Abstract
Most solutions for fully homomorphic encryption rely on hard lattice problems. Accordingly, the resulting ciphertexts must contain a certain level of noise to guarantee the security of the encryption. Running homomorphic operations on these noisy ciphertexts in turn further increases the noise level in the resulting ciphertexts. If the noise exceeds a given threshold, the ciphertexts are no longer decryptable. Bootstrapping enables to deal with this issue by resetting the noise present in a ciphertext to a nominal level.
Certain fully homomorphic encryption schemes require the use of binary keys for the bootstrapping operation. This paper describes how to extend the underlying blind rotation so as to efficiently support a wider number of key formats. It also investigates a multi-digit approach wherein multiple key digits are processed concurrently. All in all, the proposed solutions offer more flexibility in the parameter selection and yield a variety of new trade-offs for better performance.
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Notes
- 1.
As originally described, TFHE is defined over the real torus \(\mathbb {R}/\mathbb {Z}\). We rather consider the discretized torus \(q^{-1}\mathbb {Z}/\mathbb {Z}\) and identify its elements with integers modulo q.
- 2.
Starting at \(i=0\).
- 3.
Available at https://bitbucket.org/malb/lwe-estimator/src/master/.
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A Tables
A Tables
Although for higher radices the number of external products remains equal to n, the value of n is a decreasing function of m. Playing with LWE Estimator, at a security level of 128 bits, we get the following tables.
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Joye, M., Paillier, P. (2022). Blind Rotation in Fully Homomorphic Encryption with Extended Keys. In: Dolev, S., Katz, J., Meisels, A. (eds) Cyber Security, Cryptology, and Machine Learning. CSCML 2022. Lecture Notes in Computer Science, vol 13301. Springer, Cham. https://doi.org/10.1007/978-3-031-07689-3_1
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