Estimating the Cost of Generic Quantum Pre-image Attacks on SHA-2 and SHA-3

Matthew Amy,1, 2 Olivia Di Matteo,1, 3 Vlad Gheorghiu,1, 4, ∗ Michele Mosca,1, 4, 5, 6 Alex Parent,1, 3 and John Schanck1, 4 Institute for Quantum Computing, University of Waterloo, Waterloo, ON, N2L 3G1, Canada David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada Department of Combinatorics & Optimization, University of Waterloo, Waterloo, ON, N2L 3G1, Canada Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 6B9, Canada Canadian Institute for Advanced Research, Toronto, ON, M5G 1Z8, Canada