# What is the hard problem on which ElGamal encryption is based?

## What is the hard problem on which ElGamal encryption is based?

ElGamal encryption is an public-key cryptosystem. It uses asymmetric key encryption for communicating between two parties and encrypting the message. This cryptosystem is based on the difficulty of finding discrete logarithm in a cyclic group that is even if we know ga and gk, it is extremely difficult to compute gak.

**Why is the ElGamal cryptosystem considered to be secure?**

Being a public key encryption algorithm, ElGamal algorithm depends on both the private and secret keys it generates to encrypt the data. Thus the main problem becomes securing and managing these keys. This security can be achieved by using certain hardware modules with key management software.

### Is ElGamal secure?

ElGamal encryption is provably secure under CPA [19], and is insecure under CCA2. It is conjectured to be secure under CCA1, but there has been no formal proof. But DEG may still be the most efficient IND-CCA1 secure public key encryption scheme having a security proof without random oracles.

**What is ElGamal key?**

In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of PGP, and other cryptosystems.

#### Is ElGamal homomorphic?

which shows that ElGamal encryption is in fact homomorphic with respect to multiplication. After that, it calculates 4-5 in the plaintext space and then encrypts the result. Both values are compared, and should match by the homomorphic property.

**Is El Gamal an IND CPA?**

Theorem 19.1 If the Discrete Diffie-Hellman problem is hard (i.e. if the DDH assumption holds), El Gamal is IND-CPA secure.

## What is the main disadvantage of ElGamal compared to RSA?

The degree of difficulty in RSA lies in the factorization of large primes while in ElGamal lies in the calculation of discrete logarithms. After testing, it is proven that RSA performs a faster encryption process than ElGamal. However, ElGamal decryption process is faster than RSA.

**What is ElGamal used for?**

ElGamal algorithm is used in encryption and decryption, which is mainly considered for its capability to make the key predictions extremely tough. The asymmetric algorithm uses the mechanism of private and the public key, making the key predictions even tougher.

### Is ElGamal more secure than RSA?

The degree of difficulty in RSA lies in the factorization of large primes while in ElGamal lies in the calculation of discrete logarithms. After testing, it is proven that RSA performs a faster encryption process than ElGamal.

**How do you compare RSA and ElGamal?**

RSA and ElGamal both use asymmetric key techniques. The fundamental difference lies in the number of variables used. RSA uses two variables during encryption while ElGamal uses three variables. The RSA algorithm’s strength is at the difficulty level in factoring the numbers into a prime factor.

#### What is the advantage of ElGamal?

The advantage of the ElGamal algorithm is the generation of keys using discrete logarithms. Encryption and decryption techniques use a large computing process so that the encryption results are twice the size of the original size.

**What kind of encryption is used in ElGamal?**

ElGamal encryption. In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. The system provides an additional layer of security by asymmetrically encrypting keys previously used for symmetric message encryption.

## How do RSA and ElGamal key sizes compare?

You never need larger parameters than for RSA. In the worst case ElGamal parameters and RSA parameters are equal size. But you can significantly reduce ElGamal parameters depending on the setting you are using for ElGamal.

**When was the ElGamal key exchange algorithm invented?**

In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. It was described by Taher Elgamal in 1985. [1]

### How is the security of the ElGamal scheme determined?

The security of the ElGamal scheme depends on the properties of the underlying group G {displaystyle G} as well as any padding scheme used on the messages. If the computational Diffie–Hellman assumption (CDH) holds in the underlying cyclic group G {displaystyle G} , then the encryption function is one-way.