as a complaint against the removal of his thread and then he promptly continued the thread here.

I was sleeping. Now the REKTing will ensue.


I believe you are a liar. Prove it by revealing your identity. My identity is known to everyone. I have revealed my full name, where I live, my history, my LinkedIn account, my public non-anonymous writings published over the internet, etc..


Yes of course there is a combinatorial explosion of possibilities which was my point that you all can't conclude with 100% certainty that Craig can't produce a preimage of the hash, unless you can be sure he can't second preimage SHA-256 or otherwise find a collision. And I had stated that double hashing with SHA-256 might possibility have a cryptoanalysis hole that isn't known to exist in the cryptoanalysis of a single hashing. Again this was just a theory I wanted to discuss. Perhaps you don't like theories. Perhaps you would have preferred that Einstein didn't ponder riding in elevators. Well small, closed minds aren't very creative and thus don't achieve greatness. More on that with follow in a subsequent post.

However, in spite of the fact that you can't disprove any possible means of representation or permutation of the Sartre text, I wrote several times upthread that at the bare minimum, those protagonists who were claiming 100% certainty that Craig could not do something (btw a very strong claim), it would behove them to at least show that using typical representations of the Sartre text (e.g. ASCII text and perhaps UTF8/UTF16), that no contiguous portion of the text could hash to the signed hash. Moreover and more saliently, I pointed out that the protagonists were disingenuous or derelict by not pointing out the possibility that Craig might still be able to match the hash with some revealed content, Iff (if and only if) Craig had found a way to second preimage or otherwise find the necessary collision on the SHA256 hash. That the protagonists were too lazy to do this and were also too lazy to even verify if the website drcraigwright.com is Craig Wright's official communication vehicle (which apparently it is not and is now for sale here on bitcointalk.org according to a screen capture I quoted upthread), points to the lack of diligence and/or disingenuity in this tribe of Bitcoin maximalists including apparently yourself, who think they are holier than thou.

Do not disingenously quote my above two paragraphs out-of-context again. Don't cherry pick my context to make inane non-rebuttals which side-step my holistic set of points.

Note when I am done REKTing you on the technical points (again more is to follow below after this post), I never again want to waste my precious time with a useless and disingenuous turd. So this will be your last interaction with me.


You are apparently mathematically illiterate. If Craig can't find the second preimage or necessary collision, then he can't find a text that matches. Period. If he can find the second preimage or necessary collision, then he can find a text that matches. Period. When we analyze the probability, we don't start only with the Sartre text document. He could have chosen from any document on earth.

Thus his ability to use only contiguous portions of the Sartre document is mathematical plausible (again assuming he has the necessary cryptographic breakage), and thus it behoves the protagonists to explain this and even to write a quick script to prove that the contiguous portions possibilities in the common encoding formats does not hash to the signature he provided. The derelicts didn't do this. My necessary mathematical assumption in this paragraph (not impacting the prior paragraph) is that the hash function would be subject to a multi-collision attack. Thus if the breakage is not multi-collision, then Craig could not have reasonably limited himself to contiguous portions because the search for document matches in itself would probably be an intractable computational problem. My point remains that we see none of this sophisticated explanation from the protagonists. Instead they do a little bit of half-ass analysis and then everyone proclaims Craig is a fraud. This is Craig's point! I simply wanted to have a theoretical discussion in the Bitcoin Technical Discussion subforum and instead had my legitimate inquiry vaporized by the Bitcoin maximalist "forum-Hitler" moderator who uses the moniker Gmaxwell or in real life Gregory Maxwell. And we have all his underlings here who promulgate his shitty attitude and actions.

Hey TPTB_need_war, I love what you're doing, but dude, tune down the arrogance a tiny bit... You're more effective and influential as a gentle leading researcher than as a jackass with a high opinion of himself and a low opinion of less technically proficient people. Quit calling people idiots and retards if you want to have greater impact and be more appreciated by the community.


Posting what you're posting, people invested will act emotionally, and you then exacerbate the reactions with your insults. They are reflecting to you what you are putting out.

Since this thread has changed from a discussion about the deletion of the thread in question (was it ever?) to a continuece of the deleted thread itself, I guess I will give my input on the OP's original concern.

(Note that I am far from an expert on the subject). My understanding is that you can potentially sign two different "messages" with the same private key and produce the same valid signature. I would note that it is trivial to validate if any "message" is signed by a particular private key by looking at only the signature. 

If Wright wanted to sign a message that appears to be from a particular private key, that uses a particular signature then I would speculate that he would simply check a large volume of messages until he finds one that, when signed the signature matches the signature that he wishes to use. If this is true then he would have to expand a very large amount of resources to produce his supposed signed message.

