The Large Bitcoin (BTC) Collider: a Pool of Computers Attempting to Brute Force Bitcoin (BTC) Private Keys, Calculates 300-500 Million Keys Per Second and 36,080 Trillion Private Keys Generated So Far, but Would Still Take at Least 2.58X1024 Years to Find a Private Key Collision

March 21, 2019 / by Zachary Mashiach

In July 2016, Bitcointalk user Rico666 began to formulate the large Bitcoin (BTC) collider, a project to determine how feasible it is to brute force Bitcoin (BTC) private keys via a hash collision.

The initial program was able to calculate two million private keys per second. By August 2016, Rico666 launched a pool for this project where users can aggregate their computing resources to accelerate the calculation of Bitcoin (BTC) private keys. The LBC program was repeatedly improved, and as of this writing, the LBC is generating Bitcoin (BTC) private keys at the blazing speed of 300-500 million per second. After nearly three years of continuous searching and efficiency improvements, the LBC has found 36,080.1 trillion Bitcoin (BTC) private keys.

This may sound like a tremendous amount of Bitcoin (BTC) private keys, and it is, but the total number of possible Bitcoin (BTC) private keys is an astronomical 2256. In scientific notation, this is roughly 1.157X1077, as compared to 2X1023 stars in the universe, and around the 1078 to 1082 atoms in the entire universe.

Compare this to the approximately 24 million Bitcoin (BTC) addresses that have a balance greater than zero. This shows Bitcoin’s (BTC) extreme cryptographic security.

The scientific goal of the LBC project is to find a private key collision, which would be the generation of a private key that is different from the original private key that someone generated when they created a Bitcoin (BTC) address. There are 2160 possible Bitcoin (BTC) public addresses, but 2256 possible private keys, meaning that there are 296 private keys for each public address and just as many possible collisions. If a collision were to be found via brute force, it would prove that Bitcoin (BTC) is not 100 percent cryptographically secure.

However, past this noble scientific goal, the real allure of joining the LBC pool is the possibility of finding an address with Bitcoin (BTC) in it. Some Bitcointalk users have compared it to playing a Bitcoin (BTC) lottery where the tickets are free but the chances of winning are minuscule.

Perhaps users imagine they will get extremely lucky and find a Bitcoin (BTC) address with a fortune of Bitcoin (BTC) sitting in it.

The LBC scans the possible private keys up to 160 bits or 2160, instead of the full 2256 private keys. This is because there are only 2160 possible Bitcoin (BTC) public addresses. However, there is some debate as to whether this is a complete search of all Bitcoin (BTC) addresses since a fraction of the private keys in the 2160 space may be for the same public address. To be truly thorough, the LBC would have to scan the full 2256 space.

The LBC scans the 160-bit space in order so that pool members do not redundantly generate keys. So far, the LBC has searched 55 bits, and the speed to search each successive bit becomes exponentially slower as the search progresses.

It is estimated that a private key collision should occur within 134.58 bits, assuming a uniform distribution of keys through the 160-bit space. If this theory is true, 32,487,405,889,012,096,286,998,975,580 trillion keys must be computed to find a collision.

At the speed of 400 million private keys generated per second, it would take 9.18X1060 years for the LBC to generate all 2256 Bitcoin (BTC) private keys, 1.158X1032 years for the 160-bit space to be searched, and 2.58X1024 years to search the 134.58-bit space, which should theoretically be enough to find a collision.

This shows how extremely cryptographically secure Bitcoin (BTC) is. Even for the LBC — which consists of a sizeable pool of processing power, has constantly updated its code to improve efficiency, and is consistently achieving speeds of 300-500 million keys per second — there is practically no chance that the LBC will find a Bitcoin (BTC) private key with money in it.

So far, several Bitcoin (BTC) private keys that have funds in them have been found according to Rico666. The first contained 0.007899 Bitcoin (BTC) which was deposited in May 2014 and found by LBC in October 2016, a couple of months after the pool began searching. Rico666 claims that he did not place the funds in this address and speculates this is perhaps the first collision.

