Messages in mathematically scrambled waves.

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. "What comes out is a smoothly varying signal," Walter says. "On an oscilloscope, it doesn't look at all like the original speech signal."

To recover the original speech, the message's authorized receiver applies a differential operator -- the inverse of the integral operator -- to the encrypted signal, which restores is initial choppiness. However, certain integral operators may fail to hide information adequately. The human ear is remarkably resilient, Walter says. "If we aren't careful about the way we choose the integral operator, [an eavesdropper] can still understand what comes through."

Moreover, the overwhelming preponderance of digital equipment in the modern laboratory stymies the testing of analog cryptographic devices. "The problem is that we have to simulate these analog devices by digital means [on a computer], which sort of defeats the purpose," Walter says.

Nevertheless, Davida adds, "we've achieved some remarkable results in the realm of both [information] compression and encryption."

A newer, alternative approach to analog cryptography involves dividing an analog signal into small pieces, then using a relatively new mathematical technique known as wavelet analysis to break each piece up into its components. The idea is that any wave segment can be represented by a suitable collection of fundamental building blocks, or wavelets.

The wavelet technique converts each wave segment into a set of numbers representing how many of each building block are present in the given segment. Scrambling these numbers produces a new, different waveform, which can then be sent as an encrypted message. The receiver, who knows how the numbers were scrambled and which set of wavelets were used as the building blocks, reverses the process to hear the message.

One advantage of using wavelet analysis for cryptography is that the process simultaneously shuffles frequencies and times. The scheme changes not only the order in which pieces of the wave are transmitted but also mixes up the signal's characteristic frequencies.

"I'm really anxious to try this method in the laboratory," Walter says. "I think we can simulate it on a computer."

"We feel rather lonely because not many people are working in this area," Davida says. "I think they have mistakenly abandoned analog systems. I can't imagine analog signals going away entirely."

Furthermore, analog cryptographic systems may help lower the cost of assuring privacy, Davida says. "It's worthwhile to have privacy available to anyone who wants it."