Editing Probabilistic encryption (section)

== Security ==

Probabilistic encryption is particularly important when using [[public key cryptography]].  Suppose that the [[Adversary (cryptography)|adversary]] observes a ciphertext, and suspects that the plaintext is either "YES" or "NO", or has a hunch that the plaintext might be "ATTACK AT CALAIS". When a [[deterministic encryption]] algorithm is used, the adversary can simply try encrypting each of their guesses under the recipient's public key, and compare each result to the target ciphertext. To combat this attack, public key encryption schemes must incorporate an element of randomness, ensuring that each plaintext maps into one of a large number of possible ciphertexts.

An intuitive approach to converting a deterministic encryption scheme into a probabilistic one is to simply pad the plaintext with a random string before encrypting with the [[deterministic algorithm]].  Conversely, decryption involves applying a deterministic algorithm and ignoring the random padding.  However, early schemes which applied this naive approach were broken due to limitations in some deterministic encryption schemes.  Techniques such as [[Optimal Asymmetric Encryption Padding]] (OAEP) integrate random padding in a manner that is secure using any [[trapdoor permutation]].