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

Table 3

Four Adaptively Secure DIBE Schemes in the Auxiliary-Input Setting.

Schemes

of; matrix

Rounding; Parameter

Message; Space

Sample; Width

Reduction; Cost

show the size of the master public keys and ciphertexts, respectively. and denote the number of key extraction queries and the advantage, 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.
   is the smallest integer satisfying that .
and are the smallest integers satisfying that and .