lier, they represent a third phase of history with the intro- duction of new algorithms, leading to ciphers that are hopelessly hard to crack with current-generation supercomputers. Although digital cryptography may appear a tricky subject (and it really is!), the elementary basics are surprisingly simple to describe. Here, I will first look at how encryption and decryption work with binary numbers, from simple transposition to more complex algorithms, which opened the way to modern standards. Alphanumeric characters, including spaces, punctuation, numbers, and other signs, which we use as a written language, are seen by computers in the form of standard binary-number codes. As mentioned earlier, the two main alphanumerical codes used in computer communications are ASCII (American standard code for information inter- change), and its extension EBCDIC (extended binary coded decimal interchange code). These two standard codes use seven-bit and eight-bit (one byte) words, respectively. The Standard ASCII tables providing the corresponding alphanumeric/binary conversion can be found, for instance, in: http://en.wikipedia.org/wiki/ASCII, www.webopedia.com/quick.ref/asciicode.asp, www.neurophys.wisc.edu/comp/docs/ascii/. Classical and quantum cryptography Table 25.1 Ciphering by switching bit positions by pairs. Plaintext PT-ASCII 1001001 1101101 1101001 1110011 1110011 1111001 1101111 1110101 CT-ASCII 0110001 1110011 1110001 1101101 1101101 1111001 1110111 1101011 Ciphertext 1 Table 25.2 Ciphering by taking characters by pairs and swapping their center bits. Plaintext PT-ASCII 1001001 1101101 1101001 1110011 1110011 1111001 1101111 1110101 CT-ASCII 1001001 1101101 1100001 1111011 1111011 1110001 1100111 1111101 Ciphertext I ASCII and EBCDIC codes have 27 = 128 and 28 = 256 possible alphanumerical charac- ter and other keyboard-command possibilities, respectively. For cryptography purposes, this represents a huge extension of the previous 26-letter alphabet from earlier times. How to construct ciphers from binary-numbe