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Homomorphic cryptosystems over groups and rings and encrypting boolean circuits

Dimitri Grigoriev ( Institut de Recherche Mathématique de Rennes(France) )

Thursday 01 June 2006, 15.00 sharp (s.t.), b-it 2.1 (seminar room)


Two homomorphic public-key cryptosystems are designed over an arbitrary finite group. The security of the first one relies on the difficulty of integer factoring and of the second one on the membership problem for groups of integer matrices. Applying Barrington's construction we produce for any boolean circuit of the logarithmic depth its encrypted simulation of a polynomial size over an appropriate finitely generated group. Besides, homomorphic public-key cryptosystems are designed over finite commutative rings.

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