Search framework for neutral bits and boomerangs in SHA-1 collision attacks

Neutral bits and boomerangs are key techniques for accelerating collision search in SHA-1 attacks. The current acceleration techniques for SHA-1 near-collision attacks are reviewed and a generic search framework for neutral bits and boomerangs is presented. The framework can efficiently construct auxiliary paths for a given differential path and message bit relations and find and store ideal boomerangs. The framework was applied to free-start attacks for 76-step SHA-1, and the complexity was reduced from $2^{50.25}$ to $2^{47.9}$. Relaxing the boomerang's restrictions on message words, the authors propose an accelerating technique termed semi-boomerangs, combined with the search framework of boomerangs, which increases the speed of collision search by 3.48 times in a free-start attack for 80-step SHA-1 and the complexity for 80-step attack was reduced from $2^{57.5}$ to $2^{55.7}$.