Key-leakage evaluation of authentication in quantum key distribution with finite resources

Partial information leakages of generation key undoubtedly influence the security of practical Quantum Key Distribution (QKD) system. In this paper, based on finite-key analysis and deep investigation on privacy amplification, we present a method for characterizing information leakages gained by adversary in each authentication round and therefore take the theory derived by Cederlöf and Larsson (IEEE Trans Inf Theory 54:1735–1741, 2008) into practical case. As the authentication key is fed from one round of generation keys to the next except the first round, by considering its security weakness due to information leakages and finite size effect, we further propose a universal formula for calculating the lifetime of initial authentication key used in QKD with finite resources. Numerical simulations indicate that our bound for estimating information leakages strictly characterizes the stability of practical QKD against information-leakage-based attacks, and our calculation formula in terms of lifetime can precisely evaluate the usage time of initial authentication key. Our work provides a practical solution for evaluating authentication security of QKD.

[1]  Hugo Krawczyk,et al.  LFSR-based Hashing and Authentication , 1994, CRYPTO.

[2]  Jan-Åke Larsson,et al.  Security Aspects of the Authentication Used in Quantum Cryptography , 2008, IEEE Transactions on Information Theory.

[3]  Renato Renner,et al.  Security of quantum key distribution , 2005, Ausgezeichnete Informatikdissertationen.

[4]  Ueli Maurer,et al.  Generalized privacy amplification , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[5]  V. Scarani,et al.  The security of practical quantum key distribution , 2008, 0802.4155.

[6]  Larry Carter,et al.  New Hash Functions and Their Use in Authentication and Set Equality , 1981, J. Comput. Syst. Sci..

[7]  Douglas R. Stinson.  Universal Hashing and Authentication Codes , 1991, CRYPTO.

[8]  Renato Renner,et al.  Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way postprocessing. , 2007, Physical review letters.

[9]  Hoi-Kwong Lo,et al.  Efficient Quantum Key Distribution Scheme and a Proof of Its Unconditional Security , 2004, Journal of Cryptology.

[10]  Matthias Christandl,et al.  Postselection technique for quantum channels with applications to quantum cryptography. , 2008, Physical review letters.

[11]  Xiongfeng Ma,et al.  Practical issues in quantum-key-distribution postprocessing , 2009, 0910.0312.

[12]  J. Skaar,et al.  Hacking commercial quantum cryptography systems by tailored bright illumination , 2010, 1008.4593.

[13]  Lo,et al.  Unconditional security of quantum key distribution over arbitrarily long distances , 1999, Science.

[14]  Jörn Müller-Quade,et al.  Composability in quantum cryptography , 2009, ArXiv.

[15]  Johannes Skaar,et al.  Security of quantum key distribution with arbitrary individual imperfections , 2009, 0903.3525.

[16]  Xiongfeng Ma,et al.  Security proof of quantum key distribution with detection efficiency mismatch , 2008, Quantum Inf. Comput..

[17]  Jan-AAke Larsson,et al.  Security of Authentication with a Fixed Key in Quantum Key Distribution , 2011 .

[18]  Chun Zhou,et al.  Decoy-state quantum key distribution for the heralded pair coherent state photon source with intensity fluctuations , 2010, Science China Information Sciences.

[19]  Xiang‐Bin Wang,et al.  Beating the PNS attack in practical quantum cryptography , 2004 .

[20]  Johannes Skaar,et al.  Security of quantum key distribution with bit and basis dependent detector flaws , 2008, Quantum Inf. Comput..

[21]  Sellami Ali,et al.  DECOY STATE QUANTUM KEY DISTRIBUTION , 2010 .

[22]  John Preskill,et al.  Security of quantum key distribution with imperfect devices , 2002, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[23]  Shor,et al.  Simple proof of security of the BB84 quantum key distribution protocol , 2000, Physical review letters.

[24]  Christopher Portmann,et al.  Key Recycling in Authentication , 2012, IEEE Transactions on Information Theory.

[25]  Marco Tomamichel,et al.  Tight finite-key analysis for quantum cryptography , 2011, Nature Communications.

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

[27]  Hermann Kampermann,et al.  Min-entropy and quantum key distribution: Nonzero key rates for ``small'' numbers of signals , 2011 .

[28]  Robert König,et al.  The Operational Meaning of Min- and Max-Entropy , 2008, IEEE Transactions on Information Theory.

[29]  B Kraus,et al.  Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication. , 2004, Physical review letters.

[30]  R. Renner,et al.  Uncertainty relation for smooth entropies. , 2010, Physical review letters.