Quantum vernam cipher

We discuss aspects of secure quantum communication by proposing and analyzing a quantum analog of the Vernam cipher (one-time-pad). The quantum Vernam cipher uses entanglement as the key to encrypt quantum information sent through an insecure quantum channel. First, in sharp contrast with the classical Vernam cipher, the quantum key can be recycled securely. We show that key recycling is intrinsic to the quantum cipher-text, rather than using entanglement as the key. Second, the scheme detects and corrects for arbitrary transmission errors, and it does so using only local operations and classical communication (LOCC) between the sender and the receiver. The application to quantum message authentication is discussed. Quantum secret sharing schemes with similar properties are characterized. We also discuss two general issues, the relation between secret communication and secret sharing, the classification of secure communication protocols.

[1]  W. Wootters,et al.  A single quantum cannot be cloned , 1982, Nature.

[2]  D. Leung,et al.  Hiding bits in bell states. , 2000, Physical Review Letters.

[3]  G. S. Vernam,et al.  Cipher Printing Telegraph Systems For Secret Wire and Radio Telegraphic Communications , 1926, Transactions of the American Institute of Electrical Engineers.

[4]  Laflamme,et al.  Perfect Quantum Error Correcting Code. , 1996, Physical review letters.

[5]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[6]  Andris Ambainis,et al.  Private quantum channels , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[7]  Hoi-Kwong Lo,et al.  Is Quantum Bit Commitment Really Possible? , 1996, ArXiv.

[8]  Mihir Bellare,et al.  Lecture Notes on Cryptography , 2001 .

[9]  Dominic Mayers,et al.  Quantum Key Distribution and String Oblivious Transfer in Noisy Channels , 1996, CRYPTO.

[10]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[11]  Daniel Gottesman,et al.  Stabilizer Codes and Quantum Error Correction , 1997, quant-ph/9705052.

[12]  R. Cleve,et al.  HOW TO SHARE A QUANTUM SECRET , 1999, quant-ph/9901025.

[13]  Raymond Laflamme,et al.  Concatenated Quantum Codes , 1996 .

[14]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[15]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[16]  Dominic Mayers.  Unconditionally secure quantum bit commitment is impossible , 1997 .

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

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

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

[20]  Isaac L. Chuang,et al.  Prescription for experimental determination of the dynamics of a quantum black box , 1997 .

[21]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[22]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[23]  David Chaum,et al.  Advances in Cryptology: Proceedings Of Crypto 83 , 2012 .

[24]  H. Lo.  Classical-communication cost in distributed quantum-information processing: A generalization of quantum-communication complexity , 1999, quant-ph/9912009.

[25]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[26]  Yong-Sheng Zhang,et al.  Quantum key distribution via quantum encryption , 2000, quant-ph/0011034.

[27]  C. H. Bennett,et al.  Remote state preparation. , 2000, Physical review letters.