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We study the notion of multi-collision resistance of hash functions -a natural relaxation of collisionresistance that only guarantees the intractability of finding many (rather than two) inputs that map to the same image. An appealing feature of such hash functions is that unlike their collision-resistant counterparts, they do not necessarily require a key. Specifically, in the keyless setting, we only require that the size of collisions an adversarial algorithm can find is not much larger thandoi:10.1145/3188745.3188870 dblp:conf/stoc/BitanskyKP18 fatcat:wkozeczwgvhz7cmwj6ev4nmuki