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We answer the open question of the possibility of building a digital signature scheme with proven security based on the one-wayness of a trapdoor permutation and with signatures as short as possible. Our scheme is provably secure against existential forgery under chosen-message attacks (with tight reduction) in the ideal cipher model. It is a variant of the construction used in QUARTZ [11], that makes multiple calls to the trapdoor permutation to avoid birthday paradox attacks. We name our scheme the generic chained construction (GCC) and we show that the k-rounds GCC based on a k-bit one-way permutation with k-bit security generates k-bit signatures with almost k-bit security.

A Generic Scheme Based on Trapdoor One-Way Permutations with Signatures as Short as Possible