**On Evaluating Circuits with Inputs Encrypted by Different Fully Homomorphic Encryption Schemes**

*Zhizhou Li and 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.

**Category / Keywords: **foundations / Fully Homomorphic Encryption, Multi-Scheme FHE, Trivial Encryptions, Ciphertext Trees, Multiparty Computations.

**Publication Info: **under review in a iacr conference.

**Date: **received 6 Apr 2013

**Contact author: **lizh at cse ohio-state edu, lai@cse ohio-state edu

**Available format(s): **PDF | BibTeX Citation

**Version: **20130409:050704 (All versions of this report)

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