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 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. In this system, two accumulators that have accumulated a single shared prime can have it trivially discovered by calculating their GCD, even without prior knowledge of the prime. More practical accumulators use a quasi-commutative hash function where the size of the accumulator does not grow with the number of members.
The concept was introduced by J. Benaloh and M. de Mare in 1993
The concept has received renewed interest recently due to the proposed Zerocoin add on to bitcoin, which employs cryptographic accumulators to eliminate trackable linkage in the bitcoin blockchain, which would make bitcoin anonymous and untraceable, increasing privacy of transactions.