Benedikt, Barbara Jiabao ; Fischlin, Marc ; Huppert, Moritz (2022)
Nostradamus Goes Quantum.
28th International Conference on the Theory and Application of Cryptology and Information Security. Taipei, Taiwan (05.-09.12.2022)
doi: 10.1007/978-3-031-22969-5_20
Konferenzveröffentlichung, Bibliographie

Kurzbeschreibung (Abstract)

In the Nostradamus attack, introduced by Kelsey and Kohno (Eurocrypt 2006), the adversary has to commit to a hash value y of an iterated hash function H such that, when later given a message prefix P, the adversary is able to find a suitable “suffix explanation” S with H(P∥S)=y. Kelsey and Kohno show a herding attack with 22n/3 evaluations of the compression function of H (with n bits output and state), locating the attack between preimage attacks and collision search in terms of complexity. Here we investigate the security of Nostradamus attacks for quantum adversaries. We present a quantum herding algorithm for the Nostradamus problem making approximately n−−√3⋅23n/7 compression function evaluations, significantly improving over the classical bound. We also prove that quantum herding attacks cannot do better than 23n/7 evaluations for random compression functions, showing that our algorithm is (essentially) optimal. We also discuss a slightly less tight bound of roughly 23n/7−s for general Nostradamus attacks against random compression functions, where s is the maximal block length of the adversarially chosen suffix S.

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