Is there any quantum resistant public key cryptography with similar properties of elliptic curves?
Assuming lowercase for scalars and uppercase for points. The properties I'm interested are:
- Reusing the same public key.
- Given $k = a + b$ then $k \times G = (a + b) \times G$
- Distributive Scalars: $(a + b) \times G = a \times G + b \times G$
- Distributive Points: $k \times (A + B) = k \times A + k \times B$
- Commutative Sum: $(a + b) \times G = (b + a) \times G$
- Commutative Mul: $a \cdot b \times G = b \cdot a \times G$
How existing solutions map to the same properties? I'm interested in the direct applications not how it fundamentally works.