BCrypt: How to determine whether two hashes refer to the same password

Question

I wonder how BCrypt can infer the correctness of a entered password, if the generated hash is different for each run?

Example:

Given password: "password123"

Lets say, I hash the given password 10 times and receive:

$2a$10$Uw0LDj343yp1tIpouRwHGeWflT3.QjDp9DeJ2XiwTIHf1T.pjEy0i
$2a$10$uYWUCEnh4gn00w57VSrYjej.UvhzBL8Wf2doTAGSGfhUMtuGr5bha
$2a$10$cJi3XOkRxxicDjEBibNhNOg5MGM.G/.p70KE75.44ayPQo8kCDxUu
$2a$10$qLcN2obMThH544U967JM5OS0vtcfP.Iq1.f0mZdvWfyeIoWHyr422
$2a$10$5/JssXqJyGHeMQlB4pr7zebTRFSt/2iwYJHF5f7.jdlTxbH4c9Sjq
$2a$10$La1UQKu306aNWkhhfhC5XeX7mfcnfbSchBIpLG6O57gur/U/n/fua
$2a$10$xTzEGVfc1D1UHFeMO95ktOJGFT79ybKUKN.z.MidMjP1XfAeElNEi
$2a$10$i9Y.1Ix6PL1bDwoTYtC49.Y0LKpar/S5qC1SkzFB4vnafikOhHSga
$2a$10$FJNTj5xeVbIcMaf9EhodHu9jJLrJL53QHQK9OuemwMh3WuTfxXEqu
$2a$10$OXMToK5CXeNtRHC3w7eqe.Mr7p4fJanbE28E2Y3MHh6f6cq1chyE6

If we assume that I store the first hash in my database and a user tries to log in a few hours later with correct password. The hash, which is generated while the user tries to log in, is totally different to the hash I have stored in my database.

How does BCrypt determine whether the two hashes refer to the same password?

Soluk

Answer 1

The hash-values in your example contain all the necessary information to do the verification:

$2y$10$nOUIs5kJ7naTuTFkBy1veuK0kSxUFXfuaOKdOKf9xYT0KKIGSJwFa
 |  |  |                     |
 |  |  |                     hash-value = K0kSxUFXfuaOKdOKf9xYT0KKIGSJwFa
 |  |  |
 |  |  salt = nOUIs5kJ7naTuTFkBy1veu
 |  |
 |  cost-factor = 10 = 2^10 iterations
 |
 hash-algorithm = 2y = BCrypt

As you can see, this string contains the algorithm, the cost factor and the salt. With these parameters you can calculate a comparable hash value from the login password. In PHP you can use the function password_verify() to verify the password, it will extract the cost factor and the salt automatically.

// Check if the hash of the entered login password, matches the stored hash.
// The salt and the cost factor will be extracted from $existingHashFromDb.
$isPasswordCorrect = password_verify($password, $existingHashFromDb);

Discontinuance

Thanks a lot! I understand that it works, but I want to know how. From where have BCrypt the information, that two totally different hashes refer to the same password. As I know BCrypt is an hash algorithm, so it allows no more inference to the output data. How can BCrypt match the hashes? – Soluk

Now I understand why this works: The salt influences the generated hash value. While "decoding", BCrypt can check whether the two hashes matches, because with the information of the plain password (from POST Request), the algorithm, the cost-factor and the salt it is possible to determine whether the two hashes refer to the same password. Thanks for help! – Soluk

@Soluk - Exactly, whenever you calculate a hash with the same parameters, you will get the same hash-value. – Discontinuance