Example of BTC collision (2 different priv key to the same BTC address)

[MrFreeDragon]

There are almost 2^256 possible private keys, and every key could be used to generate the BTC address. However the amount of possible BTC addresses is only 2^160 (because of ripemd160 hash function).

Is there any real example of at least 2 (or may be more) DIFFERENT private keys resulting to the same bitcoin address?

[1714035491]

1714035491

[Rath_]

Is there any real example of at least 2 (or may be more) DIFFERENT private keys resulting to the same bitcoin address?

Take a look at the Large Bitcoin Collider project. See this post. They have managed to find a few collisions. This page describes in detail what kind of collision the pool is looking for.

[MrFreeDragon]

Is there any real example of at least 2 (or may be more) DIFFERENT private keys resulting to the same bitcoin address?

Take a look at the Large Bitcoin Collider project. They have managed to find a few collisions. This page describes in detail what kind of collision the pool is looking for.

Thank you. I have already read that project before making a post here.
LBC just are finding the private key to the address with the balance. Most of their found addresses were just addreses from 32 BTC transaction puzzle.

My question here is about REAL example of at leat two different private keys leading to the same bitcoin address. And it does not matter if that address has the balance.

[AdolfinWolf]

Thank you. I have already read that project before making a post here.
LBC just are finding the private key to the address with the balance. Most of their found addresses were just addreses from 32 BTC transaction puzzle.

My question here is about REAL example of at leat two different private keys leading to the same bitcoin address. And it does not matter if that address has the balance.

Without an exploit of sorts, i think it is highly unlikely that that has happend (or could happen.).

Actually finding any pair of different private keys that generate the same public key or address would be quite difficult. Either it would involve a huge amount of computation and/or luck, or it would be due to finding a serious vulnerability in the algorithm(s) used.

See: https://bitcoin.stackexchange.com/a/25071


This user posts an interesting answer which i don't fully understand to what exactly it refers to: https://bitcoin.stackexchange.com/a/27027
Anyone cares to explain?

[MrFreeDragon]

This user posts an interesting answer which i don't fully understand to what exactly it refers to: https://bitcoin.stackexchange.com/a/27027
Anyone cares to explain?

Thank you for sharing!

That user explains that the private keys out of order (bitcoin order is FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141, it is the total amount of ECDSA curve points) result to the same BTC addresses from the start.
As an example, the private keys 000000000000000000000000000000014551231950b75fc4402da1732fc9bebb and fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc leads to the same bitcoin address 136jNVfhtp7mKVfHjfkBcay1cbMG8GsC5Z (compressed).
Good finding!

However i want to find 2 different private keys inside the order leading to the same BTC address

[gmaxwell]

Take a look at the Large Bitcoin Collider project.

That project is a malware scam. They promote their activity using jibberish technobabble and have been caught distributing actual backdoored software.

[nc50lc]

Is there any real example of at least 2 (or may be more) DIFFERENT private keys resulting to the same bitcoin address?

Take a look at the Large Bitcoin Collider project. They have managed to find a few collisions. This page describes in detail what kind of collision the pool is looking for.

Those "collisions" aren't really collisions.
They mostly hunt for purposely generated "weak" private keys, for example: this puzzle transaction.

That example contains addresses derived from private keys ranging from
0000000000000000000000000000000000000000000000000000000000000001 to
000000000000000000000000000000000000000af55fc59c335c8ec67ed24826 and so on...
which apparently, can be bruteforced with enough computing power.

[MrFreeDragon]

However i want to find 2 different private keys inside the order leading to the same BTC address

Likely you will not able to find it, and I don't think it will happen even future. A single btc address could not be belongs to two or more private keys. If so, then fund will be stolen from the first address. Because when you will see that you new genarated address contained with fund then likely you will move it to another address. And I don't think blockchain designed like that.

I understand that it is very unlikely. But a BTC address is created from the private key. The total possible private keys are almost 2^256 (to be exact: FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141). The public key is also within the same range. However, later due to hash operations (SHA256 and ripemd160), the total possible combinations of final addresses is only 2^160. So, statistically each address on average could have 2^(256-160) = 2^96 possible private keys which is very large number: 79 228 162 514 264 337 593 543 950 336 (roundly 10^29). So, there should be the situation there several DIFFERENT private keys within the bitcoin order lead to the same bitcoin address.

You stated that "A single btc address could not be belongs to two or more private keys", but how is it true if the total possible combinations of bitcoin legacy addresses are 2^96 times less than the total possible combinations of priivate keys?

