I'm trying to code up BIP0032, with full test coverage and I hit a snag with these very rare edge cases:
Private parent key → private child key
In case parse256(IL) ≥ n or ki = 0, the resulting key is invalid, and one should proceed with the next value for i. (Note: this has probability lower than 1 in 2^127.)
Public parent key → public child key
In case parse256(IL) ≥ n or Ki is the point at infinity, the resulting key is invalid, and one should proceed with the next value for i.
I have not written any code around these conditions as without test cases to show I have done it correctly, it's pointless.
I've successfully tested my code with 30 million addresses generated from another library, but I think to stand a better than 50/50 chance of finding one of these edge cases I would have to check in the order of
10^19 (source: Birthday attack).
So my question is, does anyone have any test vectors for these cases?
The alternative is to have a whitebox test that passes bad
IL values directly to an otherwise private function, but I'd rather have a blackbox test.