RSA密码系统小CRT解密指数的攻击分析

On an attack on RSA with small CRT-exponents

本文旨在讨论使用中国剩余定理(CRT)表示解密指数的RSA系统.由于中国剩余定理表示可被用来提高计算速度,这样的系统具有很高的实际应用价值.文中主要分析当前文献中一个对具有小CRT解密指数的RSA系统的攻击.本文指出,该攻击巧妙地运用了格理论,但其中某些论断一般是不正确的,并为此提供了几个反例.本文改进并完善了这个小CRT解密指数的攻击方法.

This paper concerns the RSA system with private CRT-exponents.Since Chinese remainder representation provides efficiency in computation,such system is of some practical significance.In this paper,an existing attack to small private CRT-exponents is analyzed.It is indicated that this attack makes nice use of lattice in RSA analysis,but some argument does not hold in general.Several counterexamples are constructed.Refinements and more precise statements of the attack are given.