Security
The security of the ElGamal scheme depends on the properties of the underlying group as well as any padding scheme used on the messages.
If the computational Diffie–Hellman assumption holds in the underlying cyclic group, then the encryption function is one-way.
If the decisional Diffie–Hellman assumption (DDH) holds in, then ElGamal achieves semantic security. Semantic security is not implied by the computational Diffie–Hellman assumption alone. See decisional Diffie–Hellman assumption for a discussion of groups where the assumption is believed to hold.
ElGamal encryption is unconditionally malleable, and therefore is not secure under chosen ciphertext attack. For example, given an encryption of some (possibly unknown) message, one can easily construct a valid encryption of the message .
To achieve chosen-ciphertext security, the scheme must be further modified, or an appropriate padding scheme must be used. Depending on the modification, the DDH assumption may or may not be necessary.
Other schemes related to ElGamal which achieve security against chosen ciphertext attacks have also been proposed. The Cramer–Shoup cryptosystem is secure under chosen ciphertext attack assuming DDH holds for . Its proof does not use the random oracle model. Another proposed scheme is DHAES, whose proof requires an assumption that is weaker than the DDH assumption.
Read more about this topic: ElGamal Encryption
Famous quotes containing the word security:
“I feel a sincere wish indeed to see our government brought back to it’s republican principles, to see that kind of government firmly fixed, to which my whole life has been devoted. I hope we shall now see it so established, as that when I retire, it may be under full security that we are to continue free and happy.”
—Thomas Jefferson (1743–1826)
“Modern children were considerably less innocent than parents and the larger society supposed, and postmodern children are less competent than their parents and the society as a whole would like to believe. . . . The perception of childhood competence has shifted much of the responsibility for child protection and security from parents and society to children themselves.”
—David Elkind (20th century)
“We now in the United States have more security guards for the rich than we have police services for the poor districts. If you’re looking for personal security, far better to move to the suburbs than to pay taxes in New York.”
—John Kenneth Galbraith (b. 1908)