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WORLD OF SCIENCE

Breaking codes

DR. T. V. PADMA

Frequency analysis was used to break encrypted messages.

Arabic mathematicians made tremendous contributions to cryptanalysis — the science of decoding scrambled messages. Their interest stemmed partially from their religion.

The holy Koran contains revelations made by the Prophet Mohammed. The text contained dictated messages that the Prophet had received from the archangel Gabriel. However, these revelations were not necessarily placed in the order in which the Prophet had received them. To deduce the order of the revelations and place them in chronological context, Muslim scholars determined that some passages contained words coined more recently, and some contained words that were older.

Then, they counted the frequencies of words in each revelation, paying attention to the frequencies of modern and ancient words. Passages which contained a greater frequency of modern words were considered to have been written later.

How it works

In the ninth century, an Arab mathematician called Al-Kindi employed a similar technique to break encrypted messages — frequency analysis. Letters are ranked according to how commonly they occur. Then, the encrypted message is taken, and the most frequent letter appearing in the code is noted. The code is then compared to the language, and using the correspondence in rank, the encrypted message can be unscrambled. He described this in a book — A manuscript on deciphering cryptographic messages.

For instance, a code used to transmit a message in English, the most common letter is the letter e. The second most common letter is t. So if the English letter “e” was represented by the letter x in the encrypted message, then x would be the most frequently appearing letter in the code. Similarly, if the letter “q” was used in the code to represent the letter “t”, then “q” would be used to replace “t”. The method is based on averages and makes some assumptions — it is not foolproof.

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