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61 " imagined a machine whose internal workings could be altered so that it could perform all the functions of all conceivable Turing machines. The alterations would be made by inserting carefully selected tapes, which transformed the single flexible machine into a dividing machine, a multiplying machine, or any other type of machine. Turing called this hypothetical device a universal Turing machine because it would be capable of answering any question that could logically be answered. Unfortunately, it turned out that it is not always logically possible to answer a question about the undecidability of another question, and so even the universal Turing machine was unable to identify every undecidable question. "
― Simon Singh , The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography
62 " Turing knew of Babbage’s work, and the universal Turing machine can be seen as a reincarnation of Difference Engine No. 2. In fact, Turing had gone much further, and provided computing with a solid theoretical basis, "
63 " A large amount of identically encrypted material provides a cryptanalyst with a correspondingly larger chance of identifying the key. "
64 " the Germans therefore took the clever step of using the day key settings to transmit a new message key for each message. "
65 " The fundamental weakness of the Vigenère cipher is its cyclical nature. If the keyword is five letters long, then every fifth letter of the plaintext is encrypted according to the same cipher alphabet. If the cryptanalyst can identify the length of the keyword, the ciphertext can be treated as a series of five monoalphabetic ciphers, and each one can be broken by frequency analysis. However, consider what happens as the keyword gets longer. Imagine a plaintext of 1,000 letters encrypted according to the Vigenère cipher, "
66 " Rejewski had vastly simplified the task of finding the day key by divorcing the problem of finding the scrambler settings from the problem of finding the plugboard settings. On their own, both of these problems were solvable. Originally, we estimated that it would take more than the lifetime of the universe to check every possible Enigma key. However, Rejewski had spent only a year compiling his catalogue of chain lengths, and thereafter he could find the day key before the day was out. Once he had the day key, he possessed the same information as the intended receiver and so could decipher messages just as easily. "
67 " the First World War was the chemists’ war, because mustard gas and chlorine were employed for the first time, "
68 " Second World War was the physicists’ war, because the atom bomb was detonated. "
69 " it can be mathematically proved that it is impossible for a cryptanalyst to crack a message encrypted with a onetime pad cipher. In other words, the onetime pad cipher is not merely believed to be unbreakable, just as the Vigenère cipher was in the nineteenth century, it really is absolutely secure "
70 " the Third World War would be the mathematicians’ war, because mathematicians will have control over the next great weapon of war—information. Mathematicians have been responsible for developing the codes that are currently used to protect military information. "
71 " The fate of the Polish nation had depended on Rejewski, and he did not disappoint his country. Rejewski’s attack on Enigma is one of the truly great accomplishments of cryptanalysis. "
72 " it requires a great deal of time, effort and money to create a random key. The best random keys are created by harnessing natural physical processes, such as radioactivity, which is known to exhibit truly random behavior. The cryptographer could place a lump of radioactive material on a bench, and detect its emissions with a Geiger counter. Sometimes the emissions follow each other in rapid succession, sometimes there are long delays—the time between emissions is unpredictable and random. The cryptographer could then connect a display to the Geiger counter, which rapidly cycles through the alphabet at a fixed rate, but which freezes momentarily as soon as an emission is detected. "
73 " Histaiaeus shaved the head of his messenger, wrote the message on his scalp, and then waited for the hair to regrow. This was clearly a period of history that tolerated a certain lack of urgency. "
74 " Secret communication achieved by hiding the existence of a message is known as steganography "
75 " the hotline between the presidents of Russia and America is secured via a onetime pad cipher. "
76 " When Hermann Göring visited Warsaw in 1934, he was totally unaware of the fact that his communications were being intercepted and deciphered. As he and other German dignitaries laid a wreath at the Tomb of the Unknown Soldier next to the offices of the Biuro Szyfrów, Rejewski could stare down at them from his window, content in the knowledge that he could read their most secret communications. "
77 " the enemy of security: repetition leads to patterns, and cryptanalysts thrive on patterns. "
78 " By depriving Rejewski of the keys, Langer believed he was preparing him for the inevitable time when the keys would no longer be available. He knew that if war broke out it would be impossible for Schmidt to continue to attend covert meetings, and Rejewski would then be forced to be self-sufficient. Langer thought that Rejewski should practice self-sufficiency in peacetime, as preparation for what lay ahead. "
79 " quantum cryptography is a system that ensures the security of a message by making it hard for Eve to read accurately a communication between Alice and Bob. Furthermore, if Eve tries to eavesdrop then Alice and Bob will be able to detect her presence. Quantum cryptography therefore allows Alice and Bob to exchange and agree upon a onetime pad in complete privacy, and thereafter they can use this as a key to encrypt a message. "
80 " Babbage’s successful cryptanalysis of the Vigenère cipher was probably achieved in 1854, soon after his spat with Thwaites, but his discovery went completely unrecognized because he never published it. The discovery came to light only in the twentieth century, when scholars examined Babbage’s extensive notes. In the meantime, his technique was independently discovered by Friedrich Wilhelm Kasiski, a retired officer in the Prussian army. Ever since 1863, when he published his cryptanalytic breakthrough in Die Geheimschriften und die Dechiffrir-kunst (“Secret Writing and the Art of Deciphering”), the technique has been known as the Kasiski Test, and Babbage’s contribution has been largely ignored. "