1. National Institute of Standards and Technology (NIST) Special Publication 800-63B
Digital Identity Guidelines: Authentication and Lifecycle Management.
Section 5.1.1.2
Memorized Secret Verifiers: "The use of a one-way function (the approved hash algorithm) on the salt and the password value makes it computationally infeasible to reverse the process and retrieve the password from the stored hash value." This explicitly states that reversing the process is computationally infeasible.
2. MIT OpenCourseWare
6.858 Computer Systems Security
Fall 2014.
Lecture 5: Web Security
Section 3
Passwords: The lecture notes define a one-way function as: "easy to compute H(x)
hard to find x from H(x)." It then describes password cracking as a process of guessing a password x'
computing H(x')
and checking if it matches the stored hash
confirming that the process is one of guessing and comparing
not reversing.
3. Stanford University
CS 155: Computer and Network Security.
Lecture Notes on Passwords and Authentication: The course material states
"Hashes are one-way functions: given y
it is hard to find x such that h(x)=y." It further describes offline attacks (password cracking) as: "Attacker steals hash file... Tries to find x such that h(x) = y... Guess passwords x'
compute h(x')
and check if h(x') = y." This reinforces that the method is iterative guessing and hashing
not mathematical inversion.