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数字签名中的短签名由于其签名长度的优势,特别适用于通信带宽受限的场合,现有的短签名方案大多是随机预言模型下可证明安全的,但是随机预言模型通常被认为过于理想化,现实中没有一种hash函数能够模拟随机预言模型,而少数标准模型下可证安全的短签名方案,一般被认为是低效的或者基于强困难假设,即攻击者被给于一定数量的随机的已解决问题实例,要求去解决一个它自己选择的实例.可编程hash函数(programmable hash functions,PHF)是一种能模拟随机预言的某些可编程特性的特殊hash函数.可编程hash函数可嵌入到签名的基本构造中,产生标准模型下的短签名.本文利用可编程hash函数设计了一个基于因子分解假设的短签名方案,它具有的优点是:1)签名长度短,只需要一个群上的元素和一个小整数;2)签名和验证计算量小,不需要在签名过程中进行生成素数的运算;3)不需要嵌入变色龙hash函数便可实现标准模型下可证明安全.
Because of its signature length, short signatures in digital signatures are especially suitable for applications where communication bandwidth is limited. Most of the existing short signatures are provably secure under random predictive models, but the random predictive models are generally considered to be too idealistic , There is no real hash function that can simulate the random prophecy model. However, the short secure signature scheme under a few standard models is generally regarded as inefficient or based on the strong hard assumption that an attacker is given a certain amount of randomness Is an example of a problem that has been solved to solve an instance of its own choice.Programmable hash functions (PHFs) are special hash functions that simulate some of the programmable features of random predictions.Programmable hash functions Embedding into the basic structure of signature and generating a short signature under the standard model.In this paper, a short signature scheme based on factorization assumption is designed by using programmable hash function, which has the following advantages: 1) the signature length is short and only one group On the elements and a small integer; 2) small amount of signature and verification computations, do not need to generate prime numbers in the signature process; 3) To embed a chameleon hash function can be realized in the standard model provably secure.