How does the IAS stall speed vary with increasing altitude?
Airplanes do not stall at the same indicated speed or even at the same angle of attack - it all depends on circumstances.

The angle of attack dependency is discussed here. An increased pitch rate can push the stall angle of attack 50% higher than what the stall angle of attack is in stationary conditions.

The next big factor is the Mach number. When increasing the angle of attack, the flow around the airfoil's nose will develop a suction peak. This suction is equivalent to higher local speed, and if the critical speed (when local flow speed equals the local speed of sound) is exceeded, the flow past the suction peak will no longer behave similarly to the flow at the same angle of attack but a lower flight Mach number. Let's just say that the local Mach number in the suction peak has a strong influence on the stall angle of attack, and flying at a higher Mach number lowers the stall angle of attack, sometimes dramatically.

Increasing altitude will raise the flight Mach number in two ways:


The reducing density means you need to speed up to fly at the same dynamic pressure, and
the atmospheric lapse rate decreases the speed of sound in air.


Both effects conspire to reduce the stall angle of attack at 30.000 ft to a value quite a bit below that at sea level. Details depend on the airfoil and specifically on its nose radius and wing loading.

Only very light aircraft will not be affected by the change in Mach number, but even here the stall angle of attack at altitude is lower than at sea level due to the reduction of the flow's Reynolds number with increasing altitude.

In short, the indicated stall speed goes up with increasing altitude for a variety of reasons and does so nonlinearly. The magnitude of the change depends on a multitude of details.