Accumulator (cryptography)

A cryptographic accumulator is a one way membership function. It answers a query as to whether a potential candidate is a member of a set without revealing the individual members of the set. One trivial example is how large composite numbers accumulate their prime factors, as it's currently impractical to factor a composite number, but relatively easy to find a product and check if a specific prime is one of the factors. New members may be added or subtracted to the set of factors simply by multiplying or factoring out the number respectively. More practical accumulators use a quasi-commutative hash function where the size (number of bits) of the accumulator does not grow with the number of members.