Low-Communication Parallel Quantum Multi-Target Preimage Search

The most important pre-quantum threat to AES-128 is the 1994 van Oorschot–Wiener “parallel rho method”, a low-communication parallel pre-quantum multi-target preimage-search algorithm. This algorithm uses a mesh of p small processors, each running for approximately 2/pt fast steps, to find one of t independent AES keys k1, . . . , kt, given the ciphertexts AESk1(0), . . . ,AESkt(0) for a shared plaintext 0. NIST has claimed a high post-quantum security level for AES-128, starting from the following rationale: “Grover’s algorithm requires a longrunning serial computation, which is difficult to implement in practice. In a realistic attack, one has to run many smaller instances of the algorithm in parallel, which makes the quantum speedup less dramatic.” NIST has also stated that resistance to multi-key attacks is desirable; but, in a realistic parallel setting, a straightforward multi-key application of Grover’s algorithm costs more than targeting one key at a time. This paper introduces a different quantum algorithm for multi-target preimage search. This algorithm shows, in the same realistic parallel setting, that quantum preimage search benefits asymptotically from having multiple targets. The new algorithm requires a revision of NIST’s AES128, AES-192, and AES-256 security claims.