The round complexity of interactive zero-knowledge arguments is an important measure along with communication and computational complexities. In the case of zero-knowledge arguments for linear algebraic relations over finite fields, Groth proposed (at CRYPTO 2009) an elegant methodology that achieves sub-linear communication overheads and low computational complexity. He obtained zero-knowledge arguments of sub-linear size for linear algebra using reductions from linear algebraic relations to equations of the form
are committed vectors,
is a committed element, and
is a bilinear map. These reductions impose additional rounds on zero-knowledge arguments of sub-linear size. We focus on minimizing such additional rounds, and we reduce the rounds of sub-linear zero-knowledge arguments for linear algebraic relations as compared with Groth’s zero-knowledge arguments for the same relations. To reduce round complexity, we propose a general transformation from a
-round zero-knowledge argument, satisfying mild conditions, to a (
− 2)-round zero-knowledge argument; this transformation is of independent interest.