[DaCryptoRaccoon]

However i want to find 2 different private keys inside the order leading to the same BTC address

Likely you will not able to find it, and I don't think it will happen even future. A single btc address could not be belongs to two or more private keys. If so, then fund will be stolen from the first address. Because when you will see that you new genarated address contained with fund then likely you will move it to another address. And I don't think blockchain designed like that.

I understand that it is very unlikely. But a BTC address is created from the private key. The total possible private keys are almost 2^256 (to be exact: FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141). The public key is also within the same range. However, later due to hash operations (SHA256 and ripemd160), the total possible combinations of final addresses is only 2^160. So, statistically each address on average could have 2^(256-160) = 2^96 possible private keys which is very large number: 79 228 162 514 264 337 593 543 950 336 (roundly 10^29). So, there should be the situation there several DIFFERENT private keys within the bitcoin order lead to the same bitcoin address.

You stated that "A single btc address could not be belongs to two or more private keys", but how is it true if the total possible combinations of bitcoin legacy addresses are 2^96 times less than the total possible combinations of priivate keys?

This is why brainflayer runs against a bloom filter of ripemd160 hashes instead of the actual main address it hunts for the corresponding PK value in relation to the Ripemd160 hashes.
it's also open source unlike the Large Bitcoin  MALWARE Collider posted above.

https://github.com/ryancdotorg/brainflayer

[AdolfinWolf]

And I don't think blockchain designed like that.

Except that it is possible. See the quote above, (or below)

Yes, you can have two keys generate the same address.

There are 2^160 possible addresses, and 2^256 possible private keys, so each address corresponds to roughly 2^(256-160)=2^96 private keys. Any of these will generate the same address and thus be able to spend the money owned by that address. Since 2^160 is so large, however, it would take a near-eternity to find any collisions.

Whether two private keys can generate the same public key is another question. I think the answer is yes, but I am not sure on that. The public key in uncompressed form consists of two 256-bit numbers, which are X and Y coordinates on an elliptic curve. However, the compressed form is just the X coordinate plus a bit, from which you can calculate the whole public key. This means the space is (at most) 2^257. Unless there is a one-to-one mapping due to the mathematical properties of the cryptography used, each compressed public key corresponds to roughly 0.5 private keys (with the same distribution you'd get from picking a random number from 1 to 2^257, 2^256 times), so some private keys will collide, while others will not.

Actually finding any pair of different private keys that generate the same public key or address would be quite difficult. Either it would involve a huge amount of computation and/or luck, or it would be due to finding a serious vulnerability in the algorithm(s) used.

[odolvlobo]

There are almost 2^256 possible private keys, and every key could be used to generate the BTC address. However the amount of possible BTC addresses is only 2^160 (because of ripemd160 hash function).

Is there any real example of at least 2 (or may be more) DIFFERENT private keys resulting to the same bitcoin address?

Answering your question ... So far there is no known collision.

Furthermore, the probability of a collision ever occurring by chance is extremely low. Imagine that 10 billion transactions, each with a new address, are added to the block chain every year for 1 million years. That's about 2⁵³ transactions, which is still very negligible compared to 2¹⁶⁰.

[kzv]

When you find a collision, you can get your reward in BTC:
SHA256 collision cost 0.27609251 BTC
RIPEMD160 collision cost 0.11476888 BTC
RIPEMD160(SHA256()) collision cost 0.10026873 BTC
SHA256(SHA256()) collision cost 0.10026873 BTC

Read original topic of the bounty https://bitcointalk.org/index.php?topic=293382.msg3142575#msg3142575

[MrFreeDragon]

When you find a collision, you can get your reward in BTC:
SHA256 collision cost 0.27609251 BTC
RIPEMD160 collision cost 0.11476888 BTC
RIPEMD160(SHA256()) collision cost 0.10026873 BTC
SHA256(SHA256()) collision cost 0.10026873 BTC

Read original topic of the bounty https://bitcointalk.org/index.php?topic=293382.msg3142575#msg3142575

Thank you for sharing! I wanted to find such collision just for my curiosity, however it also could be paid   
Can you please explain how did you calculate these bounties for each collision?

[MrFreeDragon]

Regarding your original question i must admit I have found such addressess and possess the private key for it, but cannot for various reason share which one and how I came in possession of it.

