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Author Topic: how many possible private keys can be generated for a public key ?????  (Read 602 times)
blackhat988
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October 08, 2017, 03:22:29 PM
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how many possible private keys can be generated  for a public key Huh??






i am new to this bitcoin community....


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AdolfinWolf
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October 08, 2017, 03:31:03 PM
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how many possible private keys can be generated  for a public key Huh??






i am new to this bitcoin community....




Each public key has one private key, and each private key has one public key. The public key can be expressed in (at least) two formats: compressed and uncompressed. Uncompressed public keys start with 04 when written in hex, and compressed public keys start with 02 or 03. But they represent the same public key.

In short, for every private key, there is 1 public key, and vice versa. But this doesn't account for adresses.

There are 2*256 public keys, but only 2*160 version-0 addresses, so each address actually represents on average 2*96 different public keys.

Which basically means that for every adress, there are alot of public keys, although bruteforce is still not feasible due to the scale of these numbers.




blackhat988
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October 08, 2017, 03:43:13 PM
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how many possible private keys can be generated  for a public key Huh??






i am new to this bitcoin community....




Each public key has one private key, and each private key has one public key. The public key can be expressed in (at least) two formats: compressed and uncompressed. Uncompressed public keys start with 04 when written in hex, and compressed public keys start with 02 or 03. But they represent the same public key.

In short, for every private key, there is 1 public key, and vice versa. But this doesn't account for adresses.

There are 2*256 public keys, but only 2*160 version-0 addresses, so each address actually represents on average 2*96 different public keys.

Which basically means that for every adress, there are alot of public keys, although bruteforce is still not feasible due to the scale of these numbers.




i actually want to know the maximum number of possible private keys for 1 public address
DannyHamilton
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October 08, 2017, 03:56:37 PM
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i actually want to know the maximum number of possible private keys for 1 public address

One.

You will only ever have at most one private key for any P2PKH address.

While there exist on average 296 possible private keys for any given P2PKH address, only one of those will ever be known.

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October 08, 2017, 05:04:58 PM
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i actually want to know the maximum number of possible private keys for 1 public address

There are 2^96 private keys that will work for each address, but you only know the one you have. Finding another one is very difficult, practically impossible with computers in existence today.

But if you are extremely lucky.... 

My Address: 121f7zb2U4g9iM4MiJTDhEzqeZGHzq5wLh
smokeydog
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October 08, 2017, 06:21:22 PM
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You are asking a general question about the subject of encryption.

It's not a topic for a 1 line answer.

Google the following

"asymmetric cryptography"

"what is public private key pair encryption"

Find a copy of Simon Singh's book "The Code Book"

You will learn a lot more by starting there then what you are going to get here.

 -------

Key pair encryption is based on an obscure relationship between larger prime numbers and their products.

first prime number    982450151
second prime number 982451581

product

982450151 * 982451581 = 965209704103638731

The private is key is made up of 982450151 and 982451581
The public key is 965209704103638731

lets says our message is "good luck"
To encrypt the message, send the message  and public key of  965209704103638731 to MAGIC_FUNCTION_1 the result in something like "uhrn973hl"

To dcrypt, send "uhrn973hl" to MAGIC_FUNCTION_2 along with private key 982450151 and 982451581 and the message "good luck" is back

That's .001 percent of this monster from 10000 feet up.   If you really want to understand this type of cryptography you won't get the answer here, you will have a lot of work to do.  Once you understand the cryptography, then you can dive into the topic of digital signatures.   

The easy answers you seek are not here.
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October 13, 2017, 06:28:06 AM
 #7

One per one. It is math that produces the pair and each private key has one public key and that is it. Software wallets might look like that is not the case, but it is. There are hierarchical wallet addresses, but this is more and matter of linking keys and not producing them from the same private key. Imagine a username of 111 is used to produce the password.

The username is multiplied by 2 and the password is then 222, if that is the system, then 111 will always produce 222 and never anything different.
 

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October 15, 2017, 06:06:07 AM
 #8

You generate public key along with the public key. So you cannot generate more private keys from a single public key.

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October 15, 2017, 09:14:10 AM
 #9

just one and it is generated at the time of generating the public key by the same algorithm. so keep the private key safe, ofcourse if you use electrum you can "view" the private key anytime after entering the passphrase.. some wallets do not allow you private key access so beware of these, they have complete access to your coins 

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October 15, 2017, 10:03:24 AM
 #10

...
Key pair encryption is based on an obscure relationship between larger prime numbers and their products.

first prime number    982450151
second prime number 982451581

product

982450151 * 982451581 = 965209704103638731

The private is key is made up of 982450151 and 982451581
The public key is 965209704103638731
...
How does this play with bitcoin priv keys?
I understand these principles, and the underlying math. Also read about ECDSA and points on the curve. This is what probably happens with open or libressl?
 $ openssl ecparam -genkey -name secp256k1 -rand /dev/urandom -out $PRIVATE_KEY

However: I read, that bitcoin priv keys are a random string of hex chars (2^64 Bytes), that can be generated by rolling dice. And eventually  converted to a hex representation (see e.g. here: http://www.swansontec.com/bitcoin-dice.html).

I think I am looking to match these two different approaches to the priv key. How do they "match"?
In your example what would the private key look like? The pub key is clear, would the priv key have some additional random chars (seed)?
DannyHamilton
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October 15, 2017, 12:27:51 PM
 #11

- snip -
Key pair encryption is based on an obscure relationship between larger prime numbers and their products.
- snip -
How does this play with bitcoin priv keys?

It does not.

smokeydog doesn't know what he's talking about.  He's posting nonsense.

The difficulty of prime number factorization is what supplies the security for RSA.  Bitcoin does not use RSA, it used ECDSA.

The security of ECDSA comes from the difficulty of calculating a discrete logarithm, not prime number factorization.

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