Is there an asymmetric crypto analog to direct sequence spread spectrum?

Question

In section 12.1.1.2 of Digital Communications: Fundamentals and Applications, Bernard Sklar makes this claim about spread spectrum signals:

Therefore, not only can the spread-spectrum signal be made difficult to jam, but additionally, the signal's very existence may be rendered difficult to perceive. To anyone who does not possess a synchronized replica of the spreading signal, the spread-spectrum signal will seem "buried in the noise."

This seems analogous to symmetric cryptography; there is a symmetric "key" (the spreading signal) that allows one to both transmit and receive messages, and without the key one can neither transmit nor receive a message. Furthermore, without the key one cannot even detect the presence of a message (or, at the very least, it makes it more difficult to do so).

This makes me wonder if there's an asymmetric cryptography analog to direct sequence spread spectrum. I assume there would be a public and private "key" pair, and one could use the public key to transmit a message, but only the private key could be used to receive that message. And without the private key, it would be very difficult to even detect the presence of a coded message (i.e. only the private key could be used to "de-spread" the message).

Does such a technique exist?

Answer 1

(This does not answer your question which is a good one, so I may move this to a comment below your question)

Warning! Typical Direct Sequence Spread Spectrum that uses linear spreading codes (based on linear feedback shift registers implemented from irreducible and primitive polynomials) are NOT a good cryptographic technique. See this post where the approach to break such codes is detailed:

Minimum Output Samples needed to crack a "Gold Code" Generator (Dual LFSR)

This is because although the signal will indeed be "buried in the noise" at certain reception points, it is very rare to not be able to get closer to the transmitter (either spatially or with highly directional antennas) such that a positive SNR can be established enough to get the relatively small number of consecutive sequences to crack the code.

Use of non-linear codes together with data layer encryption are recommended. I wanted to mention this due to the common misconception that DSSS alone is a good communication security technique.

Answer 2

The military GPS signals are crypto grade CDMA signals. One can use the civilian CA signal to recover the P(Y) military signal carrier because they use a common carrier and some receivers derive some clues from P(Y) but you need to know the sequence to recover the signal. The new M code is much harder because carrier recovery is much harder and the bit sequences has nearly infinite period. You need to know the full sequence to know which partial sequence is active at the moment to recover the signal. If you know the sequence, you can recover the message. If you don't know the sequence, there is no recovery.

The spread sequence is said to consist of chips instead of bits because it doesn't convey information.

In public key encryption, you have a random sequence that is observed. In CDMA, the sequence is nearly unobservable. So I believe the answer to your question is no, and if there was, no one would say so.

There would have to be a known transformation of the signal as it is propagating that would render the transmit code sequence nonrecoverable at the receiver.

Answer 3

Some examples:

1. Watermarking: Insert info in a digital content in such a way that degradation produced by the insertion does not degrade subjective perception. Techniques exist making the info hard to extract or even notice.

2. Side channel info: codify info in non-standard features of a signal. I do not have a reference, but, for example, it could be possible to encode information in the jitter of IP packets over a network. It is, by nature, almost indetectable (jitter is kind of noisy signal).

Note that you can use any of this as is, or you can add a cryptography algorithm on top of them.