This paper presents a synchronous distributed key generation (DKG) protocol for discrete log-based cryptosystems with communication complexity of $ O(\kappa n^3) $ and tolerates up to $ t < n/2 $ Byzantine faults. The protocol avoids the need for a broadcast channel and instead uses a single Byzantine consensus invocation to achieve efficient communication and round complexity. The protocol has two variants: one with worst-case $ O(\kappa n^3) $ communication and $ O(t) $ rounds, and another with expected $ O(\kappa n^3) $ communication and expected constant rounds. The work introduces several novel primitives, including a weak gradecast protocol with $ O(\kappa n^2) $ communication, a recoverable-set-of-shares primitive for ensuring recovery of shared secrets, an oblivious leader election protocol with $ O(\kappa n^3) $ communication, and a multi-valued validated Byzantine agreement (MVBA) protocol with $ O(\kappa n^3) $ communication. These primitives are of independent interest and contribute to improving the state-of-the-art in each of them. The DKG protocol is designed to be efficient, secure, and suitable for a wide class of cryptosystems. The protocol is shown to be secure under the discrete-log assumption and uses a synchronous communication model. The paper also provides a secure DKG protocol with two broadcast rounds, which is more efficient than existing protocols that require three or more broadcast rounds. The protocol uses a combination of primitives, including gradecast, recoverable-set-of-shares, MVBA, and oblivious leader election, to achieve efficient communication and round complexity. The work addresses the challenge of achieving efficient DKG protocols in a synchronous network setting without relying on a broadcast channel. The results show that it is possible to design a synchronous DKG protocol with $ O(\kappa n^3) $ communication complexity, good latency, and tolerating a minority corruption.This paper presents a synchronous distributed key generation (DKG) protocol for discrete log-based cryptosystems with communication complexity of $ O(\kappa n^3) $ and tolerates up to $ t < n/2 $ Byzantine faults. The protocol avoids the need for a broadcast channel and instead uses a single Byzantine consensus invocation to achieve efficient communication and round complexity. The protocol has two variants: one with worst-case $ O(\kappa n^3) $ communication and $ O(t) $ rounds, and another with expected $ O(\kappa n^3) $ communication and expected constant rounds. The work introduces several novel primitives, including a weak gradecast protocol with $ O(\kappa n^2) $ communication, a recoverable-set-of-shares primitive for ensuring recovery of shared secrets, an oblivious leader election protocol with $ O(\kappa n^3) $ communication, and a multi-valued validated Byzantine agreement (MVBA) protocol with $ O(\kappa n^3) $ communication. These primitives are of independent interest and contribute to improving the state-of-the-art in each of them. The DKG protocol is designed to be efficient, secure, and suitable for a wide class of cryptosystems. The protocol is shown to be secure under the discrete-log assumption and uses a synchronous communication model. The paper also provides a secure DKG protocol with two broadcast rounds, which is more efficient than existing protocols that require three or more broadcast rounds. The protocol uses a combination of primitives, including gradecast, recoverable-set-of-shares, MVBA, and oblivious leader election, to achieve efficient communication and round complexity. The work addresses the challenge of achieving efficient DKG protocols in a synchronous network setting without relying on a broadcast channel. The results show that it is possible to design a synchronous DKG protocol with $ O(\kappa n^3) $ communication complexity, good latency, and tolerating a minority corruption.