This paper presents a powerful attack on the widely used cryptographic hash function MD5, which allows for the efficient finding of collisions. The attack is a differential attack that uses modular integer subtraction as the measure of difference, rather than the traditional XOR. This method, called a *modular differential*, is more precise and restrictive compared to the XOR differential. The authors demonstrate that their attack can find collisions in about 15 minutes to an hour of computation time. The attack is applicable to other hash functions such as MD4, HAVAL-128, and RIPEMD. The paper also provides detailed descriptions of the attack, including the selection of collision differentials, the derivation of sufficient conditions for the differential characteristics to hold, and the message modification techniques used to improve the collision probability. The complexity of the attack is analyzed, showing that it can break MD5, MD4, HAVAL-128, RIPEMD, and SHA-0 efficiently.This paper presents a powerful attack on the widely used cryptographic hash function MD5, which allows for the efficient finding of collisions. The attack is a differential attack that uses modular integer subtraction as the measure of difference, rather than the traditional XOR. This method, called a *modular differential*, is more precise and restrictive compared to the XOR differential. The authors demonstrate that their attack can find collisions in about 15 minutes to an hour of computation time. The attack is applicable to other hash functions such as MD4, HAVAL-128, and RIPEMD. The paper also provides detailed descriptions of the attack, including the selection of collision differentials, the derivation of sufficient conditions for the differential characteristics to hold, and the message modification techniques used to improve the collision probability. The complexity of the attack is analyzed, showing that it can break MD5, MD4, HAVAL-128, RIPEMD, and SHA-0 efficiently.