Quote from: TrumenPack on November 06, 2018, 06:57:35 PM

Greetings to All! If there are people who can help me? My task is to use the BitCrack program to find one private key from 10,000,000 Bitcoin Addresses. This is my scientific work. I created a theme and described:
https://bitcointalk.org/index.php?topic=5060735.msg47651430#msg47651430

This doesn't make any sense.
It is very simple to do what TrumenPack says, in this way:

1) I generate a random public key P1 (P1 is a point of secp256k1 curve)


2) Then I generate 10,000,000 consecutive public keys in this way:

   P2 = P1 + G
   P3 = P2 + G (= P1 + 2*G)
   P4 = P3 + G (= P1 + 3*G)
   ....
   P27589 = P1 + 27588*G
   .
   P10000000 = P1 + 9999999*G

3) I get from each public key the address:

   address1 = hash160 (P1)
   address2 = hash160 (P2)
   address3 = hash160 (P3)
   ....
   address10000000 = hash160 (P10000000)

Let's say now that address27589 = "18HPzD22qaUvJL69yjF3vUXx7Kfg7o5q7F". If (it is a very big if) you find out that the private key is "100A" (hex format, try to put this value here --> http://gobittest.appspot.com/Address, i. e. private key = 1*2^12 +10 = 4106), then it would be very simple to get the private keys of all the other addresses*** too:

private key of address1 = (private key of address27589 - 27588) mod n
.....
private key of address27588 = private key of address27589 - 1 = 4105
private key of address27589 = 4106
private key of address27590 = private key of address27589 + 1 = 4107
private key of address27591 = private key of address27589 + 2 = 4108
.....
private key of address10000000 = private key of address27589 + 9.972.411 = 9.976.517

***this is true only if you find the private key to the public key P27589. There are about 2^96 different valid private keys for the address27589!