How to create 2 synchronous keys?

Question

C++ / C#

Dear friends, there is a need to create a cryptosystem, only symmetric encryption is considered.
Asymmetric does not fit according to T.3.
Each pair of programs is bound by conditions and can only work with another program with the same conditions.
I decided to make it so that the key was given by solving a 4th degree equation with 1 unknown type
ax^4+bx^3+cx^2+dx = f
And selecting roots.
Where a and b are unique for each program, and are binders.
It is necessary that the key is changed automatically every hour, so the cdf variables must be changed every hour, even if there is no Internet access.
Such a system is implemented in SteamGuard, where the key is changed every minute, regardless of the presence of an Internet connection.
Tell me how to implement this, and whether there are any simpler algorithms.
I am an amateur in this matter, do not judge strictly.

Answer 1

NEVER try to come up with anything in the field of cryptography.
Everything has already been done for you. If you reinvent the wheel, there is a 99% chance your system will be vulnerable.

Answer 2

Use One Time Password. Essentially, make the key derivation algorithm time dependent and synchronize the time.