The paper discusses the construction of one-way hash functions using DES, a widely used encryption function. The authors present three methods to create secure one-way hash functions based on DES, assuming it is a "good" random block cipher. The first method uses a simple pattern of two DES applications, while the second and third methods improve efficiency by using more complex patterns of four and six DES applications, respectively. Each method is proven to be secure if DES is a random function, with the third method achieving a security level of at least 52.5 bits. The paper concludes by suggesting that more efficient patterns of DES applications may exist and can be derived using the outlined methods.The paper discusses the construction of one-way hash functions using DES, a widely used encryption function. The authors present three methods to create secure one-way hash functions based on DES, assuming it is a "good" random block cipher. The first method uses a simple pattern of two DES applications, while the second and third methods improve efficiency by using more complex patterns of four and six DES applications, respectively. Each method is proven to be secure if DES is a random function, with the third method achieving a security level of at least 52.5 bits. The paper concludes by suggesting that more efficient patterns of DES applications may exist and can be derived using the outlined methods.