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A New Variant of ElGamal's encryption and signatures schemes

In this work, the cryptosystems proposed are a slight modification of DSA, Elgamal’s schemes and generalized “Meta-Elgamal Signature Schemes” of Horster et al. However, it is not always necessary to consider the generator and its order. We can use a decryption key smaller than that of Elgamal’s scheme. In general, if we work in a cyclic subgroup of size d (with d as a large prime), then we can keep d secret and we can also use a secret exponent r for decryption of size, 0n d (where 0 n is some integer which divides , d the size of d). For example, it is possible, for different security levels, to use a 160, 190, or a 256 bit keys for decryption. Therefore, the new encryption scheme is faster than the classical Elgamal one’s for decryption process. Our variants of signatures schemes are more secure in the sense that some known vulnerabilities on the Meta-Elgamal Signatures Schemes do not work with the new modifications proposed. Furthermore, there exist much more variants for our signatures than those of “Meta-Elgamal Signature Schemes”. As Elgamal’s encryption scheme, our encryption scheme is based on DDH (Decisional Diffie-Hellman) problem. Moreover, the secrecy of the order d of the generator g (which is optional), is based on the Integer Factorization Problem.

Auteur(s) : Demba SOW, Djiby SOW
Pages : 21 à 39
Année de publication : 2011
Revue : JP Journal of Algebra, Number Theory and Applications
N° de volume : 20
Type : Article
Mise en ligne par : SOW Demba