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    基于强变色龙Hash函数的紧致安全签名通用构造

    Generic Tightly Secure Signature Schemes from Strong Chameleon Hash Functions

    • 摘要: 可证明安全性已经成为构造和分析密码方案的一个基本要求.研究可证明安全密码学领域的一个经典问题,即如何在随机预言模型下构造可证明安全的数字签名方案,而且其安全性可紧致地规约为某个基础数学问题的困难性.首先提出一种新密码原型,称作强变色龙Hash函数;然后基于强变色龙Hash函数,给出紧致安全数字签名方案的一般化构造框架及其变形,分别对应带状态和无状态2种情形;接着证明了这2种通用方案的安全性均可规约为底层强变色龙Hash函数的抗碰撞性.利用 RSA,CDH,IF等具体假设下的强变色龙Hash函数,通过所提出的一般化构造技术,可以模块化地构造相应的具体的紧致安全签名方案.2类经典的紧致安全签名方案构造范式,即Fiat-Shamir(FS)类和Full-Domain-Hash(FDH)类,可大致统一在所提出的构造框架中,而且本框架可将FDH类紧致安全签名方案解释为相应FS类紧致签名方案的优化形式.

       

      Abstract: Provable security has become one basic requirement for constructing and analyzing cryptographic schemes. This paper studies the classical issue in the field of provable security, namely how to construct provably secure digital signature schemes with tight security reduction from certain basic mathematical hard problems in the random oracle model. This paper first proposes a new cryptographic primitive called a strong chameleon Hash function. Based on a strong chameleon Hash function, we present a generic framework and its variant respectively for constructing a stateful and stateless digital signature scheme with tight security. We prove that these generic digital signature schemes are both secure under the assumption that the underlying chameleon Hash function is collision resistant in the random oracle model. By applying these generic construction methods to some concrete chameleon Hash functions under common mathematical assumptions such as RSA, CDH and IF (integer factorization), the corresponding digital signature schemes with tight security can be modularly obtained. The two existing classic paradigms to generically construct tightly secure signature schemes, i.e. Fiat-Shamir signatures and Full-Domain-Hash signatures, can be roughly unified by our generic frameworks. Furthermore, under our generic frameworks, a tightly secure signature scheme following the Fiat-Shamir methodology can be seen as the optimized variant of the corresponding tightly secure signature scheme following the Full-Domain-Hash framework.

       

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