This paper presents a new powerful attack on MD5, a widely used cryptographic hash function, which allows efficient collision finding. The attack uses a modular differential approach, which differs from traditional XOR-based differential attacks. The modular differential measures differences using modular integer subtraction rather than XOR. This method enables the researchers to find collisions in about 15 minutes to an hour of computation time. The attack is applicable not only to MD5 but also to other hash functions such as MD4, Haval-128, and RIPEMD. The attack involves finding two message blocks that produce the same hash value after processing. The first block is found with about 2^39 MD5 operations, and the second block with about 2^32 MD5 operations. The attack was demonstrated on IBM P690, where finding the first block took about an hour, and the second block took between 15 seconds to 5 minutes. Two such collisions were publicly presented at the Crypto'04 rump session. The attack is based on a differential analysis of hash functions, where the researchers identified specific characteristics that ensure the differential occurs. They used message modification techniques to improve the collision probability. The attack was also applied to other hash functions, including MD4, where collisions could be found in less than a second. The paper also discusses the application of the attack to SHA-0, where Eli Biham and Rafi Chen presented a near-collision attack. The attack on SHA-0 was further improved by A. Joux, who presented a 4-block full collision of SHA-0. The paper concludes that the attack is effective against MD5 and other hash functions, with varying time complexities depending on the function and the use of message modification techniques. The research was supported by the National Natural Science Foundation of China.This paper presents a new powerful attack on MD5, a widely used cryptographic hash function, which allows efficient collision finding. The attack uses a modular differential approach, which differs from traditional XOR-based differential attacks. The modular differential measures differences using modular integer subtraction rather than XOR. This method enables the researchers to find collisions in about 15 minutes to an hour of computation time. The attack is applicable not only to MD5 but also to other hash functions such as MD4, Haval-128, and RIPEMD. The attack involves finding two message blocks that produce the same hash value after processing. The first block is found with about 2^39 MD5 operations, and the second block with about 2^32 MD5 operations. The attack was demonstrated on IBM P690, where finding the first block took about an hour, and the second block took between 15 seconds to 5 minutes. Two such collisions were publicly presented at the Crypto'04 rump session. The attack is based on a differential analysis of hash functions, where the researchers identified specific characteristics that ensure the differential occurs. They used message modification techniques to improve the collision probability. The attack was also applied to other hash functions, including MD4, where collisions could be found in less than a second. The paper also discusses the application of the attack to SHA-0, where Eli Biham and Rafi Chen presented a near-collision attack. The attack on SHA-0 was further improved by A. Joux, who presented a 4-block full collision of SHA-0. The paper concludes that the attack is effective against MD5 and other hash functions, with varying time complexities depending on the function and the use of message modification techniques. The research was supported by the National Natural Science Foundation of China.