Geodesic
Universal quantum hashing
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 7-18 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper we propose a method of quantum hashing which mostly combines the existing constructions of universal hash families with quantum one-way functions. Next, we define the concept of a quantum hash generator and present an approach for building a large number of various quantum hash functions. The construction is based on the integration of a classical $\varepsilon$-universal hash family and a given family of functions – quantum hash generator. The proposed construction combines the properties of robust representation of information by classical error-correcting codes together with the possibility of highly reliable representation of information by quantum systems. In particular, we present a quantum hash function based on the Reed–Solomon code and prove that this construction is optimal in the sense of the number of qubits needed.
Keywords: quantum computations, quantum communications, quantum hashing. 
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F. M. Ablayev; M. F. Ablayev; A. V. Vasilev. Universal quantum hashing. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 7-18. http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a1/

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