Abstract
Transciphering allows to workaround the large expansion of the size of FHE encrypted data, thanks to the use of symmetric cryptography. Transciphering is a recryption technique that delegates the effective homomorphic encryption to the cloud. As a result, a client only has to encrypt (once) a symmetric key \({\textsf {SYM}}.\!{\textsf {sk}}\) under a homomorphic encryption system, while his payload data are encrypted under \({\textsf {SYM}}.\!{\textsf {sk}}\) using the chosen symmetric encryption algorithm.
In this work, we study the performances of some symmetric encryption algorithms in light of the TFHE cryptosystem and its properties. This allows us to unleash the use of additional existing symmetric algorithms which were not viable candidates for efficient encrypted domain execution with levelled-FHEs. In particular, we provide experimental evidences that Grain128-AEAD, a well established and well respected stream-cipher which is a finalist of the NIST competition for light-weight cryptography, is amenable to practical performances when run in the encrypted domain. As such, our work extends practical transciphering capabilities to include authenticated encryption for the first time.
The research leading to these results has been funded in part from the European Union’s Preparatory Action on Defence Research (PADR-FDDT-OPEN-03-2019). This paper reflects only the authors’ views and the Commission is not liable for any use that may be made of the information contained therein.
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Notes
- 1.
The multiplicative depth of a circuit is the maximum number of successive multiplications in the circuit.
- 2.
As a general guidelines, the first rule of optimization for FHE is to find (legitimate) ways of doing less FHE calculations.
- 3.
Linear/Non-linear feeadback shift register.
- 4.
Of course, comparison cannot be done per se in the encrypted domain, so if the \(\mu _i\)’s denotes the bits of the received MAC and the \([\mu '_i]\)’s denote the FHE encryptions of the bits of the (homomorphically) computed one, the cloud has to compute \(\prod _i(1\oplus \mu _i\oplus [\mu '_i])=[b]\).
- 5.
I.e., putting a into x when c is true, b otherwise, can be written has \(x:=ca\oplus (1\oplus c)b\).
- 6.
- 7.
A small number of additions and multiplications (only three) per round.
- 8.
LFSR/NFSR update, non linear function application and register shifting (register shifting being almost free).
- 9.
To be fair, these throughputs could be increased to around 2000 bits/min with 600 slots of batching, however with FHE security parameters which are now outdated (due to recent advances in LWE-based systems cryptanalysis); so as an order of magnitude we should expect all the throughputs given in [9] to be divided by around 5. Still, as already stated, batching-based improvements in throughput are not applicable when using TFHE.
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Bendoukha, AA., Boudguiga, A., Sirdey, R. (2022). Revisiting Stream-Cipher-Based Homomorphic Transciphering in the TFHE Era. In: Aïmeur, E., Laurent, M., Yaich, R., Dupont, B., Garcia-Alfaro, J. (eds) Foundations and Practice of Security. FPS 2021. Lecture Notes in Computer Science, vol 13291. Springer, Cham. https://doi.org/10.1007/978-3-031-08147-7_2
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