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Abstract. Cryptanalytic time memory tradeoff algorithms are tools for quickly inverting one-way functions and many consider the rainbow table method to be the most efficient tradeoff algorithm. However, it was recently announced, mostly based on experiments, that the parallelization of the perfect distinguished point tradeoff algorithm brings about an algorithm that is 50% more efficient than the perfect rainbow table method. Motivated by this claim, we provide an accurate theoretic analysis of the parallel version of the non-perfect distinguished point tradeoff algorithm. Performance differences between different tradeoff algorithms are usually not very large, but even these small differences can be crucial in practice. So we take care not to ignore the side effects of false alarms while analyzing the online time complexity of the parallel distinguished point tradeoff algorithm. Our complexity results are used to compare the parallel non-perfect distinguished point tradeoff against the non-perfect rainbow table method. The two algorithms are compared under identical success rate requirements and the pre-computation efforts are taken into account. Contrary to our anticipation, we find that the rainbow table method is superior in typical situations, even though the parallelization did have a positive effect on the efficiency of the distinguished point tradeoff algorithm.

In 2004, Matsushita and Imai proposed a k-resilient publickey traitor tracing scheme which has sublinear ciphertext size 4k + 2 + (n/2k) with efficient black-box tracing against self-defensive pirates, where n, k are the total number of subscribers and the maximum number of colluders. After that, in 2006, they presented a hierarchical key assignment method to reduce the ciphertext size into 4k + 5 + log(n/2k) by combining a complete binary tree with the former scheme.In this paper, we show that the proposed schemes are vulnerable to our attack which makes pirate keys able to avoid the black-box tracing. Their schemes are based on multiple polynomials and our attack use a combination between different polynomials. The latter scheme can be broken by other attacks which use secret values of the key generation polynomial or use partial keys.