What happens if CBC-mode uses the same IV for all processes? In CBC mode (Cipher Block-chaining mode), each block of plaintext is XOR with the previous ciphertext block before being encrypted. What happens if I use the same IV instead of the previous ciphertext block? Is it vulnerable to Chosen plaintext attack?
If the modification is done, the encryption looks like this:

$$C_i=E_K(\text{IV}\oplus P_i)$$

and assuming the "IV" is public, this is essentially ECB mode with a security-irrelevant pre-processing by XOR'ing a constant into the message.

Assuming the "IV" is non-public, this is essentially an XOR cipher encrypted with ECB mode and in particular this is still vulnerable to the standard ECB attack that you can detect repeated blocks, which means that the mode / construction can be broken under a standard (formal) ciphertext-only attack where the attacker-chosen messages are 2 blocks.