Disclosed herein are systems, methods, and non-transitory computer-readable storage media for generating a hash based on the Collatz conjecture. The Collatz conjecture is based on a set of operations for a given number n that are performed iteratively on n, with one operation performed if n is even, and another operation performed if n is odd. Operating on an input value according to the Collatz conjecture for a specified number of iterations produces an output value that can then be used as a hash in a cryptographic function. The hash function performs steps according to the Collatz conjecture, or a modification thereof, on the value n for r iterations, and outputs a resulting hash value. The hash function can apply more complex variations, such as adding multiplication, addition, modulo or other operation(s) in the even and/or odd operations. The hash value can be used to pad blocks of a message.