A Group Identification Protocol with Leakage Resilience of Secret Sharing Scheme

الملخص EN

Secret sharing has been study for many years and has had a number of real-word applications.

There are several methods to construct the secret-sharing schemes.

One of them is based on coding theory.

In this work, we construct a secret-sharing scheme that realizes an access structure by using linear codes, in which any element of the access structure can reconstruct the secret key.

We prove that our scheme is a multiprover zero-knowledge proof system in the random oracle model, which shows that a passive adversary gains no information about the secret key.

Our scheme is also a leakage-resilient secret-sharing scheme (LRSS) in the bounded-leakage model, which remain provably secure even if the adversary learns a bounded amount of leakage information about their secret key.

As an application, we propose a new group identification protocol (GID-scheme) from our LRSS.

We prove that our GID-scheme is a leakage-resilient scheme.

In our leakage-resilient GID-scheme, the verifier believes the validity of qualified group members and tolerates l bits of adversarial leakage in the distribution protocol, whereas for unqualified group members, the verifier cannot believe their valid identifications in the proof protocol.