Welcome to the resource topic for 2013/198
Title:
On Evaluating Circuits with Inputs Encrypted by Different Fully Homomorphic Encryption Schemes
Authors: Zhizhou Li, Ten H. Lai
Abstract:We consider the problem of evaluating circuits whose inputs are encrypted with possibly different encryption schemes. Let \mathcal{C} be any circuit with input x_1, \dots, x_t \in \{0,1\}, and let \mathcal{E}_i, 1 \le i \le t, be (possibly) different fully homomorphic encryption schemes, whose encryption algorithms are \Enc_i. Suppose x_i is encrypted with \mathcal{E}_i under a public key pk_i, say c_i \leftarrow \Enc_i({pk_i}, x_i). Is there any algorithm \Evaluate such that \Evaluate(\mathcal{C}, \langle \mathcal{E}_1, pk_1, c_1\rangle, \dots, \langle \mathcal{E}_t, pk_t, c_t\rangle) returns a ciphertext c that, once decrypted, equals \mathcal{C}(x_1, \dots, x_t)? We propose a solution to this seemingly impossible problem with the number of different schemes and/or keys limited to a small value. Our result also provides a partial solution to the open problem of converting any FHE scheme to a multikey FHE scheme.
ePrint: https://eprint.iacr.org/2013/198
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