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中文摘要：
针对真实环境中用直接差分的方法寻找模乘碰撞较困难的问题，提出了一种胸值聚类算法。该算法可以自适应找出模乘碰撞。在搭建的真实攻击环境下，验证了文献【8】中的碰撞攻击在ASIC真实环境中攻击效果并不明显的结论。应用改进的方法后，一对功耗曲线样本便可恢复出88％以上的密钥，实现了小样本量曲线的RSA指数的提取。讨论了对这种攻击方法的防御方案。
英文摘要：
The simple power analysis attacks （SPA） of chosen-message contrary pairs is proposed by Miyamoto, which is an attack method based on searching the collision of modular multiplication. But in the real environment searching the collision is difficult. For this problem, the K-means clustering algorithm is proposed which can identify the modular multiplication collision automatically. The insignificant effects of collision attack are validated in the ASIC environment which suggested by Miyamoto. After the improvement method, by using a couple of power consumption curves it can recover more than 88% of the secret keys. Finally, the countermeasure of this attack method is discussed.
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