In A fast quantum mechanical algorithm for database search, Grover provided an algorithm that is threatening to industry-standard symmetric cryptography, like the Advanced Encryption Standard (AES).

Grover’s algorithm can find the input of a black box function, given its output, to a high probability in O(√n) time. Grover’s algorithm is asymptotically optimal. That is, Grover’s algorithm helps quantum computers search possible permutations as fast as is theoretically possible.

The consequence of Grover’s algorithm on industry-standard symmetric cryptosystems is that an attack utilizing Grover’s algorithm would reduce the security of AES-256 to the equivalent security of AES-128.

The general rule of thumb for designing schemes which are resistant to attacks through Grover’s algorithm is to simply double the bit size of the scheme (i.e. use AES-256 instead of AES-128) as Grover’s algorithm can be used to crack a 256-bit scheme in 2^128 iterations rather than 2^256.