Is there a known way to reduce the space complexity of quantum collision search (PDF) beyond what is offered by the built-in time-space tradeoff, while keeping the time complexity significantly below what is achieved by the classical Pollard's rho method?
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$\begingroup$ Related paper Daniel J. Bernstein. "Cost analysis of hash collisions: Will quantum computers make SHARCS obsolete?" Workshop Record of SHARCS'09: Special-purpose Hardware for Attacking Cryptographic Systems. $\endgroup$ – CodesInChaos Jul 5 '15 at 13:51