I would say that a "worse case" scenario would be that Wright figured out a way to trivially figure out multiple "messages" when both the public key and signature are known. Since he has an unlimited amount of messages that he can sign to make it look like he has possession of an unencrypted version of a given private key, this does not matter because no matter what message that he signs, it will appear that he owns the private key in question.

However to spend BTC that was previously sent to a particular BTC address, you will need to sign a message that contains the specific inputs that you are trying to spend and you (should) control the private key at which the message spends the BTC to. This will greatly reduce the potential valid messages that you can "sign" when knowing only the public key and the signature. I think it is probably safe to say that no money will be lost even if the largest unspent input was one satoshi.

In both of the above scenarios, the "value" of a signed message is decreased, however if the person validating the signed message provides the specific message that needs to be signed then this is a non-issue, at least if my understanding is correct, which it may not be.

So more of an exploit then? IMO, these are good questions to ask and if someone thinks it's just a misunderstanding then let's enlighten each other instead of bashing the questioner. I would also like to hear an answer to your question.

If you believe that, you are dumber than I thought.

Perhaps you aren't even a programmer?

Of course one can write a script to hash all continuous portions of the Sartre document and check against the hash and then show that he could not possibly be correct with any contiguous portion of the Sartre document that was claim to have been signed for.

Please don't waste my time with your inane inability to understand rudimentary concepts.  Even Yarkol already explained it.


I will proceed to explain once you confirm that do not understand why Merkle–Damgård construction is relevant? Either explain or admit you don't know. So I can proceed to teach you something. You are wasting my scarce time with your stalling/deception tactics and trolling.

Next time you will realize not to fuck with me, because I know a lot more than you assume.

Specifically I am not alleging something is maliciously hiding in the source code.

I am asking if the double hashing could possibly be itself a cryptographic hole that enables someone to preimage via collisions an existing signature so as to prove they signed a message from that key.

Apparently the double hash is also on the public key as well as on the hash that is signed? If true, this means that someone might be able to preimage a collision on the hash(hash(public key)) and thus spend other people's coins as well.

You could at a minimum disprove that any contiguous portion of the document can't match the hash. You all haven't done that, thus you are derelict. You all shouldn't go spouting off "Craig a fraud" without even attempting to verify some basic things such as whether drcraigwright.com is his website and whether any portion of the text could match the hash that was signed.


'backsplaining.


See above. REKTED.


Which is technically incorrect, but I will come back to that point to REKT you after we finish this.


So tell me the reason? Obviously I didn't ask the question to only receive a "yes". Anyone can say "yes". I want you to prove you understand how cryptographic hash functions are constructed and prove you have knowledge about how collision attacks are often constructed. Because these are things I had researched in the past. You've had enough delay to google it by now, so surely you can cheat and tell me?


That is the sort of reply which the linked article explains you would make. So you've confirmed it. Thanks.

Jezee guys he is just asking us to look at the code. It's not a bad idea to peek at the publicly available source code from time to time. Fortunately this is an open source project and that allows us to be certain that nothing malicious is in the code. I'll go through it tonight and see for myself. A "backdoor" is not hide-able in the source.

I do not remember making any such insult. Please quote them and don't allege something you can't demonstrate, for that is a very slimy tactic.


Even when threads are moved to the Trashcan, we get a link showing they have been. Gmaxwell has some sort of super powers as a mod. I have no idea what kind of incestuous relationship is going on between theymos and Gmaxwell, but it doesn't really matter since Bitcoin is basically destroyed now with 70% of the mining controlled by China, soon to be 98+%, and with Blockstream implementing their SegWit soft fork Trojan Horse so as Matonis admits can end up increasing the 21 million coins limit.

The entire ecosystem is headed for a clusterfuck.


Not at all. If the drcraigwright.com is a farce, then nothing has been shown to be untrue about what Wright allegedly proved in private.

This is a masterful chess game being played.

And it is making everyone look like a fool, including those who said Craig was confirmed to be a fraud.

And including yourself for alleging that I speak FUD.

Those who have disingenuous intentions and attitudes eventually get what they deserve and that will include yourself.

If we are basing it on the drcraigwright.com website "proof", then the Sartre document is the one claimed to have been hashed, but he didn't disclose what portion of that document.

Nice try. Fail.

My point is the you Bitcoin zealots didn't do your homework. Haha. You also didn't even validate if that was his official website. You guys are derelict, as well as censoring free speech and technical discussion. No wonder you will end up in failure mindlessly following Blockstream's SegWit soft forking Trojan Horse.


I asked you a specific question, "Do you for example even understand why two SHA256 hash function applications in series is not equivalent to 2 x 64 rounds?". I see you are unable to answer it?

After we confirm that you can't answer it, then I will REKT the rest of your technically incorrect response above.


Try reading the linked article to learn more about your character.

Btw, why are you so defensive of a coin that is 70% controlled by China's miners and allegedly soon to be 98.5% controlled. Can you even look in the mirror and not laugh at yourself.