Programmable hash functions (PHFs) is a new cryptographic primitive, which can mimic certain
programmability properties of random oracles. Due to these properties, PHFs are very useful to con-
struct short signatures in standard models. Based on (m,1)-PHF, we propose an efficient construction
of short signature from factoring problem. Our signature doesn’t require the generation of primes at
signing, and it can resist the information leakage to some extent.