We propose three differential power analysis (DPA) countermeasures for securing the public key cryptosystems. All countermeasures are based on the window method, and can be used in both RSA and elliptic curve cryptosystems (ECC). By using the optimal countermeasure, performance penalty is small. In comparison with k-ary method, computation time of our countermeasure is only 105% in 1024-bit RSA and 119% in 160-bit ECC.

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Abstract. At CRYPTO2005, Xiaoyun Wang, Hongbo Yu and Yiqun Lisa Yin proposed a collision attack on SHA-0 that could generate a collision with complexity 2 39 SHA-0 hash operations. Although the method of Wang et al. can find messages that satisfy the sufficient conditions in steps 1 to 20 by using message modification, it makes no mention of the message modifications needed to yield satisfaction of the sufficient conditions in steps 21 and onwards.In this paper, first, we give sufficient conditions for the steps from step 21, and propose submarine modification as the message modification technique that will ensure satisfaction of the sufficient conditions from steps 21 to 24. Submarine modification is an extension of the multimessage modification used in collision attacks on the MD-family. Next, we point out that the sufficient conditions given by Wang et al. are not enough to generate a collision with high probability; we rectify this shortfall by introducing two new sufficient conditions. The combination of our newly found sufficient conditions and submarine modification allows us to generate a collision with complexity 2 36 SHA-0 hash operations. At the end of this paper, we show the example of a collision generated by applying our proposals.

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