key stretching VS key stengthening

Question

To quote from this wiki article -

An alternative approach, called key strengthening, extends the key with a random salt, but then (unlike in key stretching) securely deletes the salt. This forces both the attacker and legitimate users to perform a brute-force search for the salt value.

I am comfortable with what key stretching does, But I am confused on how key strengthening is achieved. How the key can be validated again if the salt is deleted?

Answer 1

The paper on the key strengthening scheme cited in the wiki article is available here.

It seems they're breaking a larger salt up into two smaller salts, a public salt, which is no different than normal salting, and a private salt, which is discarded in order to make password verifications slower. The idea is that all password verifications will be slower because the private salt must always be brute-forced but this will be negligible when the correct password is provided. However, the added processing will slow down brute forcing of the password.