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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. 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.

The concept was introduced by J. Benaloh and M. de Mare in 1993^{[1]}

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.^{[2]}^{[3]}^{[4]}

**^**J. Benaloh and M. de Mare, One-way accumulators: a decentralized alternative to digital signatures, Advances in Cryptology—Eurocrypt’93, LNCS, vol. 765, Springer-Verlag, 1993, pp. 274–285.**^**Miers, Ian. Zerocoin: Anonymous Distributed E-Cash from Bitcoin. isi.jhu.edu**^**"A Few Thoughts on Cryptographic Engineering: Zerocoin: making Bitcoin anonymous". Archived from the original on 21 May 2014.. Blog.cryptographyengineering.com (11 April 2013). Retrieved on 20 April 2013.**^**Zerocoin: Anonymous Distributed E-Cash from Bitcoin Archived 8 February 2014 at the Wayback Machine.