Cryptic message spelling millions

On January 13 1999, The Times published a front-page story about Sarah Flannery, a 16-year-old from County Cork whose project on cryptography (the mathematics of secret codes) had just won her the title of Ireland's Young Scientist of the Year 1999. In a television interview the evening of the award announcement, one of the judges of the competition, referring to a new system Sarah had proposed for encrypting messages, had made the ill-considered comment that "if she plays her cards right I think she should make a lot of money".

The Times and a host of other newspapers, magazines and radio and television stations found the combination of Sarah's youth, gender and rumours of impending wealth so enticing that she became an instant celebrity. She was interviewed by media from the United States to Singapore, the Spice Girls used her as an example of "girl power" in their magazine and she was besieged by offers from patent lawyers, venture capitalists, high-tech start-up businesses and others, all insisting that they had the perfect formula to help her maximise the profits from her crypto-system. The Daily Express announced that "this girl has invented a computer code that could make her a billionaire."

A direct consequence of The Times story was Profile Books's invitation to Sarah and her father and mentor David Flannery to publish an account of her experiences. This book is the happy result.

Sarah writes charmingly of her fascination with mathematical ideas, fostered by her parents. There is a blackboard in the Flannery kitchen and from their earliest years Sarah and her four younger brothers were encouraged to tackle mathematical puzzles and explain their reasoning to the rest of the family.

Interspersed with Sarah's account of her life and the various scientific competitions she won are mathematical puzzles and a non-technical explanation of the mathematics of public-key crypto-systems. (For Sarah's algorithm itself and the attack on it, the reader is referred to Sarah's website: www.cayley-purser.ie) Sarah's style is lively, her story exciting, and her mathematical exposition lucid. This is a book that could be read with enjoyment and profit by maths and science students and teachers as well as parents seeking to provide academic encouragement to their children.

After all the commotion in the press and predictions of dramatic practical consequences of Sarah's project, it is natural to ask whether her work had any impact on cryptography. It did not. As she explains in the book, her crypto-system was soon shown to be insecure.

In fact, if any of the journalists who covered the story had consulted an expert in the mathematical analysis of crypto-systems, they would have been told that the type of construction Sarah used, based on matrix multiplication, is very risky; such a system can almost certainly be broken using linear algebra or matrix algebra. Also, as in other branches of science, it is foolish to herald a new breakthrough before specialists have had the chance to examine it for flaws.

But two points should be made here. First, Sarah and her parents are entirely blameless - they made no exaggerated claims and did nothing to encourage the hype and sensationalism in the press. Second, the flaw in Sarah's crypto-system in no way detracts from her achievement.

Even systems proposed by leading cryptographers have often turned out to be insecure. For example, in the late 1970s two of the early pioneers of public-key cryptography, Martin Hellman and Ralph Merkle, proposed a clever and fast method of encryption based on the mathematical problem of stuffing a knapsack with objects so as to leave no wasted space. Despite initial high hopes, a few years later knapsack crypto-systems were broken.

Sarah has little to say about gender in the book. However, part of the reason for the intense public interest in her accomplishments was that they contradicted popular stereotypes about gender roles. Unfortunately, in most parts of the world women still encounter obstacles when they attempt to enter traditionally male professions. According to our internet search of all university maths departments in the Irish Republic, out of more than 30 full professors none is a women; women also make up less than 10 per cent of the roughly 120 lecturers with doctorates. Ireland is not unique in this respect; many countries (including the UK) still have very low percentages of women in high-status jobs in the mathematical professions.

On the other hand, some countries (such as Turkey, Italy and France) have done better in this regard. In view of the talent and enthusiasm of young women such as Sarah Flannery, there is no excuse for allowing the severe under-representation of women in the mathematical sciences to continue.

Ann Hibner Koblitz is professor of women's studies, Arizona State University. Neal Koblitz is professor of mathematics, University of Washington, Seattle.