Tightly Secure Lossy Trapdoor Functions: Constructions and Applications

Box 4

A collection of ABO-LTFs from the DDH assumption.

System Parameter.   It returns . The branch space is .

Key Generation.   For any branch , it randomly chooses two vectors

and , and computes .

It returns and .

Evaluation.   On input and a branch , it computes

an image .

Inversion.   Suppose that and . For , it computes

, and lets be such that . It returns .