## Function Secret Sharing: Improvements and Extensions

### Elette Boyle

**Abstract:**

Function Secret Sharing (FSS) provides a way for additively secret sharing a function from a given function family: eg, splitting f into f1 and f2 such that f1(x) + f2(x) = f(x) for every input x. FSS schemes are useful for applications that involve privately reading from or writing to distributed databases while minimizing the amount of communication.

We discuss several recent improvements and extensions of FSS based on any one-way function:

• Optimized FSS for the class of point functions (namely, functions f_{u,v} that evaluate to v on the input u and to 0 on all other inputs) and corresponding Private Information Retrieval related applications.

• FSS for new function families.

• Verifiable FSS, i.e. protocols for efficiently determining whether shares f1, f2 are valid shares of a proper function f.

Joint work with Niv Gilboa and Yuval Ishai.