Rabin's cryptosystem was proved to be as hard as factorization. However, Ra
bin's digital signature schemes is probabilistic.
This paper shows two efficient Rabin type digital signature schemes, a basi
c scheme and an improved scheme. Both schemes run much faster than Rabin's
scheme. They are deterministic and the size of a signature is much smaller
than that of a signature in Rabin's scheme.
Furthermore, it is proved that, by applying the technique of Bellare and Ro
gaway, the proposed scheme is secure against chosen plaintext attack. More
precisely, breaking the proposed digital signature scheme by chosen plainte
xt attack is as hard as factoring N.