How to construct a variable length IND-CPA cipher from a fixed length one? Suppose we can construct a secure (IND-CPA) encryption scheme for fixed length messages. I was wondering if there is a natural way to extend this construction for messages of variable length such that it is still an IND-CPA secure scheme.
The typical way to make an encryption scheme work for variable length message is to use a mode of operation.

Since you are starting with an already IND-CPA secure cipher, even the often despised ECB mode will work. That said, you will still need padding to make the plaintext length a multiple of the blocksize. If adding padding is out of the question, a streaming mode such as CTR will work.