Smooth Projective Hash Functions (SPHF)

Let X X X be the domain of these functions and let L L L be a certain subset of points of this domain (a language).

A key property of these functions is that, for points in L L L, their values can be computed by using either a s e c r e t secret secret hashing key or a p u b l i c public public projected key.

A projective hash function family is said to be s m o o t h smooth smooth if the value of the function on inputs that are outside the particular subset L of the domain are independent of the projected key.

(Crypto 09)Smooth Projective Hashing for Conditionally Extractable Commitments