Security of Randomized Encryption Scheme I have the following question which I'm struggling with


  Suppose we are interested in encrypting bit strings. Consider a
  randomized encryption scheme that always produces ciphertexts of the
  same length as the plaintexts.
  
  Show that this scheme cannot be IND-CPA secure


Intuitively to me this kind of scheme shouldn't even be decryptable if the randomness lies in the mapping between plaintexts and ciphertexts. How can a single plaintext map to multiple ciphertexts (of the same length) without avoiding collisions and whilst also being decryptable? Am I misunderstanding what it means for an encryption scheme to be "randomized"?

I remember seeing a rough solution once which used the idea of mapping plaintexts to sets of ciphertexts but can't see how that would work / solve the problem.
Ciphertext Indistinguishability means that if you encrypt a message many times, each time the ciphertexts must be different.

For example, think about a device that searches flaws in a dam. Every time, when this device traverses, it will send "Yes" or "No" signals that it means for a receiver that the device has found a flaw or not. If an eavesdropper sniffs these signals, because of the number of "no" signals are more Than "yes" signals, he could understand the meaning of these signals even though they are encrypted and could not break their encryption. This weakness happens because the encryption algorithm is DETERMINISTIC and it means that always it produces same encryptions for "YES" signal and same encryptions for "NO" signals, in other words, the attacker could distinguish these encrypted messages without knowing the nature of the encryptions.

The solution for making messages resistance against distinguishability is using Non-Deterministic encryption and use parameters like IV and so for make ciphertext Random and each time giving the same message, it produces different ciphertexts and the attacker could not distinguish them.