Everyone is welcome to attend the N&O seminar of Raghu Meka (UCLA) with the title ' Secret Sharing Resilient against Leakage and Tampering' .
Secret sharing is one of the most classical and widely used cryptographic primitives. In the most basic and perhaps the most important setup, a secret needs to be shared between n parties such at that any t of them can recover the secret but no fewer can gain any information even with collusion. As useful as this model, such schemes are still susceptible to attacks where someone 'leaks' tiny amount of information from the parties. Here we seek to counteract such threats.
We say that a secret sharing scheme is p-party leakage-resilient, if the secret remains statistically hidden even after an adversary learns a bounded amount of leakage, where each bit of leakage can depend jointly on the shares of an adaptively chosen subset of p parties. We give an unconditional compiler that transforms any standard secret sharing scheme into a p-party leakage-resilient one for p logarithmic in the number of parties. This yields the first secret sharing schemes secure against adaptive and joint leakage for more than two parties. Our constructions rely on a clean connection we draw to communication complexity in the well-studied number-on-forehead (NOF) model.
Based on joint work with Ashutosh Kumar (UCLA) and Amit Sahai (UCLA).