A family of one-way hash functions is an infinite sequence of families of functions , where , with the following properties: ① For any integer and any is computable in polynomial time in ② for any probabilistic, polynomial-time algorithm A, (3) is satisfied, where the probability is taken over the random choice of and the random coins of .
Quasi-commutativity
A function is said to be quasi-commutative if (4) is satisfied.
One-way accumulator
A one-way accumulator is defined as a family of one-way hash functions with quasi-commutativeness. This description is elegant and simple, but, in order to clarify the basic function of the security cryptographic accumulator, the ability to intuitively accumulate set L as a small value can be proved only for element . In fact, the one-way property imposed by the second requirement is often too weak for applications where the attacker can choose some value to accumulate.
Strongly one-way hash function
A family of strongly one-way hash functions is an infinite sequence of families of functions , where , having the following properties: ① For any integer and any is computable in polynomial time in ; ② for any probabilistic, polynomial-time algorithm , (7) is satisfied, where the probability is taken over the random choice of and the random coins of .
The cryptographic accumulator scheme is a 4-tuple of polynomial-time algorithm (Gen, Eval, Wit, and Ver)
N-times collision-freeness
A cryptographic accumulator scheme is said to be N-times collision-free if, for any integer and for any probabilistic, polynomial-time algorithm , probability is taken from Gen, Eval, and random coins of .
Collision-free
When a cryptographic accumulator scheme is -times collision-free for any value of polynomial in λ, it is called collision-free.
