This paper presents new collision search attacks on the SHA-1 hash function, demonstrating that collisions can be found with complexity less than 2^69 hash operations. This is the first attack on the full 80-step SHA-1 with complexity below the theoretical bound of 2^80. The attack involves several strategies to overcome major obstacles in collision search, including finding near-collision differential paths with low Hamming weight, adjusting differential paths to avoid impossible collisions, and transforming near-collision paths into full collision paths. The techniques are applied to SHA-0 and reduced variants of SHA-1, with real collisions found for SHA-0 with less than 2^39 hash operations and for 58-step SHA-1 with less than 2^33 hash operations. The analysis also shows that the collision complexity of 70-step SHA-1 is less than 2^50. The paper describes the SHA-1 algorithm, previous work on SHA-0 and SHA-1, the new techniques used in the attack, and detailed analysis of a 58-step collision. The results show that the full SHA-1 can be attacked with complexity less than 2^69, and the techniques can be applied to improve attacks on other hash functions like MD5. The paper concludes that the analysis provides insights into the design of more secure hash functions.This paper presents new collision search attacks on the SHA-1 hash function, demonstrating that collisions can be found with complexity less than 2^69 hash operations. This is the first attack on the full 80-step SHA-1 with complexity below the theoretical bound of 2^80. The attack involves several strategies to overcome major obstacles in collision search, including finding near-collision differential paths with low Hamming weight, adjusting differential paths to avoid impossible collisions, and transforming near-collision paths into full collision paths. The techniques are applied to SHA-0 and reduced variants of SHA-1, with real collisions found for SHA-0 with less than 2^39 hash operations and for 58-step SHA-1 with less than 2^33 hash operations. The analysis also shows that the collision complexity of 70-step SHA-1 is less than 2^50. The paper describes the SHA-1 algorithm, previous work on SHA-0 and SHA-1, the new techniques used in the attack, and detailed analysis of a 58-step collision. The results show that the full SHA-1 can be attacked with complexity less than 2^69, and the techniques can be applied to improve attacks on other hash functions like MD5. The paper concludes that the analysis provides insights into the design of more secure hash functions.