Quantum cryptography
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Abstract
After a short introduction to classic cryptography we explain thoroughly how quantum cryptography works. We present then an elegant experimental realization based on a self-balanced interferometer with Faraday mirrors. This phase-coding setup needs no alignment of the interferometer nor polarization control, and therefore considerably facilitates the experiment. Moreover it features excellent fringe visibility. Next, we estimate the practical limits of quantum cryptography. The importance of the detector noise is illustrated and means of reducing it are presented. With present-day technologies maximum distances of about 70 km with bit rates of 100 Hz are achievable. Cryptography is the art of hiding information in a string of bits meaningless to any unauthorized party. To achieve this goal, one uses encryption: a message is combined according to an algorithm with some additional secret information – the key – to produce a cryptogram. In the traditional terminology, Alice is the party encrypting and transmitting the message, Bob the one receiving it, and Eve the malevolent eavesdrop-per. For a crypto-system to be considered secure, it should be impossible to unlock the cryptogram without Bob's key. In practice, this demand is often softened, and one requires only that the system is sufficiently difficult to crack. The idea is that the message should remain protected as long as the information it contains is valuable. There are two main classes of crypto-systems, the public-key and the secret-key crypto-systems: Public key systems are based on so-called one-way functions: given a certain x, it is easy to compute f(x), but difficult to do the inverse, i.e. compute x from f(x). " Difficult " means that the task shall take a time that grows exponentially with the number of bits of the input. The RSA (Rivest, Shamir, Adleman) crypto-system for example is based on the factoriz-ing of large integers. Anyone can compute 137 × 53 in a few seconds, but it may take a while to find the prime factors of 28 907. To transmit a message Bob chooses a private key (based on two large prime numbers) and computes from it a public key (based on the product of these numbers) which he discloses publicly. Now Alice can encrypt her message using this public key and transmit it to Bob, who decrypts it with the private key. Public key systems are very convenient and became very popular over the last 20 years, however, they suffer from two potential major flaws. …