Quantum cryptography

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 kmwith bit rates of 100 Hzare achievable. PACS: 03.67.Dd; 85.60; 42.25; 33.55.A 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 eavesdropper. 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 publickey and the secret-key crypto-systems: Public key systems are based on so-called one-way functions: given a certainx, it is easy to computef(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 factorizing 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. To date, nobody knows for sure whether or not factorizing is indeed difficult. For known algorithms, the time for calculation increases exponentially with the number of input bits, and one can easily improve the safety of RSA by choosing a longer key. However, a fast algorithm for factorization would immediately annihilate the security of the RSA system. Although it has not been published yet, there is no guarantee that such an algorithm does not exist. Second, problems that are difficult for a classical computer could become easy for a quantum computer. With the recent developments in the theory of quantum computation, there are reasons to fear that building these machines will eventually become possible. If one of these two possibilities came true, RSA would become obsolete. One would then have no choice, but to turn to secret-key cryptosystems. Very convenient and broadly used are crypto-systems based on a public algorithm and a relatively short secret key. The DES (Data Encryption Standard, 1977) for example uses a 56-bit key and the same algorithm for coding and decoding. The secrecy of the cryptogram, however, depends again on the calculating power and the time of the eavesdropper. The only crypto-system providing proven, perfect secrecy is the “one-time pad” proposed by Vernam in 1935. With this scheme, a message is encrypted using a random key of equal length, by simply “adding” each bit of the message to the orresponding bit of the key. The scrambled text can then be sent to Bob, who decrypts the message by “subtracting” the same key. The bits of the ciphertext are as random as those of the key and consequently do not contain any information. Although perfectly secure, the problem with this system is that it is essential for Alice and Bob to share a common secret key, at least as long as the message they want to exchange, and use it only for a single encryption. This key must be transmitted by some trusted means or personal meeting, which turns out to be complex and expensive.