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Alternate quantum walk is a kind of quantum walk which attracts a lot of attentions 13, 14, 15, 16, 17, 18, 19, 20. Quantum walk, one famous quantum computation model, has widely applications in quantum computation and quantum information 5, 6, 7, 8, 9, 10, 11, 12. Therefore, we present the quantum hash function based on controlled alternate quantum walks (CAQW) here to avoid these defects. The second one is that realization of controlled two-particle interacting quantum walks needs more resource than one-particle quantum walks. One of that is for the quantum hash function 2, 3, predictable collisions happens for some special states as initial coin state. But this quantum hash function still have two unsatisfactory defects. improved the CIQW based quantum hash function and found its applications in the privacy amplification process of quantum key distribution, pseudorandom number generation and image encryption. This quantum hash function guarantees the security of hash function by infinite possibilities of the initial state and the irreversibility of measurement rather than hard mathematic problems. presented a kind of quantum hash function based on two-particle controlled interacting quantum walks (CIQW) 2, 3. Besides, classical hash functions are used extensively in other quantum protocols to ensure the safety of quantum communication, yet it is contradictory with the fact that the quantum computer could solve difficult mathematical problems. As an important step of QKD, privacy amplification is implemented by adopting universal hash functions 1. QKD generally contains three steps: (1) raw key sifting, (2) error reconciliation, and (3)privacy amplification.

In the field of quantum communication, Quantum key distribution(QKD) is the most mature branch of quantum communication. These hash functions are generally constructed based on mathematics complexity and thus they are computationally secure. There are many theoretical studies about classical hash functions and mature hash functions such as MD5, SHA1 and SHA512. Hash function, as an important part of modern cryptography, has wide applications in message authentication, signature protocol and Public Key Infrastructure.

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