Codemakers versus Codebreakers

Abstract

At almost regular intervals over the last ten years there have been newspaper and/or magazine headlines like 'Mathematician breaks top secret codes', 'National security threatened by recent mathematical developments', 'Banking security destroyed'. In most cases, the mathematical result referred to was a development in the problem of factoring large numbers, and the claim was wrong because the author had misunderstood the cryptographic significance of the result. However, these headlines indicate a growing awareness of our reliance on cryptography and reflect public concern about the potentially disastrous consequences if some of the (supposedly) secure networks were broken.The protection and security of communications is a subject that has been continuously growing in importance since the introduction of the telegraph in the mid-19th century. Coding messages so that their contents remain secret has been carried out for centuries, and the need for encryption in the traditional military and political environments has always been recognized. But recently, as our society has become highly dependent on its modern communications systems, the use of encryption has spread into the public and commercial domains. Banks now transfer exceedingly large amounts of money by means of computers and it is, of course, crucial that they secure these transactions against alterations by unwelcome third parties.In this review we look at some of the techniques used to design a secure system and at some possible attacks which might be launched against it. The subject is, essentially, a battle of wits between the designer of the system (the codemaker) and the attacker (the codebreaker) with potentially disastrous consequences if the codebreaker wins. This 'battle' has been revolutionised by the advent of high-speed computers, and systems which were virtually unbreakable in the 19th century can now be broken in a few seconds. Thus, as we shall illustrate, the mathematical and statistical knowledge required by both the codemaker and codebreaker has increased dramatically, and the 'rules' of the contest are continually changing. It is a fascinating subject.