整数分解问题下的基于证书数字签名方案

已知的基于证书签名方案主要是在双线性对下设计的，而双线性对是公认的计算复杂度最高的。为了提高基于证书签名方案的效率，利用大整数分解问题构造了一个新的基于证书签名方案。方案的证书生成算法和签名算法都利用雅可比符号分别将用户信息和待签消息的Hash值映射成二次剩余。将证书和签名的不可为造型建立在模Blum整数求二次根困难问题上。并在随机预言机模型下，形式化证明了方案的安全性。所构造方案的不需要任何双线性对计算，只计算雅可比符号和幂指数运算，提高了基于证书签名方案的效率。

Certificate-based signature scheme from factorization

The known Certificate-Based Signature（CBS） schemes are designed under bilinear pairing, however, as is known to all, the computation of bilinear pairing is most difficult. In order to improve the efficiency of certificate-based signature scheme, based on the Integer Factorization Problem（IFP）, a new efficient certificate-based signature scheme is proposed. Certificate generation algorithm and signature generation algorithm of the scheme are designed by using the Jacobi symbol, the Hash value of user information and message to be signed are mapped into quadratic residue by this way. Certificate and signature’s unforgery are under the difficult problem of modulo Blum integer square root. The new scheme security is proved under the Random Oracle Model（ROM）and the scheme does not need any bilinear pairing computation, just needs compute Jacobi symbol and power exponentiation, so it is very efficient.