Take all possible input strings
Given any input string, the sensitivity of that string is how many bits you could flip that cause the output to flip.
Now take the /maximum/ of all input string sensitivities.
For e.g. a hash function, you'd want either a minimum or something like a 1st percentile.
As far as I know, all cryptographic hash functions are sensitive to single bit-flips by design.
Finding those inputs is essentially impossible, but for a true 'random oracle ' they are likely to exist.
And I thought they had ways to construct hash functions so that all the inputs of the same length have a different output?
That's trivially impossible for fixed-size hashes, by the pigeon hole principle.
The point being, for at least that case you can guarantee a sensitivity of one bit.
The sensitivity of that string is the minimum number of bits that need to be changed in order to change the output?
Not being snarky - just want to see if I understand. The phrase "how many bits you could flip" is ambiguous.
From the article: "If, say, there are seven different lies you could have told that would have each separately flipped the outcome, then for your loan profile, the sensitivity of the Boolean function is seven."