Now, RSA patents have expired. Diffie-Hellman enables two parties to agree a common shared secret that can be used subsequently in a symmetric algorithm like AES. It can be considered as the asymmetric algorithm where the encryption and decryption happen by the use of public and private keys. The ElGamal cryptographic algorithm is a public key system like the Diffie-Hellman system. • We can infer whether a ciphertext is quadratic residue or not. The ElGamal cryptosystem was first described by Taher Elgamal in 1985 and is closely related to the Diffie-Hellman key exchange. The Diffie-Hellman key exchange provides a method of sharing a secret key between Alice and Bob, but does not allow Alice and Bob to otherwise communicate securely. Diffie-Hellman (DH) is a key agreement algorithm, ElGamal an asymmetric encryption algorithm. The ElGamal cryptographic algorithm is comparable to the Diffie-Hellman system. Notably, ElGamal is homomorphic (given the encryption of x and the encryption of y, one can from the outside compute the encryption of the product xy), which is a nice property in some cases, but can be bothersome in other conditions. Introduction. It all depends on what padding scheme is used. Semantic Security of ElGamal • Note that the generic ElGamal encryption scheme is not semantically secure. As this title suggests the security of this cryptosystem is based on the notion of discrete logarit ElGamal is a public key encryption algorithm that was described by an Egyptian cryptographer Taher Elgamal in 1985. I don't know if this has a significant influence for a 4096 bit RSA key. ElGamal cryptosystem can be defined as the cryptography algorithm that uses the public and private key concept to secure the communication occurring between two systems. For example, given an encryption of some (possibly unknown) message , one can easily construct a valid encryption of the message . • We can use the above fact to come up with two message where one of them is a quadratic residue and the other one is a quadratic non-residue so that Stick to RSA. Erik-Oliver Blass and I found that the implementations of ElGamal encryption in libgcrypt, PyCrypto, PyCryptodome, and CryptoPP are not secure. Nowadays, RSA is more convenient but not necessarily safer than ElGamal. While ElGamal over appropriate prime order subgroups is semantically secure and ElGamal over ∗ is not we should not conclude that any ElGamal implementation using the group ∗ is immediately insecure and any system using a prime order subgroup is secure. DSA and Elgamal; RSA (Sign only) DSA (Sign only) I found this Superuser question, but it may be outdated. As for ElGamal versus RSA: An encrypted ElGamal message is simply about twice the size of an encrypted RSA message for the same security level. The cryptosystem takes its name from its founder the Egyptian cryptographer Taher Elgamal who introduced the system in his 1985 paper entitled " A Public Key Cryptosystem and A Signature Scheme Based on Discrete Logarithms ". ElGamal encryption is unconditionally malleable, and therefore is not secure under chosen ciphertext attack. RSA keys seem to be less secure since it's known that the NSA infiltrated RSA and made their key generation algorithm weaker. It is mainly used to establish common keys and not to encrypt messages. ElGamal encryption is an example of public-key or asymmetric cryptography. Be cyber secure. The one use case where I see ElGamal being used over RSA is when a multiplicatively homomorphic cryptosystem is needed (noe that both ElGamal and RSA are multiplicatively homomorphic). 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