ElGamal encryption

In <a href="/facts/Cryptography/e94PEVau">cryptography</a>, the ElGamal encryption system is an <a href="/facts/Asymmetric_key_encryption_algorithm/gowoFTxS">asymmetric key encryption algorithm</a> for <a href="/facts/Public-key_cryptography/gowoFTxS">public-key cryptography</a> which is based on the <a href="/facts/Diffie%E2%80%93Hellman_key_exchange/xR4YQcaD">Diffie–Hellman key exchange</a>. It was described by <a href="/facts/Taher_Elgamal/mx5Ers0r">Taher Elgamal</a> in 1985. ElGamal encryption is used in the free <a href="/facts/GNU_Privacy_Guard/EqmGmx7V">GNU Privacy Guard</a> software, recent versions of <a href="/facts/Pretty_Good_Privacy/4BELG9BW">PGP</a>, and other <a href="/facts/Cryptosystem/GyDVJ4D0">cryptosystems</a>. The <a href="/facts/Digital_Signature_Algorithm/0o0FK486">Digital Signature Algorithm</a> (DSA) is a variant of the <a href="/facts/ElGamal_signature_scheme/cChGpj4K">ElGamal signature scheme</a>, which should not be confused with ElGamal encryption.
ElGamal encryption can be defined over any <a href="/facts/Cyclic_group/JL5zfFuL">cyclic group</a> 
 
 
 
 G
 
 
 {\displaystyle G}
 
, like <a href="/facts/Multiplicative_group_of_integers_modulo_n/IACS6cgH">multiplicative group of integers modulo n</a> if and only if n is 1, 2, 4, pk or 2pk, where p is an odd prime and k > 0. Its security depends upon the difficulty of the <a href="/facts/Decisional_Diffie%E2%80%93Hellman_assumption/n1A9uKcH">Decisional Diffie Hellman Problem</a> in 
 
 
 
 G
 
 
 {\displaystyle G}
 
.

ElGamal encryption open-in-new

ElGamal encryption