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Zapiski Nauchnykh Seminarov POMI, 2002, Volume 293, Pages 39–58
(Mi znsl1675)
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This article is cited in 3 scientific papers (total in 3 papers)
On non-abelian homomorphic public-key cryptosystems
D. Yu. Grigor'eva, I. N. Ponomarenkob a Institute of Mathematical Research of Rennes
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
We construct homomorphic cryptosystems being (secret) epimorphisms $f\colon G\to H$, where $G$, $H$ are (publically known) groups and $H$ is finite. A letter of a message to be encrypted is an element $h\in H$, while its encryption $g\in G$ is such that $f(g)=h$. A homomorphic cryptosystem allows one to perform computations (operating in a group $G$) with encrypted information (without knowing the original message over $H$).
In this paper certain homomorphic cryptosystems are constructed for the first time for non-abelian groups $H$ (earlier, homomorphic cryptosystems were known only in the Abelian case). In fact, we present such a system for any solvable (fixed) group $H$.
Received: 07.12.2002
Citation:
D. Yu. Grigor'ev, I. N. Ponomarenko, “On non-abelian homomorphic public-key cryptosystems”, Computational complexity theory. Part VII, Zap. Nauchn. Sem. POMI, 293, POMI, St. Petersburg, 2002, 39–58; J. Math. Sci. (N. Y.), 126:3 (2005), 1158–1166
Linking options:
https://www.mathnet.ru/eng/znsl1675 https://www.mathnet.ru/eng/znsl/v293/p39
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Abstract page: | 315 | Full-text PDF : | 92 |
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