A generic scheme based on trapdoor one-way permutations with signatures as short as possible

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.