The assumption that a cipher like AES scrambles data so well that it looks random to anyone without the key.
The idea: A block cipher like AES takes a key and a 16-byte block and returns a scrambled block. The bet is that, without the key, its outputs look like those of a truly random function. That's what makes encryption work: run the cipher on a counter (1, 2, 3...) to get a random-looking stream and mix it into your data. If the stream had any pattern, the pattern would leak into the data.
Why it matters: Protects nearly all data sent over the internet and stored on disks.
On the map: AES ≈ random permutation ChaCha20 ≈ random function
The assumption that AES behaves like a random permutation[1], and ChaCha20 like a random function[2], to anyone without the key.
It isn't provable, but rests on decades of cryptanalysis: the best attacks on full AES barely beat brute force[3]. Grover's algorithm halves the effective key length in theory, so 256-bit keys are recommended for the long term.
If any of these breaks, this breaks too.
If this breaks, these break with it.