Deterministic Identity-Based Encryption from Lattice-Based Programmable Hash Functions with High Min-Entropy

Table 1

Comparison of Adaptively Secure DIBE Schemes in the Auxiliary-Input Setting.

Schemes	of; matrix	Rounding; Parameter	Message; Space	Sample; Width	Reduction; Cost
XXZ12 [3]
Ours:

shows the size of the master public key. and denote the number of key extraction queries and the advantage of the adversary, respectively. represents a fixed but large polynomial that does not depend and . To measure the reduction cost, we show the advantage of the LWE algorithm constructed from the adversary against the corresponding DIBE scheme.
, is the constant satisfying , where is the relative distance of the underlying error correcting code. We can take as close to as one wants.
, and are the smallest integers satisfying that and .
, is the smallest integer satisfying that .