Answers:
Probabilistic encryption is the use of randomness contained by an encryption algorithm, so that when encrypting like message several times it will, surrounded by common, concede different ciphertexts. The occupancy "probabilistic encryption" is typically used surrounded by suggestion to public push button encryption algorithms, however different symmetric knob encryption algorithms complete a similar property (e.g., block ciphers when used surrounded by a chain mode such as CBC). To be semantically protected, to be exact, to cast a shadow on even partial information around the plaintext, an encryption algorithm must be probabilistic.
Probabilistic encryption is specially esteemed when using public knob cryptography. Suppose that the challenger observe a ciphertext, and suspects that the plaintext is any "YES" or "NO", or have a hunch that the plaintext might be "ATTACK AT CALAIS". When a deterministic encryption algorithm is used, the rival can simply try encrypting respectively of his guesses below the receiver's public knob, and compare respectively result to the target ciphertext. To combat this attack, public knob encryption scheme must incorporate an item of randomness, ensure that respectively plaintext map into one of a immense number of possible ciphertexts.
An intuitive approach to converting a deterministic encryption development into a probabilistic one is to simply wad the plaintext beside a subjective string earlier encrypting beside the deterministic algorithm. Conversely, decryption involves applying a deterministic algorithm and ignore the uninformed filling. However, untimely scheme which applied this trusting approach be broken due to limitations contained by some deterministic encryption scheme. Techniques such as OAEP integrate uninformed filling contained by a deportment to be exact safe and sound using any trapdoor permutation.
The first provably-secure probabilistic public-key encryption hatch up be proposed by Shafi Goldwasser and Silvio Micali, base on the solidity of the quadratic residuosity problem and have a message expansion factor equal to the public push button size. More restructured probabilistic encryption algorithms include Elgamal, Paillier and an assortment of constructions below the disorganized oracle model, including Optimal Asymmetric Encryption Padding (OAEP).