Quantum walks public key cryptographic system

Quantum Cryptography is a rapidly developing field of research that benefits from the properties of Quantum Mechanics in performing cryptographic tasks. Quantum walks are a powerful model for quantum computation and very promising for quantum information processing. In this paper, we present a quantum public-key cryptographic system based on quantum walks. In particular, in the proposed protocol the public-key is given by a quantum state generated by performing a quantum walk. We show that the protocol is secure and analyze the complexity of public key generation and encryption/decryption procedures.

[1]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[2]  Stephen Wiesner,et al.  Conjugate coding , 1983, SIGA.

[3]  Aharonov,et al.  Quantum random walks. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[4]  Oded Goldreich,et al.  Public-Key Cryptosystems from Lattice Reduction Problems , 1996, CRYPTO.

[5]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[6]  Keisuke Tanaka,et al.  Quantum Public-Key Cryptosystems , 2000, CRYPTO.

[7]  Dominic Mayers,et al.  Unconditional security in quantum cryptography , 1998, JACM.

[8]  Daniel A. Spielman,et al.  Exponential algorithmic speedup by a quantum walk , 2002, STOC '03.

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

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

[11]  R. Laflamme,et al.  Experimental implementation of a discrete-time quantum random walk on an NMR quantum-information processor , 2005, quant-ph/0507267.

[12]  Takeshi Koshiba,et al.  Computational Indistinguishability Between Quantum States and Its Cryptographic Application , 2005, EUROCRYPT.

[13]  H. Weinfurter,et al.  Experimental Demonstration of Free-Space Decoy-State Quantum Key Distribution over 144 km , 2007, 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference.

[14]  M. Santha Quantum Walk Based Search Algorithms , 2008, TAMC.

[15]  G. M. Nikolopoulos,et al.  Applications of single-qubit rotations in quantum public-key cryptography , 2008, 0801.2840.

[16]  Neil B. Lovett,et al.  Universal quantum computation using the discrete-time quantum walk , 2009, 0910.1024.

[17]  Takeshi Koshiba,et al.  Computational Indistinguishability Between Quantum States and Its Cryptographic Application , 2004, Journal of Cryptology.

[18]  G. Vallone,et al.  Two-particle bosonic-fermionic quantum walk via integrated photonics. , 2011, Physical review letters.

[19]  R. Portugal Quantum Walks and Search Algorithms , 2013 .

[20]  Andrew M. Childs,et al.  Universal Computation by Multiparticle Quantum Walk , 2012, Science.

[21]  Jingbo B. Wang,et al.  Physical Implementation of Quantum Walks , 2013 .

[22]  Lance Fortnow,et al.  The Golden Ticket - P, NP, and the Search for the Impossible , 2013, Bull. EATCS.

[23]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..

[24]  André Souto,et al.  Oblivious transfer based on quantum state computational distinguishability , 2014, ArXiv.

[25]  André Souto,et al.  Enhancing Privacy with Quantum Networks , 2014, Communications and Multimedia Security.

[26]  Yu-Guang Yang,et al.  Novel Image Encryption based on Quantum Walks , 2015, Scientific Reports.