International Association for Cryptologic Research

International Association
for Cryptologic Research


Ilaria Chillotti

Affiliation: Université de Versailles


Improved Bootstrapping for Approximate Homomorphic Encryption 📺
Hao Chen Ilaria Chillotti Yongsoo Song
Since Cheon et al. introduced a homomorphic encryption scheme for approximate arithmetic (Asiacrypt ’17), it has been recognized as suitable for important real-life usecases of homomorphic encryption, including training of machine learning models over encrypted data. A follow up work by Cheon et al. (Eurocrypt ’18) described an approximate bootstrapping procedure for the scheme. In this work, we improve upon the previous bootstrapping result. We improve the amortized bootstrapping time per plaintext slot by two orders of magnitude, from $$\sim $$∼1 s to $$\sim $$∼0.01 s. To achieve this result, we adopt a smart level-collapsing technique for evaluating DFT-like linear transforms on a ciphertext. Also, we replace the Taylor approximation of the sine function with a more accurate and numerically stable Chebyshev approximation, and design a modified version of the Paterson-Stockmeyer algorithm for fast evaluation of Chebyshev polynomials over encrypted data.
TFHE: Fast Fully Homomorphic Encryption Over the Torus
This work describes a fast fully homomorphic encryption scheme over the torus (TFHE) that revisits, generalizes and improves the fully homomorphic encryption (FHE) based on GSW and its ring variants. The simplest FHE schemes consist in bootstrapped binary gates. In this gate bootstrapping mode, we show that the scheme FHEW of Ducas and Micciancio (Eurocrypt, 2015) can be expressed only in terms of external product between a GSW and an LWE ciphertext. As a consequence of this result and of other optimizations, we decrease the running time of their bootstrapping from 690 to 13 ms single core, using 16 MB bootstrapping key instead of 1 GB, and preserving the security parameter. In leveled homomorphic mode, we propose two methods to manipulate packed data, in order to decrease the ciphertext expansion and to optimize the evaluation of lookup tables and arbitrary functions in $${\mathrm {RingGSW}}$$RingGSW-based homomorphic schemes. We also extend the automata logic, introduced in Gama et al. (Eurocrypt, 2016), to the efficient leveled evaluation of weighted automata, and present a new homomorphic counter called $$\mathrm {TBSR}$$TBSR, that supports all the elementary operations that occur in a multiplication. These improvements speed up the evaluation of most arithmetic functions in a packed leveled mode, with a noise overhead that remains additive. We finally present a new circuit bootstrapping that converts $$\mathsf {LWE}$$LWE ciphertexts into low-noise $${\mathrm {RingGSW}}$$RingGSW ciphertexts in just 137 ms, which makes the leveled mode of TFHE composable and which is fast enough to speed up arithmetic functions, compared to the gate bootstrapping approach. Finally, we provide an alternative practical analysis of LWE based schemes, which directly relates the security parameter to the error rate of LWE and the entropy of the LWE secret key, and we propose concrete parameter sets and timing comparison for all our constructions.
Multi-Key Homomorphic Encryption from TFHE
Hao Chen Ilaria Chillotti Yongsoo Song
In this paper, we propose a Multi-Key Homomorphic Encryption (MKHE) scheme by generalizing the low-latency homomorphic encryption by Chillotti et al. (ASIACRYPT 2016). Our scheme can evaluate a binary gate on ciphertexts encrypted under different keys followed by a bootstrapping.The biggest challenge to meeting the goal is to design a multiplication between a bootstrapping key of a single party and a multi-key RLWE ciphertext. We propose two different algorithms for this hybrid product. Our first method improves the ciphertext extension by Mukherjee and Wichs (EUROCRYPT 2016) to provide better performance. The other one is a whole new approach which has advantages in storage, complexity, and noise growth.Compared to previous work, our construction is more efficient in terms of both asymptotic and concrete complexity. The length of ciphertexts and the computational costs of a binary gate grow linearly and quadratically on the number of parties, respectively. We provide experimental results demonstrating the running time of a homomorphic NAND gate with bootstrapping. To the best of our knowledge, this is the first attempt in the literature to implement an MKHE scheme.

Program Committees

Crypto 2020