Rob P.



Offline



Activity: 84

Merit: 10







MemberActivity: 84Merit: 10 Re: How many possibly bitcoin addresses are there exactly? And how long does it... June 29, 2011, 11:12:01 PM #5



To put that in perspective, there are only 2^63 grains of sand on all of the beaches of the Earth (



Before you run out and build an RPC program to generate addresses, do some math first.



Or read this: http://forum.bitcoin.org/index.php?topic=1387.0



The total pool of Bitcoin addresses in use is so minuscule compared to the total population of addresses you *could* create, that the odds of you creating a private key for an address that is already in use is so small (near zero), that you'd be better off just writing malware to infect computers and just steal them. The total address space is 2^160To put that in perspective, there are only 2^63 grains of sand on all of the beaches of the Earth ( http://www.hawaii.edu/suremath/jsand.html Before you run out and build an RPC program to generate addresses, do some math first.Or read this: http://forum.bitcoin.org/index.php?topic=1387.0The total pool of Bitcoin addresses in use is so minuscule compared to the total population of addresses you *could* create, that the odds of you creating a private key for an address that is already in use is so small (near zero), that you'd be better off just writing malware to infect computers and just steal them. --



If you like what I've written here, consider tipping the messenger:

1GZu4CtHa6ai8iWoWiVFxV5VVoNte4SkoG



If you don't like what I've written, send me a Tip and I'll stop talking.

gigabytecoin



Offline



Activity: 280

Merit: 250







Sr. MemberActivity: 280Merit: 250 Re: How many possibly bitcoin addresses are there exactly? And how long does it... June 30, 2011, 08:53:43 PM #7 Quote from: JoelKatz on June 29, 2011, 03:21:07 PM And if you're thinking what I think you're thinking, remember that you don't actually have to find their private key to claim someone else's bitcoins. All you have to do is find any one of the roughly 2^96 private keys whose corresponding public key hashes to that address.

Ok so for somebody to be lucky enough to steal the bitcoins out of my main backup address...



They first need to generate my address which could be any one of 2^160 possibilities. And then they must generate the corresponding public key that gives them access to the bitcoins in my address? Of where there at 2^96 possibilities?



Or must they simple generate 2^96 bitcoin keys... at which point they would control every single bitcoin address in the world? Ok so for somebody to be lucky enough to steal the bitcoins out of my main backup address...They first need to generate my address which could be any one of 2^160 possibilities. And then they must generate the corresponding public key that gives them access to the bitcoins in my address? Of where there at 2^96 possibilities?Or must they simple generate 2^96 bitcoin keys... at which point they would control every single bitcoin address in the world?

JoelKatz



Offline



Activity: 1596

Merit: 1010





Democracy is vulnerable to a 51% attack.







LegendaryActivity: 1596Merit: 1010Democracy is vulnerable to a 51% attack. Re: How many possibly bitcoin addresses are there exactly? And how long does it... July 01, 2011, 12:35:02 AM #8 Quote from: gigabytecoin on June 30, 2011, 08:53:43 PM Quote from: JoelKatz on June 29, 2011, 03:21:07 PM And if you're thinking what I think you're thinking, remember that you don't actually have to find their private key to claim someone else's bitcoins. All you have to do is find any one of the roughly 2^96 private keys whose corresponding public key hashes to that address.

Ok so for somebody to be lucky enough to steal the bitcoins out of my main backup address...



They first need to generate my address which could be any one of 2^160 possibilities. And then they must generate the corresponding public key that gives them access to the bitcoins in my address? Of where there at 2^96 possibilities? Ok so for somebody to be lucky enough to steal the bitcoins out of my main backup address...They first need to generate my address which could be any one of 2^160 possibilities. And then they must generate the corresponding public key that gives them access to the bitcoins in my address? Of where there at 2^96 possibilities?



Quote Or must they simple generate 2^96 bitcoin keys... at which point they would control every single bitcoin address in the world? The most sensible way to attempt the attack (which is still insane) is to generate random private keys, calculate the corresponding addresses, and then see if that address has a non-zero balance. I believe there are 2^160 possible addresses. So even if there are 1,000,000,000 addresses with non-zero balances, your odds of getting a non-zero balance on a single key are 1 in 2^128.



