Cryptographic Accumulator and Its Application: A Survey

Table 5

Cryptographic accumulator schemes.

Known order group
2005 [22]	A dynamic accumulator scheme is proposed, which is suitable for paired-friendly groups with prime p.; It is secure under the t-SDH assumption and allows up to values to be accumulated from the domain.
2008 [32]	Extended 2005 scheme with general functions.
Hidden order group
The accumulative domain is limited to primes
1997 [5]	Improved the original RSA scheme in 1993 and strengthened the original concept of collision-free safety.
1999 [21]	It is recommended to use unknown decomposed RSA modules to construct trapdoor-free accumulators.
2002 [2]	The scheme in 1997 is extended to have the ability to dynamically add/delete values to the cryptographic accumulator, and the first dynamic accumulator is constructed.
2007 [24]	In 2002, support for nonmembership witnesses was increased, so a universal dynamic accumulator was obtained, and an optimization scheme was proposed to update the documents of nonmembership witnesses more effectively.
2012 [34]	The RSA accumulator is broadly defined as a module over a Euclidean ring.
The accumulative domain is limited to semiprimes
2003 [37]	It is allowed to accumulate semiprimes.
2007 [29]	The cryptographic accumulator scheme allows arbitrary integers to be accumulated and supports batch updates of witnesses.
2019 [39]	Dynamic accumulator based on hash greatly reduces storage space.
2011 [38]	The upper limit t for accumulating elements of the t-SDH accumulator is canceled.