Messages in Mathematically Scrambled Waves
Peterson, Ivars, Science News
When White House chief of staff John H. Sununu travels, he has with him special equipment to scrable telephone calls and keep communications secure from eavesdroppers. This kind of sophisticated, expensive technology for assuring privacy, however, generally lies beyond the reach of someone who merely wants to keep neighbros from inadvertently listening to or deliberately intercepting conversations over a cellular or portable telephone.
"There are only a few cases where you want to use the best [technology available]," says mathematician and cryptography expert G.R. Blakley of Texas A&M University in College Station. "Just as we put locks on sliding glass doors, we want to be able to enclose certain [information] in envelopes that are relatively inexpensive and keep out casual browsers."
Blakley is one of a small group of computer scientist and mathematicians now exploring the applicability of several mathematical techniques for scrambling analog information -- such as a telephone conversation or a television signal -- which is represented as a continuous wave rather than digitally as a sequence of numbers. "We're trying to build up a zoo of mathematical choices to that ... people can search among them to find things that are both reasonably secure and cost-effective to implement," he says.
Blakley and several other speakers described recent developments in analog cryptography at the International Conference on Industrial and Applied Mathematics, which convened last week in Washington, D.C.
Practically all present-day cryptographic systems for hiding information depend on having signals in a digital form. Scrambling a telephone conversation, for example, requires converting speech into a digital signal, which is then mathematically manipulated to produce the encrypted message.
One possible way to simplify the whole procedure involves working directly with the continuous wave itself, circumventing the time-consuming and costly process of converting the analog signal into a digital form. But finding the right set of mathematical manipulations that not only effectively hide information, but also permit their easy unraveling by a receiver, remains a challenge.
Computer scientist George I. Davida and mathematician Gilbert G. Walter of the University of Wisconsin-Milwaukee have studied several candidates for an analog cryptographic system that would provide a reasonable level of security. One scheme requires applying a so-called "integral operator" to a speech signal. This mathematical process takes all the bumps and sudden shifts out of the original waveform. …