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We provide a positive result about the Fiat-Shamir (FS) transform in the standard model, showing how to use it to convert threemove identification protocols into two-tier signature schemes with a proof of security that makes a standard assumption on the hash function rather than modeling it as a random oracle. The result requires security of the starting protocol against concurrent attacks. We can show that numerous protocols have the required properties and so obtain numerous efficient two-tier schemes. Our first application is a two-tier scheme based transform of any unforgeable signature scheme into a strongly unforgeable one. (This extends Boneh, Shen and Waters [8] whose transform only applies to a limited class of schemes.) The second application is new one-time signature schemes that, compared to one-way function based ones of the same computational cost, have smaller key and signature sizes.

Two-Tier Signatures, Strongly Unforgeable Signatures, and Fiat-Shamir Without Random Oracles