I'd also note that zero-knowledge proofs (which are considered a branch of cryptography) often do rely on NP-complete problems like the three-color maps.
That's completely unrelated, the reliance there is because you want to be able to prove "any statement in NP" in zero knowledge. It then suffices to give a protocol for just 3-colorings, because "any statement in NP" can then be reduced to a 3-coloring.
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I'd also note that zero-knowledge proofs (which are considered a branch of cryptography) often do rely on NP-complete problems like the three-color maps.
That's completely unrelated, the reliance there is because you want to be able to prove "any statement in NP" in zero knowledge. It then suffices to give a protocol for just 3-colorings, because "any statement in NP" can then be reduced to a 3-coloring.