This paper introduces the concept of truncated differentials and higher-order differentials in the context of cryptographic analysis. Truncated differentials are partial differentials where only a part of the difference in the ciphertexts after a certain number of rounds can be predicted, while higher-order differentials involve derivatives of discrete functions of more than one order. The paper demonstrates that ciphers which are secure against conventional differential attacks can be vulnerable to attacks using truncated and higher-order differentials. Specifically, it presents a differential attack on a 6-round DES using only 46 chosen plaintexts, with an expected running time of about 3,500 encryptions. Additionally, the paper provides a method to determine the minimum nonlinear order of a block cipher using higher-order differentials. The author also discusses the implications of these findings and highlights open problems, such as the applicability of higher-order differentials to ciphers with more than 5 rounds and the potential for combining truncated differentials with conventional differentials to enhance attacks on DES.This paper introduces the concept of truncated differentials and higher-order differentials in the context of cryptographic analysis. Truncated differentials are partial differentials where only a part of the difference in the ciphertexts after a certain number of rounds can be predicted, while higher-order differentials involve derivatives of discrete functions of more than one order. The paper demonstrates that ciphers which are secure against conventional differential attacks can be vulnerable to attacks using truncated and higher-order differentials. Specifically, it presents a differential attack on a 6-round DES using only 46 chosen plaintexts, with an expected running time of about 3,500 encryptions. Additionally, the paper provides a method to determine the minimum nonlinear order of a block cipher using higher-order differentials. The author also discusses the implications of these findings and highlights open problems, such as the applicability of higher-order differentials to ciphers with more than 5 rounds and the potential for combining truncated differentials with conventional differentials to enhance attacks on DES.