So brute-forcing a single bitcoin address with a non-zero balance (assuming there are a billion of them, which is generous), is as hard as, say, brute-forcing a given 128-bit AES key.

Generating the public key is trivial.The most sensible way to attempt the attack (which is still insane) is to generate random private keys, calculate the corresponding addresses, and then see if that address has a non-zero balance. I believe there are 2^160 possible addresses. So even if there are 1,000,000,000 addresses with non-zero balances, your odds of getting a non-zero balance on a single key are 1 in 2^128.So brute-forcing a single bitcoin address with a non-zero balance (assuming there are a billion of them, which is generous), is as hard as, say, brute-forcing a given 128-bit AES key. I am an employee of Ripple. Follow me on Twitter @JoelKatz

1Joe1Katzci1rFcsr9HH7SLuHVnDy2aihZ BM-NBM3FRExVJSJJamV9ccgyWvQfratUHgN

PGSystemTester



Offline



Activity: 1

Merit: 7







NewbieActivity: 1Merit: 7 Re: How many possibly bitcoin addresses are there exactly? And how long does it... July 07, 2018, 08:50:09 PM

Last edit: July 18, 2018, 08:29:05 PM by PGSystemTester Merited by theymos (2), DarkStar_ (2), o_e_l_e_o (2), ETFbitcoin (1) #16 Quote from: schnuber on December 22, 2013, 04:36:31 PM Ok so the quote that there are 2^96 private keys is wrong then



I realize this is an old discussion but this thread now appears towards the top of searches for "How many bitcoin addresses are there."



Here are some exact numbers for Bitcoin and Ethereum... and all of their relatives.



The total possible number of addresses is exactly 2^160.

As a decimal number (what most people consider "normal") this is 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,975.

As a hexidecimal, this number is: FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF



The total number of possible private keys is frequently listed as 2^256 and for all sensible discussion, this is correct.

However, technically there are a few less because of the secp256k1 Curve usage. Words cannot express how insignificant of a difference this is from 2^256. Imagine all of earth's beaches. Now imagine them with one less grain of sand. Even that is overstating the difference.



But since we're talking exact numbers, here are the exact number of private keys possible. I'll list them compared to 2^256

Code: Decimal

115,792,089,237,316,195,423,570,985,008,687,907,852,837,564,279,074,904,382,605,163,141,518,161,494,336 (exact private key maximum)

115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,935 (2^256)



Hexidecimal

FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4140 (exact private key maximum)

FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF (2^256)





Going back to the discussion of how long it would take to brute force attack a specific address -- quite simply not possible with today's technology. The quote of 2^96 represented how many potential PRIVATE keys would work for a single PUBLIC key if they were evenly distributed (not how many total private keys were there). A brute force attack would require an approach of using all 2^256 since there's no way to tell if a private key will generate an address that's been used or not. At some point (2^200?) all 2^160 addresses would be accounted for, but again, impossible with today's technology. I realize this is an old discussion but this thread now appears towards the top of searches for "How many bitcoin addresses are there."Here are some exact numbers for Bitcoin and Ethereum... and all of their relatives.The total possible number of addresses is exactlyAs a decimal number (what most people consider "normal") this is 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,975.As a hexidecimal, this number is: FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFFThe total number of possible private keys is frequently listed asand for all sensible discussion, this is correct.However, technically there are a few less because of the secp256k1 Curve usage. Words cannot express how insignificant of a difference this is from. Imagine all of earth's beaches. Now imagine them with one less grain of sand. Even that is overstating the difference.But since we're talking exact numbers, here are the exact number of private keys possible. I'll list them compared to 2^256Going back to the discussion of how long it would take to brute force attack a specific address -- quite simply not possible with today's technology. The quote of 2^96 represented how many potential PRIVATE keys would work for aif they were(not how many total private keys were there). A brute force attack would require an approach of using all 2^256 since there's no way to tell if a private key will generate an address that's been used or not. At some point (2^200?) all 2^160 addresses would be accounted for, but again, impossible with today's technology.