Distributed key generation (DKG) is a key building block in developing many efficient threshold cryptosystems. This work initiates the study of communication complexity and round complexity of DKG protocols over a point-to-point (bounded) synchronous network. Our key result is the first synchronous DKG protocol for discrete log-based cryptosystems with $O(\kappa n^3)$ communication complexity ($\kappa$ denotes a security parameter) that tolerates any $t < n/2$ Byzantine faults among $n$ parties. We present two variants of the protocol: (i) a protocol with worst-case $O(\kappa n^3)$ communication and $O(t)$ rounds, and (ii) a protocol with expected $O(\kappa n^3)$ communication and expected constant rounds. In the process of achieving our results, we design (1) a novel weak gradecast protocol with a communication complexity of $O(\kappa n^2)$ for linear-sized inputs and constant rounds, (2) a protocol called “recoverable-set-of-shares” for ensuring recovery of shared secrets, (3) an oblivious leader election protocol with $O(\kappa n^3)$ communication and constant rounds, and (4) a multi-valued validated Byzantine agreement (MVBA) protocol with $O(\kappa n^3)$ communication complexity for linear-sized inputs and expected constant rounds. Each of these primitives is of independent interest.