This paper introduces universal one-way hash functions (UOWHFs), a new cryptographic primitive that enables secure data compression. A UOWHF is a family of hash functions where it is computationally hard to find two different inputs that produce the same output. The authors prove that UOWHFs exist if any one-to-one one-way functions exist. They also show how to construct UOWHFs based on any one-to-one one-way function. The paper discusses various applications of UOWHFs, including a one-way based secure digital signature scheme. This scheme is provably secure and relies on the existence of any one-to-one one-way functions, rather than the stronger assumption of trapdoor one-way functions. The signature scheme is designed to be efficient and secure against adaptive chosen plaintext attacks. The authors also explore the relationship between UOWHFs and other cryptographic primitives, such as pseudorandom generators and collision intractable hash functions. They show that UOWHFs can be used to construct secure cryptographic protocols, including zero-knowledge proofs and digital signatures. The paper concludes with a discussion of the efficiency of the proposed schemes and the potential for further improvements. The authors also highlight the importance of UOWHFs in cryptographic applications, particularly in scenarios where data compression and security are required. The work provides a foundation for future research in cryptographic security and data compression.This paper introduces universal one-way hash functions (UOWHFs), a new cryptographic primitive that enables secure data compression. A UOWHF is a family of hash functions where it is computationally hard to find two different inputs that produce the same output. The authors prove that UOWHFs exist if any one-to-one one-way functions exist. They also show how to construct UOWHFs based on any one-to-one one-way function. The paper discusses various applications of UOWHFs, including a one-way based secure digital signature scheme. This scheme is provably secure and relies on the existence of any one-to-one one-way functions, rather than the stronger assumption of trapdoor one-way functions. The signature scheme is designed to be efficient and secure against adaptive chosen plaintext attacks. The authors also explore the relationship between UOWHFs and other cryptographic primitives, such as pseudorandom generators and collision intractable hash functions. They show that UOWHFs can be used to construct secure cryptographic protocols, including zero-knowledge proofs and digital signatures. The paper concludes with a discussion of the efficiency of the proposed schemes and the potential for further improvements. The authors also highlight the importance of UOWHFs in cryptographic applications, particularly in scenarios where data compression and security are required. The work provides a foundation for future research in cryptographic security and data compression.