ElGamal encryption, by its efficiency, is one of the most used schemes in cryptographic applications. However, the original ElGamal scheme is only provably secure against passive attacks. Damg̊ard proposed a slight modification of ElGamal encryption scheme (named Damg̊ard’s ElGamal scheme) that provides security against non-adaptive chosen ciphertext attacks under a knowledge-of-exponent assumpti...

This paper introduced a detail ElGamal digital signature scheme, and mainly analyzed the existing problems of the ElGamal digital signature scheme. Then improved the scheme according to the existing problems of ElGamal digital signature scheme, and proposed an implicit ElGamal type digital signature scheme with the function of message recovery. As for the problem that message recovery not being...

This study is mainly about the discrete logarithm problem in the ElGamal cryptosystem over the abelian group U(n) where n is one of the following forms p, or 2p where p is an odd large prime and m is a positive integer. It is another good way to deal with the ElGamal Cryptosystem using that abelian group U(n)={x: x is a positive integer such that x<n and gcd(n,x)=1} in the setting of the discre...

A design of secure and efficient public key encryption schemes under weaker computational assumptions has been regarded as an important and challenging task. As far as the ElGamal-type encryption is concerned, some variants of the original ElGamal encryption scheme whose security depends on weaker computational assumption have been proposed: Though the security of the original ElGamal encryptio...

In this paper, we give security proofs for ElGamal encryption scheme and its variant by Damg̊ard (DEG). For the ElGamal encryption, we show that (1) under the delayed-target discrete log assumption and a variant of the generalized knowledge-of-exponent assumption, ElGamal encryption is one-way under non-adaptive chosen cipher attacks; (2) one-wayness of ElGamal encryption under non-adaptive chos...

The well-known Signed ElGamal scheme consists of ElGamal encryption with a non-interactive Schnorr proof of knowledge. While this scheme should be intuitively secure against chosen-ciphertext attacks in the random oracle model, its security has not yet been proven nor disproven so far, without relying on further non-standard assumptions like the generic group model. Currently, the best known po...

Hwang et al. proposed an ElGamal-like scheme for encrypting large messages, which is more efficient than its predecessor in terms of computational complexity and the amount of data transformation. They declared that the resulting scheme is semantically secure against chosenplaintext attacks under the assumptions that the decision Diffie–Hellman problem is intractable. Later, Wang et al. pointed...

PVSS stands for publicly verifiable secret sharing. In PVSS, a dealer shares a secret among multiple share holders. He encrypts the shares using the shareholders' encryption algorithms and publicly proves that the encrypted shares are valid. Most of the existing PVSS schemes do not employ an ElGamal encryption to encrypt the shares. Instead, they usually employ other encryption algorithms like ...

In this paper we find a secure routing protocol for computer networks, which finds minimum optimum path using homomorphic encryption schemes. We briefly look into the existing homomorphic encryption algorithms. We make use of ElGamal encryption, Elliptic Curve encryption and a privacy homomorphism, which exhibits the property of homomorphism in our new routing protocol. Elliptic curve exhibits ...

In 1985 a powerful and practical public-key scheme was produced by ElGamal; his work was applied using large prime integers. El-Kassar et al. and El-Kassar and Haraty modified the ElGamal public-key encryption scheme from the domain of natural integers, Z, to two principal ideal domains, namely the domain of Gaussian integers, Z[ i ], and the domain of the rings of polynomials over finite field...