Code and ciphers: Julius Caesar, the Enigma and the internet
Code and ciphers: Julius Caesar, the Enigma and the internet
Code and ciphers: Julius Caesar, the Enigma and the internet
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numbers, 0 to 31 inclusive, into binary, thus providing five binary digits<br />
each time. Binary digits are commonly known as bits <strong>and</strong> are frequently<br />
referred to in that way. Binary keys are frequently used in cryptography.<br />
Not only have <strong>the</strong>y <strong>the</strong> great merit that non-carrying addition (mod 2) is<br />
particularly simple <strong>and</strong> identical to non-carrying subtraction (mod 2),<br />
which makes encipherment <strong>and</strong> decipherment <strong>the</strong> same, but also (mod 2)<br />
arithmetic is very easy to simulate electronically, <strong>and</strong> so is particularly<br />
suitable both for cipher machines <strong>and</strong> for simulators on computers.<br />
Lottery type draws<br />
The system used to draw lottery (or bingo) numbers could be used provided<br />
it was modified so that a number which has been drawn is immediately<br />
returned to <strong>the</strong> pool. Thus 100 balls numbered 00 to 99 are spun in a<br />
barrel <strong>and</strong> selected one by one, each number selected is noted <strong>and</strong> provides<br />
two decimal digits for <strong>the</strong> table of r<strong>and</strong>om numbers. The selected<br />
ball must be put back in <strong>the</strong> barrel for o<strong>the</strong>rwise it couldn’t be drawn again<br />
<strong>and</strong> each page of 100 two-digit decimal numbers would contain each<br />
number once, <strong>and</strong> only once, <strong>and</strong> so would not be r<strong>and</strong>om. A typical page<br />
of 100 two-digit r<strong>and</strong>om numbers would be expected to contain some<br />
numbers three, or even four, times whilst between 30 <strong>and</strong> 40 numbers<br />
might not occur at all. (For an explanation see M8.)<br />
Cosmic rays<br />
Cosmic rays are produced when particles from <strong>the</strong> Sun enter <strong>the</strong> Earth’s<br />
atmosphere <strong>and</strong> generate cascades of o<strong>the</strong>r particles by collisions <strong>and</strong> so<br />
provide a ‘natural’ source of (presumably) r<strong>and</strong>om events. If we were to<br />
install ten detectors, such as Geiger counters, numbered 0 to 9, in a room<br />
<strong>and</strong> record <strong>the</strong> order in which <strong>the</strong> detectors ‘fire’ we would obtain a genuinely<br />
unpredictable decimal sequence. Care would have to be taken that<br />
when a detector has ‘fired’ no o<strong>the</strong>r event is recorded until that detector<br />
has had time to ‘recover’, for o<strong>the</strong>rwise <strong>the</strong>re is likely to be a deficiency of<br />
‘doublets’ such as 00, 11 etc. in <strong>the</strong> resultant sequence.<br />
Amplifier noise<br />
Producing r<strong>and</strong>om numbers <strong>and</strong> letters 97<br />
Noise in electrical circuits is usually regarded as a problem, but it can also<br />
be turned to good use in cryptography. The noise can be converted into a