This paper introduces the concepts of truncated differentials and higher order differentials, and presents attacks on ciphers that are secure against conventional differential attacks but vulnerable to these advanced techniques. The authors demonstrate that truncated differentials can be used to attack DES reduced to 6 rounds with only 46 chosen plaintexts and an expected running time of about 3,500 encryptions. They also show how to determine the minimum nonlinear order of a block cipher using higher order differentials. Truncated differentials are defined as differentials that predict only parts of the difference in ciphertexts after a certain number of rounds. The paper shows that some Feistel ciphers are secure against first-order differential attacks but vulnerable to attacks using truncated differentials and higher order differentials. This highlights the importance of considering these advanced techniques when assessing the security of cryptographic systems. Higher order differentials are defined as derivatives of cryptographic functions, and the paper discusses their application in cryptanalysis. It shows that for certain round functions, such as f(x,k) = (x + k)^2 mod p, the second-order derivative is constant, which can be exploited in differential attacks. The paper also presents a theorem that provides a method to determine the minimum nonlinear order of a block cipher using higher order differentials. The paper also presents a differential attack on a 5-round Feistel cipher using second-order differentials, which requires only 8 chosen plaintexts and has a running time of about p^2. The attack is shown to be effective for certain round functions and can be generalized to other ciphers. Finally, the paper discusses the use of truncated differentials in attacking the DES. It shows that truncated differentials can be used to construct a four-round differential for DES with probability one, which provides information about the difference of eight bits in the ciphertext after four rounds. This differential can be used to attack the DES with 6 rounds using only a few chosen plaintexts. The paper also presents a detailed attack on a 6-round DES using truncated differentials, which requires 46 chosen plaintexts and an expected running time of about 3,500 encryptions. The attack successfully recovers 45 bits of the 56-bit secret key, with the remaining 11 bits found through exhaustive search.This paper introduces the concepts of truncated differentials and higher order differentials, and presents attacks on ciphers that are secure against conventional differential attacks but vulnerable to these advanced techniques. The authors demonstrate that truncated differentials can be used to attack DES reduced to 6 rounds with only 46 chosen plaintexts and an expected running time of about 3,500 encryptions. They also show how to determine the minimum nonlinear order of a block cipher using higher order differentials. Truncated differentials are defined as differentials that predict only parts of the difference in ciphertexts after a certain number of rounds. The paper shows that some Feistel ciphers are secure against first-order differential attacks but vulnerable to attacks using truncated differentials and higher order differentials. This highlights the importance of considering these advanced techniques when assessing the security of cryptographic systems. Higher order differentials are defined as derivatives of cryptographic functions, and the paper discusses their application in cryptanalysis. It shows that for certain round functions, such as f(x,k) = (x + k)^2 mod p, the second-order derivative is constant, which can be exploited in differential attacks. The paper also presents a theorem that provides a method to determine the minimum nonlinear order of a block cipher using higher order differentials. The paper also presents a differential attack on a 5-round Feistel cipher using second-order differentials, which requires only 8 chosen plaintexts and has a running time of about p^2. The attack is shown to be effective for certain round functions and can be generalized to other ciphers. Finally, the paper discusses the use of truncated differentials in attacking the DES. It shows that truncated differentials can be used to construct a four-round differential for DES with probability one, which provides information about the difference of eight bits in the ciphertext after four rounds. This differential can be used to attack the DES with 6 rounds using only a few chosen plaintexts. The paper also presents a detailed attack on a 6-round DES using truncated differentials, which requires 46 chosen plaintexts and an expected running time of about 3,500 encryptions. The attack successfully recovers 45 bits of the 56-bit secret key, with the remaining 11 bits found through exhaustive search.