Low-gate Quantum Golden Collision Finding [article]

Samuel Jaques, André Schrottenloher
2020 IACR Cryptology ePrint Archive  
The golden collision problem asks us to nd a single, special collision among the outputs of a pseudorandom function. This generalizes meet-in-the-middle problems, and is thus applicable in many contexts, such as cryptanalysis of the NIST post-quantum candidate SIKE. The main quantum algorithms for this problem are memory-intensive, and the costs of quantum memory may be very high. The quantum circuit model implies a linear cost for random access, which annihilates the exponential advantage of
more » ... e previous quantum collision-nding algorithms over Grover's algorithm or classical van Oorschot-Wiener. Assuming that quantum memory is costly to access but free to maintain, we provide new quantum algorithms for the golden collision problem with high memory requirements but low gate costs. Under the assumption of a two-dimensional connectivity layout, we provide better quantum parallelization methods for generic and golden collision nding. This lowers the quantum security of the golden collision and meet-in-the-middle problems, including SIKE.
dblp:journals/iacr/JaquesS20 fatcat:nkuetroefvfzlana4xvb2p7egm