On nonAbelian homomorphic publickey cryptosystems
 D. Grigoriev,
 I. Ponomarenko
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An important problem of modern cryptography concerns secret publickey computations in algebraic structures. We construct homomorphic cryptosystems, which are (secret) epimorphisms f : G → H, where G and H are (publically known) groups and H is finite. A letter of a message to be encrypted is an element h ∈ H, while its encryption is an element g ∈ G such that f(g) = h. A homomorphic cryptosystem allows one to perform computations (in the group G) with encrypted information (without knowing the original message over H).
In this paper, homomorphic cryptosystems are constructed for the first time for nonAbelian groups H (earlier, homomorphic cryptosystems were known only in the Abelian case). In fact, we present such a system for any (fixed) solvable group H. Bibliography: 24 titles.
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 Title
 On nonAbelian homomorphic publickey cryptosystems
 Journal

Journal of Mathematical Sciences
Volume 126, Issue 3 , pp 11581166
 Cover Date
 20050301
 DOI
 10.1007/s1095800500773
 Print ISSN
 10723374
 Online ISSN
 15738795
 Publisher
 Kluwer Academic PublishersConsultants Bureau
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