Discuss elgmal digital signature scheme in.Cryptography
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ElGamal signature
The ElGamal signature scheme is a digital signature scheme which is based on the difficulty of computing discrete logarithms. It was described by Taher Elgamal in 1985.
The ElGamal signature algorithm is rarely used in practice. A variant developed at the NSA and known as the Digital Signature Algorithm is much more widely used. There are several other variants. The ElGamal signature scheme must not be confused with ElGamal encryption which was also invented by Taher Elgamal.
Overview
The ElGamal signature scheme is a digital signature scheme based on the algebraic properties of modular exponentiation, together with the discrete logarithm problem. The algorithm uses a key pair consisting of a public key and a private key. The private key is used to generate a digital signature for a message, and such a signature can be verified by using the signer's corresponding public key. The digital signature provides message authentication (the receiver can verify the origin of the message), integrity (the receiver can verify that the message has not been modified since it was signed) and non-repudiation (the sender cannot falsely claim that they have not signed the message).
History
The ElGamal signature scheme was described by Tahir Elgamal in 1985.
Operation
The scheme involves four operations: key generation (which creates the key pair), key distribution, signing and signature verification. The ElGamal paper and the Handbook of Applied Cryptography state to select the private key in the range . Tsiounis and Yung showed the lower limit as in On the Security of EIGamal Based Encryption.