Improved Analysis Method of the Modular Multiplication Collision Attack

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.