Probabilistic public-key encryption is a public-key encryption scheme (see public key cryptography) where the ciphertext of the same message under the same public key differs on every run of a probabilistic Turing machine. That is, a random coin toss of the Turing machine is used in the encryption algorithm. The notion was proposed in contrast to the RSA public-key encryption scheme, which is deterministic in the sense that the ciphertext is always fixed given a public key and a plaintext.
The early date examples of probabilistic public key encryption schemes are the Goldwasser Micali encryption scheme and the ElGamal public-key encryption scheme, and many others followed. It is known that an encryption scheme that satisfies provable security such as semantic security must be probabilistic. Since the original RSA encryption scheme was not probabilistic, several padding techniques such as OAEPare considered so that the padded RSA scheme becomes probabilistic and satisfies security...
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References
Goldwasser, S. and S. Micali (1984). “Probabilistic encryption.” Journal Computer and System Sciences, 28, 270–299.
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Sako, K. (2005). Probabilistic Public-Key Encryption. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_319
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