Numbers, Codes and Secrets case study

What do you do when you're faced with a set of numerical tables that supposedly contain important coded information?

Codes have been used throughout history to ensure that information is read and understood only by the intended receiver. From Mary Queen of Scots to the Enigma code of the Nazis, there are many famous examples of the encoder's art and the work of those whose task it is to break them.

In 1996, the maths department of Surrey University received a diary kept by an RAF officer. Each page of the diary was divided into a grid of boxes. Each box contained four digits. The pages of the diary were headed "Russel's Mathematical Tables". This was the diary-keeper's way of disguising what he was doing, as this was forbidden by his captors.

The senior mathematics lecturer who agreed to help decode the diary began by looking into the fundamental principles of numerical codes. He didn't believe that this code would be particularly difficult to break - after all it had been written in a prison camp with a pencil and paper - and the mathematician had the advantage of computer technology to help him.

Most numerical codes use a single number to replace a single letter. Their weakness stems from the tendency of language to follow predicted patterns. So, for example, in English, the letter "e" appears more frequently than any other, and the letter "t" is often followed by the letter "h". The mathematician carried out computerised searches to reveal the likely numbers for these common combinations of letters, expecting that the coding system would be revealed quickly.

When this proved unsuccessful, the academic realised that the diarist must have used a multi-stage coding process that replaces one letter with another, perhaps over and over again, before converting it to a number. This meant that the diarist had to have used key words or phrases to construct his code. A seemingly simple task for the mathematician began to take on epic proportions as he laboured for almost six months in his free time to try to find the key to the code.

Close to the point of admitting defeat, the academic experienced a classic "eureka" moment, awaking with an image in his mind of the inside cover of the diary, at the bottom of which were two names printed in the diarist's handwriting: DONALD SAMUEL HILL and PAMELA SEELY KIRRAGE. These names contained 34 letters, a number that corresponded exactly to the number of digits in each of the diary's coded lines. Realising that the order of the letters in the two names must be the key to cracking the code in the diary, the maths lecturer set about translating the pages.

But the diarist had one more trick up his sleeve: rather than reading the coded information from left to right across the rows, the diary had been written from the top to the bottom of the columns. The academic set his computer to translate the diary according to this new configuration and found that recognisable words appeared on his screen. Working slowly, as every line required separating into words, the code-breaker typed two pages of the diary every evening, reading in instalments. The diary covered the fall of Hong Kong, where the diarist had been posted in December 1941, followed by his doomed attempts to evade capture and his subsequent transfer to a PoW camp.

Donald Hill and his wife Pamela, who married in 1946 were never to enjoy a happy marriage, Hill's mind too scarred by the experience of imprisonment. But through the efforts of Philip Aston, the University mathematician, Pamela had been able to understand what lay behind her late husband's sadness, never expressed to her directly, but hidden in code in a wartime diary.