The chances of such a collision are infinitesimally small and unlikely to happen by chance. It has been speculated that someone planted the funds in that address as a canary in the coal mine for brute force attacks since this address was in an easy and early part of the domain of Bitcoin (BTC) keys.

The private key for this address consisted mostly of zeroes. Also, users other than Rico666 have been known to plant Bitcoin (BTC) near the LBC search space for fun. Any finds should be treated with skepticism due to this.

Another Bitcoin (BTC) address was found in January 2017 and contained 0.0001 Bitcoin (BTC). The funds were deposited into this address 3 months before the LBC launched, raising skepticism that it was planted. Another address found in March 2017 contained 0.00001 Bitcoin (BTC), and Rico666 claimed this to be legitimate. However, these funds were suspiciously deposited around the same day the LBC project started.

No private keys that contain a balance have been discovered by the LBC in the 2 years since March 2017.

Even if these addresses are legitimate and not pre-planted by anyone, they are not confirmation of a collision, because another private key corresponding to the same address would have to be known about or found to prove a collision. This shows how extremely difficult the LBC project is. That being said, there is only a 1.26X10-29 chance that any keys found by LBC are the original key the address was created with, so any keys containing funds that are found by LBC would likely be collisions.  

As for the funds found in these few addresses, they were transferred to a custodial address, and the original owner of the address was given 6 months to claim the Bitcoin (BTC) before funds were distributed to the LBC pool. This is the system going forward for LBC. This is apparently in accordance with European law for “finders keepers.”

That being said, it is extremely unlikely that someone who has their funds compromised by LBC would know about LBC or this custodial system. Therefore, if LBC finds funds in any address, it will likely take them for profit.

Controversy Over Program Backdoor

Users discovered that the LBC administrator can remotely access any computer which is running the program. Rico666 claims this is a necessity so that users are not maliciously saying work has been completed when the work had not been done. However, this does mean users of LBC must trust Rico666. Regarding this, Rico666 says “Let us rephrase it in simple terms: If you want to board a plane, for the planes’ — and thus also your security, you have to undergo certain scanning procedures and comply to restrict some of your freedom or you will not board that plane. Same story.” And “If you don’t trust the LBC, don’t use the LBC.”

It is up to each user to decide whether they trust the founder of a program whose sole purpose is to brute force Bitcoin (BTC) private keys.

It gets worse. Rico666 is a member of the Proof of Capacity Consortium (PoCC), which was discovered to be using pool mining power to merge mine and attack Bitcoin HD (BHD) without miner’s permission. This ultimately resulted in the PoCC resigning from being the lead Burstcoin (BURST) dev team while stubbornly offering no compensation to miners.

Connecting these two stories, it is interesting that PoCC member Rico666 is the one behind the LBC, a program designed to brute force Bitcoin (BTC) private keys while also having backdoor access to users’ computers, and that eventually the PoCC was found to be abusing its backdoor access to miners’ computers for profit. This certainly raises suspicion that the LBC’s backdoor to users’ computers may be used for profit.

The LBC Proves Bitcoin’s (BTC) Security

Ultimately, regardless of any controversy regarding the LBC backdoor, the LBC project demonstrates how secure Bitcoin (BTC) is. Rico666 and others users worked hard for years to make the LBC program as fast as possible at generating keys, and numerous users have been pooling their computing power for nearly three years now, and even with that effort, it would likely take 2.58X1024 years to find any legitimate private key collision.

There is plenty of doubt surrounding the three keys the LBC claims to have found, and these are likely not legitimate collisions.

So what all this means is that Bitcoin (BTC) is extremely cryptographically secure, and the LBC has demonstrated how a team of hackers working together for years cannot compromise Bitcoin (BTC) private keys with brute force. Even with the best modern day technology and far more processing power and efficiency than the LBC has, it would take many orders of magnitude longer than the age of the universe to brute force attack a Bitcoin (BTC) private key that actually had money in it.