plaintext, into a "secret" message, called ciphertext. Such words come from cryptology, the science, and history of cryptography, 16 15 For various lists of prime numbers, see, for instance: http://primes.utm.edu/lists/small/1000.txt, http:// en.wikipedia.org/wiki/List_of_prime_numbers http://primes.utm.edu/; www.prime-numbers.org/; WWW. rsok.com/~jrm/printprimes.html. For riveting and historical accounts of cryptology, see S. Singh, The Code Book (New York: Anchor Books, 1999), S. Levy, Crypto (Harmondsworth: Penguin Books, 2001), and D. Kahn, The Codebreakers, the Story of Secret Writing (New York: Scribner, 1967). For an easy but detailed overview of crypto-algorithms 20.7 Public-key cryptography whereby text messages were encrypted for the purposes of military, state, security, trade, or simply private communications. In the computer age, however, any "text" to be SO encrypted may be anything from email to computer files, sensitive data, up to the payload of Internet frames (as used in the so-called IPv6 standard or other secure-communication protocols). Note that the word "cipher" indifferently designates the algorithm specifically used for encryption, or the ciphertext material itself. The destinee of the ciphertext (and only this person or entity), should be able to make sense of it and translate it back into readable plaintext, an operation which is called decryption. For this, he or she must use a secret key. By definition, the secret key must be difficult to find or figure out, just like the combination of a bank safe, or a "good" computer or network password. 17 Traditional cryptography, thus, requires that the sender does communicate, by some indirect means, his or her key to the destinee, SO that the latter may be able to complete the decryption. In contrast, PKC came as a revolution to this age-long principle by offering the possibility that the sender does not know or use any secret key. Indeed, PKC is based on the "asymmetric" principle of using two different cipher keys, one for encryption (publi