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 divide a specific prime into another number to see if it is one of the factors and/or to factor it out. 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.