In this paper, we propose a new construction algorithm for finding differential paths of Round 1 of SHA-1 for use in the collision search attack. Generally, the differential path of Round 1 is very complex, and it takes much time to find one by hand. Therefore, we propose a new search algorithm that consists of three sub searches, naming the forward search, the backward search, and the joint search, so that we can find a differential path by computers. By implementing our new algorithm and doing some experiments on a computer, we actually found 383 differential paths in the joint search that are different from Wang's. Since it is designed by quite a new policy, our algorithm can search a range of space that was not examined by existing algorithms.
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