/KX

This was the exact thing i want to know    If you can not tell everything, can you just say how many private keys do you have to the same address? And also how many addresses do you have with more than one private key?

[pooya87]

can you just say how many private keys do you have to the same address? And also how many addresses do you have with more than one private key?

we are not "mapping" keys to addresses to have 1:X ratio. we are hashing the public key which returns a random result so there is no fixed ratio. there is a chance of collision because the hash size (160 bits) is smaller than the number of private keys (a little less than 256 bit) but so far nobody has found any collisions and will not find any for a very long time. anybody who claims otherwise without proof is most probably lying.

[MrFreeDragon]

can you just say how many private keys do you have to the same address? And also how many addresses do you have with more than one private key?

we are not "mapping" keys to addresses to have 1:X ratio. we are hashing the public key which returns a random result so there is no fixed ratio. there is a chance of collision because the hash size (160 bits) is smaller than the number of private keys (a little less than 256 bit) but so far nobody has found any collisions and will not find any for a very long time. anybody who claims otherwise without proof is most probably lying.

As for the ratio I knoe that this ratio could not be. There just ann average chance that one address could have 2^96 private keys.
I asked "how many" because this guy wrote that he had such keys, but didnot want to give the example and did not say the reason why he cuuld not tell:

Regarding your original question i must admit I have found such addressess and possess the private key for it, but cannot for various reason share which one and how I came in possession of it.

/KX

[bartekjagoda]

can you just say how many private keys do you have to the same address? And also how many addresses do you have with more than one private key?

we are not "mapping" keys to addresses to have 1:X ratio. we are hashing the public key which returns a random result so there is no fixed ratio. there is a chance of collision because the hash size (160 bits) is smaller than the number of private keys (a little less than 256 bit) but so far nobody has found any collisions and will not find any for a very long time. anybody who claims otherwise without proof is most probably lying.

As for the ratio I knoe that this ratio could not be. There just ann average chance that one address could have 2^96 private keys.
I asked "how many" because this guy wrote that he had such keys, but didnot want to give the example and did not say the reason why he cuuld not tell:

Regarding your original question i must admit I have found such addressess and possess the private key for it, but cannot for various reason share which one and how I came in possession of it.

/KX

And post got deleted.

[turndealer]

can you just say how many private keys do you have to the same address? And also how many addresses do you have with more than one private key?

we are not "mapping" keys to addresses to have 1:X ratio. we are hashing the public key which returns a random result so there is no fixed ratio. there is a chance of collision because the hash size (160 bits) is smaller than the number of private keys (a little less than 256 bit) but so far nobody has found any collisions and will not find any for a very long time. anybody who claims otherwise without proof is most probably lying.

As for the ratio I knoe that this ratio could not be. There just ann average chance that one address could have 2^96 private keys.
I asked "how many" because this guy wrote that he had such keys, but didnot want to give the example and did not say the reason why he cuuld not tell:

Regarding your original question i must admit I have found such addressess and possess the private key for it, but cannot for various reason share which one and how I came in possession of it.

/KX

Talking about Wif format

Here are some privatekeys Leading to same addresses [Compressed and Uncompressed]

KxqjPLtQqydD8d6eUrpJ7Q1266k8Mw8f5eoyEztY3Kc6jtMsgkXp
cPCirFtGH3KUJ4ZusGdRUiW5iL3Y2PEM9gxSMRM3YSG6Eon9heJj
5JBb5A38fjjeBnngkvRmCsXN6EY4w8jWvckik3hDvYQMnakxLRd

Leads to
1C4LeCvgTFJJjxiuPMGgW26PAqmfEBfSL5 [Compressed]
1DU46StbrH652jBv7dE8DWMg4rTRy2rU5W [Uncompressed]

Thanks

[PrivatePerson]

Privkeys:
KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYpCemuaUp7NigjvtJug
L5oLkpV3aqBjhki6LmvChTCV6odsp4SXM6LBVeqHTSj1w9XhwfuR   (outside of bitcoins curve range)
Address:
1Me6EfpwZK5kQziBwBfvLiHjaPGxCKLoJi

[BrewMaster]

Here are some privatekeys Leading to same addresses

there are different ways of representing numbers:

Code:

1
I
one
0x01
00000001

but it doesn't mean we have dozens of number one! we only have 1 value that we use different encodings for it to represent it (numeral, roaman, text, hex, binary). what you did here was only to change the encoding.

and what you did here is just playing with modular arithmetic.

neither one of these have anything to do with this topic: collision.