CollisionEntropy

CollisionEntropy is a concept used in information theory and cryptography to measure the likelihood of two independent inputs producing the same output when passed through a function or hash algorithm. It quantifies how well a function avoids collisions, which are instances where different inputs map to the same output. A function with high collision entropy is considered to have a good distribution of outputs, making it difficult to find two inputs that produce the same hash value.

The theoretical maximum collision entropy for a function with an output of N bits is N bits. This means that ideally, each possible output is equally likely, and finding a collision would require, on average, checking 2^(N/2) inputs. In practical terms, collision entropy is a crucial metric for evaluating the security of cryptographic hash functions. A hash function with low collision entropy is more susceptible to collision attacks, where an attacker attempts to find two distinct inputs that hash to the same value. This can have serious security implications, particularly in digital signatures and message authentication.

Measuring collision entropy precisely can be challenging. However, it is often approximated by analyzing the distribution of outputs for a large number of inputs. Cryptographic standards and security evaluations often consider collision entropy as a key indicator of a hash function's resistance to attacks.