What is the mathematical term for a one-to-one correspondence?
In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set. (Wikipedia)
What is the name for the best single-key attack against AES?
A biclique attack is a variant of the meet-in-the-middle (MITM) method of cryptanalysis. It utilizes a biclique structure to extend the number of possibly attacked rounds by the MITM attack. Since biclique cryptanalysis is based on MITM attacks, it is applicable to both block ciphers and (iterated) hash-functions. Biclique attacks are known for having broken both full AES[1] and full IDEA,[2] though only with slight advantage over brute force. It has also been applied to the KASUMI cipher and preimage resistance of the Skein-512 and SHA-2 hash functions. The biclique attack is still (as of April 2019) the best publicly known single-key attack on AES. (Wikipedia)