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发明公开
CN103580869A 一种CRT-RSA签名方法及装置 有权

一种CRT-RSA签名方法及装置
摘要：
本发明公开了一种CRT-RSA签名方法，该方法包括：生成随机数r，所述r的比特位长小于或等于RSA的两个素数p和q的比特位长；使用CRT-RSA算法计算所述r的逆元次幂R，其中对应的CRT-RSA的私钥五元组数据为(p,q,p-1-dp,q-1-dq,qInv)，qInv=q-1mod p，R=[(rp-1-dpmod p-rq-1-dqmod q)*qInv mod p]*q+rq-1-dqmod q；使用所述r对待签名数据D进行随机化处理，得到随机化处理后的待签名数据D′；使用CRT-RSA算法计算所述D′的签名值S′，相应的私钥五元组数据为（p,q,dp,dq,qInv），S′=[((D′mod p)dpmod p-(D′mod q)dqmod q)*qInv mod p]*q+(D′mod q)dqmod q；使用所述R对所述S′进行去随机化处理，得到签名结果S。该方法相对于现有的CRT-RSA签名算法，在提升了安全性的同时，不改变CRT-RSA签名算法的整体结构，实现简单，不受硬件平台限制。
摘要（英）：

The invention discloses a CRT-RSA signature method. The method includes the steps that a random number r is generated, and the bit length of the r is smaller than or equal to the bit length of two prime numbers p and q of the RSA; the inverse element power R of the r is calculated by the adoption of a CRT-RSA algorithm, wherein the corresponding private key quintuple data of the CRT-RSA are (p, q, p-1-dp, q-1-dq and qInv), qInv=q-1mod p, and R=[(rp-1-dpmodp-rq-1-dqmod q)*qInv mod p]*q+rq-1-dqmod q; randomization processing is conducted on the data D to be signed by the adoption of the r, so that the data D' to be signed after randomization processing are obtained; a signature value S' of the D' is calculated through the CRT-RSA algorithm, the corresponding private key quintuple data are (p, q, dp, dq and qInv), and S'=[((D'mod p) dpmod p-(D'mod q) dqmod q)*qInv mod p]*q+(D' mod q) dqmod q; randomization processing is conducted on the data S' by the adoption of the R, and a signature result S is obtained. Compared with an exiting CRT-RSA signature algorithm, the safety is improved, meanwhile, the overall structure of the CRT-RSA signature algorithm is not changed, implementation is easy, and the CRT-RSA signature method can not be limited by a hardware platform.

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