how to prove our algorithm is secure against chosen plaintext attack? I am working on a topic in cryptography where I have tried to develop an encryption scheme. 


How could I prove mathematically that my algorithm is secure against chosen plaintext attacks?.
Will it be sufficient to say that as my algorithm is uniformly distributed, it is secure against chosen plaintext attacks?
The usual approach to prove IND-CPA security is to construct a logical argumentation called "reduction". In this argumentation you first start with the assumption that certain computational problem is hard (for example, the Decisional Diffie-Hellman assumption), and then you proceed to demonstrate that if your crypto scheme were insecure with respect to IND-CPA (which means that the adversary has access to an encryption oracle), then you could construct an algorithm that uses your scheme to break the hard problem. If our current knowledge dictates that indeed the chosen problem is hard, then your scheme must be IND-CPA-secure.
No. A trivial counterexample would be a deterministic encryption scheme. It is a well-known fact that an encryption function that is deterministic cannot be IND-CPA-secure. This is true regardless if its output is uniformly distributed.