Applied Quantum Cryptography by C. Kollmitzer (auth.), Christian Kollmitzer, Mario Pivk

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By C. Kollmitzer (auth.), Christian Kollmitzer, Mario Pivk (eds.)

Using the quantum houses of unmarried photons to interchange binary keys among companions for next encryption of mystery information is a completely novel know-how. just a couple of years in the past quantum cryptography – or greater: quantum key distribution – used to be the area of uncomplicated study laboratories at universities. yet over the past few years issues replaced. QKD left the laboratories and was once picked up by way of more effective orientated groups that labored difficult to boost a virtually acceptable expertise out of the unbelievable result of easy research.

One significant milestone in the direction of a QKD know-how was once a wide learn and improvement undertaking funded through the eu fee that geared toward combining quantum physics with complementary applied sciences which are essential to create a technical resolution: electronics, software program, and community elements have been extra in the venture SECOQC (Development of an international community for safe conversation in keeping with Quantum Cryptography) that teamed up all services on ecu point to get a expertise for destiny encryption.

The sensible software of QKD in a regular optical fibre community was once proven October 2008 in Vienna, giving a glimpse of the way forward for safe verbal exchange. even if many steps have nonetheless to be performed in an effort to in achieving a true mature know-how, the nook stone for destiny safe verbal exchange is already laid.

QKD are not the Holy Grail of protection, it's going to no longer be ready to resolve all difficulties for evermore. yet QKD has the aptitude to switch one of many weakest elements of symmetric encryption: the alternate of the major. it may be confirmed that the main alternate procedure can't be corrupted and that keys which are generated and exchanged quantum cryptographically could be safe for ever (as lengthy as a few extra stipulations are kept).

This e-book will express the cutting-edge of Quantum Cryptography and it'll comic strip the way it might be carried out in typical communique infrastructure. The becoming vulnerability of delicate information calls for new ideas and QKD can be a potential option to conquer a few of today’s limitations.

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2 Preliminaries 19 Message m’ m1 ,1 h1 m2 ,1 h2 m|m'|/|t| ,1 hlog(|m’|/|t|) Split key h m1 m2 m3 mn r1 rn mj ,k= hk-1( m2j-1 ,k-1)||hk-1( m2j ,k–1) if mj ,k does not exist mj ,k=0 t’= lb|t’|( hlog(|m’|/|t|)( m1 ,log(|m’|/|t|)) ) r2 r3 ti = h(mi) Å ri t’ t1 t2 t3 tn Fig. 3 Entropy Entropy is a key concept in the field of information theory, which is a branch of applied mathematics concerned with the process to quantifying information. In the following a short part is presented, which we need in later chapters.

36 M. Pivk With the fact that a ideal reconciliation protocol depends on a open question in complexity, which is unlikely to be true, we have to find another solution. In Sect. 1 (universal hashing) we had a similar problem. There we define a str ongly univer sal2 class of hash functions, where the size of this class becomes too large and unpractical. But just a small change of the probability on the theoretical bound makes these classes useful. Here again if we do not demand optimality and allow the reconciliation protocol to transmit a small amount of leaked information above the theoretical bound the protocol becomes efficient and useful.

The next theorem is a direct consequence of the noiseless coding theorem. 1 (∀ p ≤ 12 ) (∀reconciliation protocol R p ) If there exists 0 ≤ ε ≤ 1 such that R p = [S, Q] is ε-robust then lim n→∞ I E (S|Q) ≥ 1, nh( p) 3 Quantum Key Distribution 35 where n is the length of the transmitted string. In other words, Eve’s information of S is greater than or equal to the information of A given B. Eve cannot have less than this information if the reconciliation protocol R p is successful. But if these two pieces of information are equal the protocol is optimal.

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