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1. 发明授权

US07925011B2 Method for simultaneous modular exponentiations 有权
标题翻译：同时采用模幂分析的方法
公开(公告)号：US07925011B2
公开(公告)日：2011-04-12
申请号：US11610919
申请日：2006-12-14
申请人： Vinodh Gopal , Erdinc Ozturk , Kaan Yuksel , Gunnar Gaubatz , Wajdi Feghali , Gilbert M. Wolrich
发明人： Vinodh Gopal , Erdinc Ozturk , Kaan Yuksel , Gunnar Gaubatz , Wajdi Feghali , Gilbert M. Wolrich
IPC分类号： H04L9/00
CPC分类号： G06F7/723 , H04L9/302
摘要： The present disclosure provides a method for performing modular exponentiation. The method may include generating a first remainder (xp) based on an encrypted message (X) modulo a first prime number (p) and generating a second remainder (xq) based on the encrypted message (X) modulo a second prime number (q). The method may further include generating a third remainder (v1) based on the first remainder (xp) raised to a first private key number (d1) modulo the first prime number (p) and simultaneously generating a fourth remainder (v2) based on the second remainder (xq) raised to a second private key number (d2) modulo the second prime number (q). The method may also include subtracting the fourth remainder (v2) from the third remainder (v1) to yield a result (v1−v2) and multiplying the result (v1−v2) by a constant (c) to produce a second result. The method may additionally include generating a sixth remainder (h) by taking the second result modulo the first prime number (p) and multiplying the sixth remainder (h) by the second prime number (q) to produce a third result. The method may further include adding the third result and the fourth remainder (v2) to yield a final result (Y) and generating, at least in part, a public key based on the final result (Y). Of course, many alternatives, variations and modifications are possible without departing from this embodiment.
摘要翻译：本公开提供了一种用于执行模幂运算的方法。该方法可以包括基于第一素数（p）模数的加密消息（X）生成第一余数（xp），并且基于加密消息（X）生成第二余数（xq），第二素数（q））。该方法还可以包括：基于第一余数（xp）产生第三余数（v1），所述第一余数（xp）基于所述第一余数（xp）生成第一素数（p）的第一私钥数（d1）并同时生成第四余数第二余数（xq）升至第二素数（q）的第二私钥号（d2）。该方法还可以包括从第三余数（v1）中减去第四余数（v2）以产生结果（v1-v2）并将结果（v1-v2）乘以常数（c）以产生第二结果。该方法可以另外包括通过将第二结果以第一素数（p）取模并将第六余数（h）乘以第二素数（q）产生第三结果来产生第六余数（h）。该方法还可以包括添加第三结果和第四余数（v2）以产生最终结果（Y），并且至少部分地基于最终结果（Y）生成公钥。当然，在不脱离本实施例的情况下，可以进行许多替代，变化和修改。

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