Title: New Construction for MPC from the Variable Density Learning Parity
with Noise (LPN) assumption
Abstract: Multiparty computation (MPC) allows users to compute various
functions of their secret inputs, while ensuring that these inputs remain perfectly
hidden. In the early 2000, correlated secret randomness was shown to be a
useful resource for realizing efficient MPC protocols. Thus, many efforts have
been deployed to improve the generation of correlated randomness. I will present
a series of works that have led to the successive creation of Pseudorandom
Correlation Generators (PCGs), an analogue of pseudorandom generators,
and Pseudorandom Correlation Functions (PCFs), an analogue of pseudorandom
functions.
PCFs are a very powerful tool, but their construction is very complex. It relies on
the creation of a new weak WPRF, and on the use of a Function Secret Sharing (FSS).
The security of this new WPRF is based on a Variable Density variant of the Learning
Parity with Noise assumption called (VDLPN). In this variant, the matrix is no longer
a randomly chosen matrix, but a matrix whose density decreases exponentially. The
presentation will discuss the security proof of the WPRF, which supports the security
of our PCF.
This is a joint work with Geoffroy Couteau.
