Lift for power. Use mid range reps per set (6-8) with whatever weight you generally use for those reps and lift as fast as possible then lower the weight in control. You really need to workout your whole body but probably focus on chest, shoulders, and triceps (bench press). Also eat plenty to add lean muscle mass but remember there is a difference between lifting for power and lifting for size.

Bigger muscles on your arms slow you down. That's like someone is tying heavy bags on your arms(easy to imagine that you then start to slow down, because you need just enough energy to lift the weight up).

Here are the things you can do to increase punching power, without getting big muscles:

1. work the heavy bag

2. make bodyweight exercises(for example pull ups, push ups or squats)

3. use a chest expander or fitness band

4. you can also train with weights, but only power training(Power is the strenght you can produce in a short time period. You train power, when you put so much weight on your dumbbell/barbell or machine, that you can make 5 reps in 4 sets)

5. train with kettlebells

6. boxing with weight wristbands

7. boxing with dumbbells

8. punching against the wooden dummy(or plastic dummy)

9. punching against the wall(there are some wall schooners made of polyester ecc.)

10. shadow boxing

Quote Mike Tyson Once Said In an interview "Power Puncher Hitters are Born Not Created" But if you want too get some power I recommended lifting weights and working on the heavy bag a lot

Building muscle does help increase punching power, but power is not the only factor. Twisting your hips when throwing a punch actually does increase your punching power and having good balance helps putting leverage in your punch and some weight in it as well. Flat out muscle strength doesn't make a good punch.

In order to increase punching power, you have to increase the function of your fast-twitch muscles. Usually, these fast-twitch muscles are the ones that aid in the speed and explosiveness of a punch. In order to train these, you have to do many repetitions of fast push-ups because push-ups are the exercises that use your arm's fast-twitch muscles to the maximum increasing shoulder, forearm, bicep, triceps, and wrist power and support. I prefer the close-grip push-ups, the normal push-ups, the clap push-ups, and the explosive push-ups for push-up routines.

Lastly, do mid-speed fist push-ups on the ground until failure. The knuckles will not only harden, but it will also be one of the parts that will support the heavy up & down movement of the push-up exercise which will also increase arm speed and power.

Don't do too much weights. Weights are slow lifts only increasing your carrying strength but not punching power. It will only strengthen slow-twitch muscles used for lifting, supporting, or providing stronger leverage.

I also believe in the use of technique to increasing punch power. Mike Tyson knocked people out not just because he is a physical boxing specimen, but he also used his legs, position, angle, footwork, and shoulders to deliver a massive superman-like punch towards the opponents he fought, and surprisingly, he knocks the lights out of them.

lift weights and eat lots of protein

No , don't tell me how to punch (rotating hips, footwork) if it was technique that made the punch hard , any motherfker that knows how to punch would knock people out like Mike Tyson.

So what exercises do I do to increase punching power ? Do I need bigger muscles or ?