Discrete-time interacting quantum walks and quantum Hash schemes

Through introducing discrete-time quantum walks on the infinite line and on circles, we present a kind of two-particle interacting quantum walk which has two kinds of interactions. We investigate the characteristics of this kind of quantum walk and the time evolution of the two particles. Then we put forward a kind of quantum Hash scheme based on two-particle interacting quantum walks and discuss their feasibility and security. The security of this kind of quantum Hash scheme relies on the infinite possibilities of the initial state rather than the algorithmic complexity of hard problems, which will greatly enhance the security of the Hash schemes.

[1]  Chuan Wang,et al.  Quantum secret sharing protocol with four state Grover algorithm and its proof-of-principle experimental demonstration , 2011 .

[2]  Julia Kempe,et al.  Quantum random walks: An introductory overview , 2003, quant-ph/0303081.

[3]  G. S. Agarwal,et al.  Quantum random walk of two photons in separable and entangled states , 2007 .

[4]  Gregor Tanner,et al.  Quantum search algorithms on a regular lattice , 2010 .

[5]  Y. Omar,et al.  Quantum walk on a line with two entangled particles (7 pages) , 2006 .

[6]  S. D. Berry,et al.  Quantum-walk-based search and centrality , 2010, 1010.0764.

[7]  K. Birgitta Whaley,et al.  Quantum random-walk search algorithm , 2002, quant-ph/0210064.

[8]  Frédéric Magniez,et al.  An $O(n^{1.3})$ Quantum Algorithm for the Triangle Problem , 2003 .

[9]  Moni Naor,et al.  Theory and Applications of Models of Computation , 2015, Lecture Notes in Computer Science.

[10]  Takeshi Koshiba,et al.  Non-Interactive Statistically-Hiding Quantum Bit Commitment from Any Quantum One-Way Function , 2011, 1102.3441.

[11]  I. Jex,et al.  Directional correlations in quantum walks with two particles , 2011, 1102.4445.

[12]  C. M. Chandrashekar,et al.  Spatial entanglement using a quantum walk on a many-body system , 2009, 0901.0671.

[13]  A. Politi,et al.  Quantum Walks of Correlated Photons , 2010, Science.

[14]  Michael Mc Gettrick,et al.  Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin. , 2010, Physical review letters.

[15]  Dong Zhou,et al.  Two-particle quantum walks applied to the graph isomorphism problem , 2010, 1002.3003.

[16]  Moni Naor,et al.  Universal one-way hash functions and their cryptographic applications , 1989, STOC '89.

[17]  Salvador E. Venegas-Andraca,et al.  Quantum Walk-based Generation of Entanglement Between Two Walkers , 2009, 0901.3946.

[18]  J. B. Wang,et al.  A classical approach to the graph isomorphism problem using quantum walks , 2007, 0705.2531.

[19]  Andris Ambainis,et al.  Quantum walk algorithm for element distinctness , 2003, 45th Annual IEEE Symposium on Foundations of Computer Science.

[20]  S. D. Berry,et al.  Two-particle quantum walks: Entanglement and graph isomorphism testing , 2011 .

[21]  Viv Kendon,et al.  Entanglement in coined quantum walks on regular graphs , 2005 .

[22]  Mridul Nandi,et al.  Security Analysis of the Mode of JH Hash Function , 2010, FSE.

[23]  R. Blatt,et al.  Realization of a quantum walk with one and two trapped ions. , 2009, Physical review letters.

[24]  Andris Ambainis,et al.  QUANTUM WALKS AND THEIR ALGORITHMIC APPLICATIONS , 2003, quant-ph/0403120.

[25]  Will Flanagan,et al.  Controlling discrete quantum walks: coins and initial states , 2003 .