Fully Homomorphic Encryption (FHE) is a powerful tool to achieve non-interactive privacy preserving protocols with optimal computation/communication complexity. However, the main disadvantage is that the actual communication cost (bandwidth) is high due to the large size of FHE ciphertexts. As a solution, a technique called transciphering (also known as Hybrid Homomorphic Encryption) was introduced to achieve almost optimal bandwidth for such protocols. However, all existing works require clients to fix a precision for the messages or a mathematical structure for the message space beforehand. It results in unwanted constraints on the plaintext size or underlying structure of FHE based applications.
In this article, we introduce a new approach for transciphering which does not require fixed message precision decided by the client, for the first time. In more detail, a client uses any kind of FHE-friendly symmetric cipher for
{
0
,
1
}
to send its input data encrypted bit-by-bit, then the server can choose a precision
p
depending on the application and homomorphically transforms the encrypted bits into FHE ciphertexts encrypting integers in
ℤ
p
. To illustrate our new technique, we evaluate a transciphering using FiLIP cipher and adapt the most practical homomorphic evaluation technique [CCS'22] to keep the practical latency. As a result, our proof-of-concept implementation for
p
from
2
2
to
2
8
takes only from
13
ms to
137
ms.