基于可编程hash 函数的短签名

A short signature, which is a type of digital signature, has an advantage in terms of its length. Short signatures are particularly suitable for scenarios in which communication bandwidth is constrained. Most of the existing short signature schemes have been proven secure under a random oracle, which is considered to be too idealistic. There is no hash function that can simulate a random oracle. A few of the provable secure short signature schemes in the standard model are considered to be inefficient or subject to strong hard assumptions, where the attacker is required to solve a chosen instance given a certain number of solved instances. Programmable hash functions (PHFs) can mimic some of the programmability properties of random oracles. Thus, PHFs can be plugged into the generic construction of signatures to yield short signatures in the standard model. We propose a short signature scheme based on a factoring assumption that uses programmable hash functions. The advantages are that: 1) the short signature only involves one element in a group and one small integer; 2) the scheme is efficient in terms of computational cost and does not require the generation of primes at signing; and 3) it is provably secure under the standard model without Chameleon hashes. This scheme is especially suitable for resource constrained applications such as wireless sensor networks and the Internet of things.