Philosopher Abu Yusuf al-Kindi (801-873) is author of the oldest known book on cryptology whose use of frequency analysis is an early example of statistical inference (Broemeling, The American Statistician, 2010). Physicist Simon Singh writes about al-Kindi’s use of frequency analysis to break codes:
Usually, encryption meant substituting conventional letters with other letters (or symbols), a system known as the substitution cipher. So instead of writing A the sender might write J, instead of B he might write W, and so on. The Swedish singing sensation of the seventies would then be encrypted as JWWJ.
The substitution cipher, at first sight, offers a high level of security. An enemy interceptor looks at the encrypted message and has to guess which of the 26 letters does A really represent? If by some fluke he guesses right, then he has to guess which of the other 25 letters for B really represent? And so on. The chances of correctly guessing all 26 letters is 1 in (26x25x…x1), or 1 in 400 million billion billion, or effectively zero. Checking all possible substitutions would take longer than the age of the universe.
However, there is a shortcut, which enables a codebreaker to crack the substitution cipher within a matter of minutes. Historians of science have long been trying to track down the inventor of the shortcut, and over the last decade Professor Mohammed Mrayati has at last made a breakthrough. Myrayati, an engineer and historian based with the UN in Lebanon, while sifting through the Sulaimaniyyah Ottoman Archive in Istanbul uncovered a hitherto unknown document entitled A Manuscript on Deciphering Cryptographic Messages, first published in around 850 AD. The author was Abu Yusuf al-Kindi, otherwise known as ‘the philospher of the Arabs’.
Al-Kindi was director of the House of Wisdom, a research institute and library, based in Baghdad. The House of Wisdom was also a centre of translation, and texts were brought from all over the ancient world in order to gain more knowledge. In some cases, the texts were encrypted, so al-Kindi’s motivation for codebreaking may have been his craving to access these encrypted secrets. Al-Kindi’s breakthrough, known as frequency analysis, may seem obvious to modern eyes, but at the time it was a radical breakthrough that destroyed the security of the existing encryption system. He realised that letters of the alphabet appear with varying frequencies in written text, e.g., on average E accounts for 12.7 per cent of letters in an English text, whereas J, Q, X and Z combined add up to less than 1%. If encryption involves substituting each letter for a different one, then the new letters will take on the frequencies of the letters that they actually represent. Hence, al-Kindi advised codebreakers to count the frequencies of letters in an encrypted text, and then identify their true meaning according to the frequencies, e.g. the most common letter probably represents E.
Explain why the “chances of correctly guessing all 26 letters” in a message is “is 1 in (26x25x…x1),”
Explain in your own words how to use frequency analysis to break a code.
Three encrypted English-language coded texts (F20.coded1.txt, F20.coded2.txt, and F20.coded3.txt) are posted in Blackboard. Use a frequency analysis to break any one of these three coded passages and translate the first 25 words of the text. I left punctuation marks and letters with accents unencrypted so you can leave those as is. Word breaks are also (mostly) still present, which may help speed the code breaking. Hint: Find a reputable source online for the estimates of the frequency of English letters. While the frequency of letters in the coded passages would not be expected to align perfectly with the source’s frequencies – they are a sample after all – this gives you a starting point for your strategy. Note that if you don’t fully break the code, that is OK! You will receive pretty much full credit for providing details on your frequency analysis of the code and as much of it as you think you have figured out.
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Ohm's Law is a formula used to calculate the relationship between voltage, current and resistance in an electrical circuit. To students of electronics, Ohm's Law (E = IR) is as fundamentally important as Einstein's Relativity equation (E = mc²) is to physicists. E = I x R.