Avalanche Effect Target

This formula gives the ideal avalanche target for a hash function: if you change one input bit, each output bit should have about a 50% chance of flipping. That means the expected number of changed output bits is half the hash length, because the output bits behave like independent coin flips in a well-designed construction. The target comes from the idea that a secure hash should make small input changes produce outputs that are statistically indistinguishable from random with respect to the old output.

Use this when evaluating or teaching hash-function diffusion, comparing two candidate hashes, or checking whether a design has enough sensitivity to input changes. It is also useful in cryptographic testing, where you measure whether observed bit-flip counts are close to the ideal half-output-length benchmark.

• Thinking the formula says exactly half the bits must flip every time, instead of on average
• Using the number of input bits instead of the output size n
• Assuming a poor hash is acceptable just because some output bits change