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A new variant of Elgamal's encryption and signatures schemes

In this work, the crytosystems proposed are a slight modification of DSA, Elgamal'schemes and generalizes "Meta-Elgamal Signature Schemes" of Horster and al. But, it is not always necessary to publish the generator (directly used) and his order, and one can use a decription key more small than those of Elgamal's scheme. In general, if we work in a cyclic subgroup of size $d$ (with $d$ a large prime), we can keep $d$ secret and we can also use a secret exponent $r$ for decryption of size $\frac{|d|}{n_{0}}$,( where $n_{0}$ 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 key for decryption. Therefore, the new encryption scheme is more fast than the classical Elgamal one's for decription 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 exists 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) : Sow, Demba and Sow, Djiby
Pages : 21–39
Année de publication : 2011
Revue : JP J. Algebra Number Theory Appl.
N° de volume : 20
Type : Article
Mise en ligne par : SOW Djiby