What are the factors required to estimate the minimum required power for an experimental aircraft of a specific mass?
A good engineer will first check existing designs: How much power is installed in comparable designs? Use airplanes of similar speed and built quality, such as the Super Diamond Mk 1 which needs 50 to 60 hp. Cruise speed is 90 knots and the MTOW is 450 kg.

Next, try to estimate the minimum wing area. Starting from the minimum speed requirement of 35 kts ( = 18 m/s), and assuming a maximum lift coefficient with flaps down of 1.6, the area to support 340 kg at sea level is $$S = \frac{2\cdot m\cdot g}{\rho\cdot c_L\cdot v^2} = \frac{2\cdot 340\cdot 9.81}{1.225\cdot 1.6\cdot 18^2} = 10.5 m^2$$

Now calculate the drag coefficient in cruise, using the parabolic drag equation. First, establish the lift coefficient at which drag is minimized: $$c_{L_{opt}} = \sqrt{c_{D0}\cdot\pi\cdot\epsilon\cdot AR}$$
The total drag coefficient at this point is simply twice the zero-lift drag coefficient $c_{D0}$, so a low drag design is important. Still, with a fixed gear your zero-lift drag coefficient will hardly be lower than 0.035, so your cruise lift coefficient is 0.938 (assuming an aspect ratio $AR$ of 10 and an Oswald factor $\epsilon$ of 0.8), resulting in a flight speed of just 23.51 m/s = 45.7 kts. Total drag at this point is $$D_{min} = 2\cdot c_{D0}\cdot S\cdot\rho\cdot\frac{v^2}{2} = 249 N$$

To sustain flight at this point only requires $P = v\cdot D$ = 5.85 kW, and assuming a prop efficiency of 0.75, the installed power should be 7.8 kW. But you want to fly faster, so we need the drag at 100 kts ( = 51.4 m/s):
$$D = \left(c_{D0} + \frac{c_L^2}{\pi\cdot\epsilon\cdot AR}\right)\cdot S\cdot\rho\cdot\frac{v^2}{2}$$
There, your lift coefficient is only 0.196 but the dynamic pressure rises to 1,621 N/mm². Since the Reynolds number is higher, your zero-lift drag could drop to 0.031, resulting in a drag force of 550 N. At that speed, the required power is 28.3 kW. Under the heroic assumption that your prop will still be 75% efficient at that speed, the installed power needs to be 37.8 kW or 50.65 hp.

If you "only" want to achieve a TAS of 100 kt at altitude, here is what you need to do in the case of cruise at 10,000 ft ( = 3048 m). First you need the density at that altitude, which is 0.9 kg/m³ or 74% of the value at sea level. This means that the dynamic pressure is 1,191 N/mm² and the lift coefficient 0.267, resulting in a drag force of 419 N. This needs a continuous power of 21.56 kW to overcome. Now I assume the 75% efficient propeller again and that you run the engine at 75% of max. power, so the installed power in 10,000 ft should be at least 38.3 kW or 51.4 hp. Assuming a normally aspirated engine, this would translate to a rated power of 70 hp at sea level.

Considering that similar designs require similar power, this looks about right. Normally, you now need to compute the climb speed with the excess power of 35.15 kW to check how usable this design is, but at 10.5 m/s I doubt this will be not enough.

If you manage to include a retractable gear with your limited mass budget, the zero-lift drag might be as low as 0.024. Now the drag force in cruise at 10,000 ft will be only 324.4 N and the installed rated power at sea level only 40.4 kw or 54 hp.

With piston aircraft, your power needs increase with the cube of airspeed. I leave it as an exercise to you to calculate how much more power the last 10 knots require: Repeat the calculation with only 90 kt cruise and your rated engine power can be as low as 51 hp with a fixed gear.