> If Signal works, as was pointed out during the recent scandal, it only protects messages in transit. The application on your phone is not especially secure and anyone who can access your phone can access your Signal messages (and thus any of your correspondents' messages that they share with you).

Device compromise is outside the threat model for Signal or any software for that matter.

> Why do you say that? Very often the vulnerabilities are not in the mathematics but in the implementation.

This is why we use primitives that are well understood and have straightforward implementations. I'm no expert but you can look at design of say Salsa20 or Curve25519 -- it was designed for straightforward constant time implementation. Yes NIST suite has implementation subtleties such as constant time implementations, but those ward off issues that are of pretty low concern / infeasible to attack (i've yet to see a timing channel or cache side channel be exploited in the wild except for the XBox 360 MAC verification). Also CFRG has been publishing guidance so we know how to properly implement KEMs, (hybrid) encryption, PAKE, hash to curve, signatures, ECDH, ECDSA, etc. Compound this with a lot of footgun free crypto libraries such as Go crypto, libsodium, monocypher, BoringSSL, Tink, etc. and these days you'd be hard pressed to make a misstep cryptography wise.

In my opinion, NSA advantage is not that it has a virtually unlimited budget, it's that they have better vantage point to carry out multi-user attacks. So does the likes of FAANG, Fastly, Cloudflare, etc.