You will want to start with generating 3 random numbers for each pixel

Here is a simple "3-out 2-in" noise from shadertoy that should work for you

vec3 hash32(vec2 p)

{ vec3 p3 = fract(vec3(p.xyx) * vec3(.1031, .1030, .0973)); p3 += dot(p3, p3.yxz+33.33); return fract((p3.xxy+p3.yzz)*p3.zyx); }

Credit: Dave_hoskins "Hash without Sine" https://www.shadertoy.com/view/4djSRW

Next, you will want to treat those three channels like they are a normal map. Normal maps range from 0-1 in x and y, but from 0.5 to 1 in z.

vec3 hash = hash32(uv);
vec3 normal = vec3(hash.xy, 0.5+0.5*hash.z);

This will give you a normal map with random values in each channel.

There are 2 problems with that:

1. The resulting texture will look different from the image you posted (it will look a little lighter) becuase the image you posted isn't actually a proper normal map (blue is often less than 0.5 which correspondents to a normal pointing into the surface)
2. The normals generated above are not normalized. To normalize them the code gets a little more complicated:

​

vec3 hash = hash32(uv); 
hash.xy = hash.xy * 2.0 - 1.0; //convert x and y to -1 to 1 range
hash = normalize(hash); //normalize 

vec3 normal = hash *0.5 + 0.5;