secret key to encrypt and decrypt messages over a public channel, using DES or AES cryptoalgorithms, for instance. 20 19 Note that the same result can be obtained the other way around: over a public channel, Alice tells Bob which bases she used to code each of the polarized photons, namely ZZXX ZZXZ ZXXZ XXXZ, and then Bob tells Alice which of his measurements were right. What matters is that both Alice and Bob know which bits are to be discarded in the sequence. Here, I am not addressing the issue of photon loss due to effects such as atmospheric or fiber absorption. Put simply, all photons must be generated within a certain time slot. The absence of photons in a given time slot does not mean a measurement failure, but rather an absence of measurement (or a global, zero SPD1-SPD2 count). It is a basic engineering issue to predict the probability that, given the link budget and the photon generation and measurement apparatus used by Alice and Bob, a polarized photon is successfully measured from either end. Alice and Bob, thus, have an accurate knowledge of the photon-transmission capability of their link, namely, how many photons can be successfully transmitted on average. Hence, any observed deviation from this communication quality immediately betrays any wiretapping action on the link. Classical and quantum cryptography One may wonder how "safe" the above-described key-distribution approach is. How can Alice and Bob be certain that no malicious Eve is able to intercept the key? The answer is, in fact, quite simple: there is no possibility whatsoever for Eve to eavesdrop the key-distribution channel. The proof of this statement is also quite simple: photons cannot be split. The photon communications channel is, therefore, reputed "absolutely invulnerable," according to this fundamental law of quantum mechanics. There are many subtleties associated with such a concept of "invulnerability," which I reserve for the reader to the end, see Section 25.13. 25.10 The BB84 protocol for QKD In this section, I describe t