Is there an asymmetric crypto analog to direct sequence spread spectrum?
(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 &quot;Gold Code&quot; 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.