Cryptographic Accumulator and Its Application: A Survey

Table 4

Security assumptions.

	1993 [1]	Proposing the first cryptographic accumulator which is asymmetric and requires witness verification.
Hash-based construction	2000 [18] 2002 [19]	Proposing the first universal dynamic accumulator satisfying nonrepudiation.
	2008 [20]	A universal accumulator structure based on the hash tree is proposed, which satisfies the concept similar to the nonrepudiation, called a strong universal accumulator.
RSA assumption	1996 [15]	Imposing one-way property (applications where some adversaries can access the list of values to accumulate may not succeed).
Strong RSA assumption	1999 [21]	Proposing a trapdoor-free accumulator.
	2002 [2]	Dynamic accumulator.
	2005 [22]	Dynamic accumulator for bilinear pairs.
t-SDH	2004 [23]	Elliptic curves construction of cryptographic accumulator.
	2007 [24]	(Nonmembership proof is inevitable) providing a dynamic accumulator, then called a universal accumulator.
	2009 [25]	Dynamic pairing accumulator (more efficient witness update algorithm).
t-DHE	2005 [26]	Bilinear map accumulator.
	2009 [25]	t-bound accumulator scheme based on t-DHE assumption is presented.