From quantum code-making to quantum code-breaking

1 What is wrong with classical cryptography ? Human desire to communicate secretly is at least as old as writing itself and goes back to the beginnings of our civilisation. Methods of secret communication were developed by many ancient societies, including those of Mesopotamia, Egypt, India, and China, but details regarding the origins of cryptology remain unknown (Kahn 1967). We know that it was the Spartans, the most warlike of the Greeks, who pioneered military cryptography in Europe. Around 400 BC they employed a device known as a the scytale. The device, used for communication between military commanders, consisted of a tapered baton around which was wrapped a spiral strip of parchment or leather containing the message. Words were then written lengthwise along the baton, one letter on each revolution of the strip. When unwrapped, the letters of the message appeared scrambled and the parchment was sent on its way. The receiver wrapped the parchment around another baton of the same shape and the original message reappeared. Julius Caesar allegedly used, in his correspondence, a simple letter substitution method. Each letter of Caesar’s message was replaced by the letter that followed it alphabetically by three places. The letter A was replaced by D, the letter B by E, and so on. For example, the English word COLD after the Caesar substitution appears as FROG. This method is still called the Caesar cipher, regardless the size of the shift used for the substitution. These two simple examples already contain the two basic methods of encryption which are still employed by cryptographers today namely transposition and substitution. In transposition (e.g. scytale) the letters of the plaintext, the technical term for the message to be transmitted, are rearranged by a special permutation. In substitution (e.g. Caesar’s cipher) the letters of the plaintext are replaced by other letters, numbers or arbitrary symbols. In general the two