With bits, when we do the equivalent of what was described above as shifting a letter along the alphabet, wrapping from Z to A if necessary, we are either doing nothing, if the shift is by an even amount, or simply switching \(0\) and \(1\) otherwise.Īnother way of saying that is to say that is that if the message and the key are both written all out in bits – think of them as the elements \(,\in\ZZ/2\ZZ\) – then the encryption consists exactly of adding the corresponding bits mod \(2\). In modern times, after the advent of digital communications networks, messages are written as computer data, so everything is stored (and transmitted) as bits, meaning \(1\)s and \(0\)s. In fact, at that point the message can usually be determined quickly. If so, an attacker can take the letter-by-letter difference of the two ciphertexts and this will completely remove the pad from the calculation. It is also important never to use the same pad more than once. and for this proof.] Other cryptosystems we shall meet below are only secure if we assume the attacker has access to a computer of a particular type (a probabilistic polynomial-time Turing machine is the usual assumption this is the subject within computer science called computational complexity, see, e.g., ). In computer science, this is called information theoretically secure, because the proof of security does not rely upon any assumptions about the computational resources available to the attacker. The good news is that one can prove that with a truly random one-time pad, the resulting cryptosystem is in fact perfectly secure. It is important to have a good key sequence in a one-time pad cryptosystem. (A one-time pad is sometimes called – inappropriately, given the true intellectual history of the cryptosystem – a Vernam Cipher. Nevertheless, after a couple of hundred years in which it was considered unbreakable and used as the principle diplomatic cipher in the courts of Europe, approaches to breaking Vigenère were developed.Īs one final variant of the Vigenère cipher, suppose we go in the opposite direction from the \(\ell=1\) extreme, and instead take \(\ell\) as long as possible.Ī one-time pad is a Vigenère cryptosystem in which the key is as long as the message, chosen randomly, and never re-used. 1\)” coming from the fact that Eve doesn’t even know \(\ell\).
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