Abstract: In this talk we discuss the problem of outsourcing computations to untrusted servers using homomorphic signcryption. More precisely, we address the question of whether it is possible to homomorphically compute arbitrary functions on signcrypted data. The answer is affirmative and we propose a new cryptographic primitive, homomorphic signcryption with public verifiability and message privacy that can evaluate arbitrary circuits over signcrypted data. Public verifiability implies that anyone is able to publicly verify the validity of a message-signcryption pair. We achieve a rather strong notion of message privacy, which implies that even if we publish the pair (c_{f,y}, y), where c_{f,y} certifies y as the output of some
computation f over a dataset m (i.e., y = f(m)), no information is revealed about the data m, beyond what is revealed by y and f.
Furthermore, we give some highlights about employing this primitive in verifiable differentially privacy.
Algorithmic Number Theory, Coding and Cryptography
