However caution should be taken as the idealistic work estimates above assume an ideal (perfect) hash function and are limited to attacks that target only a single preimage at a time. It is known under a conventional computing model that if 23"n"/5 preimages are searched, the full cost per preimage decreases from 2"n"/2 to 22"n"/5. Selecting the optimum element size taking into account the collection of multiple message digests is an open problem. Selection of larger element sizes and stronger hash functions, such as 512-bit elements and SHA-512, ensures greater security margins to manage these unknowns.