Large-Precision Homomorphic Sign Evaluation using FHEW/TFHE Bootstrapping

A comparison of two encrypted numbers is an important operation needed in many machine learning applications, for example, decision tree or neural network inference/training. An efficient instantiation of this operation in the context of fully homomorphic encryption (FHE) can be challenging, especially when a relatively high precision is sought. The conventional FHE way of evaluating the comparison operation, which is based on the sign function evaluation using FHEW/TFHE bootstrapping (often referred in literature as programmable bootstrapping), can only support very small precision (practically limited to 4-5 bits or so). For higher precision, the runtime complexity scales linearly with the ciphertext (plaintext) modulus (i.e., exponentially with the modulus bit size). We propose sign function evaluation algorithms that scale logarithmically with the ciphertext (plaintext) modulus, enabling the support of large-precision comparison in practice. Our sign evaluation algorithms are based on an iterative use of homomorphic floor function algorithms, which are also derived in our work. Further, we generalize our procedures for floor function evaluation to arbitrary function evaluation, which can be used to support both small plaintext moduli (directly) and larger plaintext moduli (by using a homomorphic digit decomposition algorithm, also suggested in our work). We implement all these algorithms using the PALISADE lattice cryptography library, introducing several implementation-specific optimizations along the way, and discuss our experimental results

FPT: a Fixed-Point Accelerator for Torus Fully Homomorphic Encryption

Fully Homomorphic Encryption is a technique that allows computation on encrypted data. It has the potential to change privacy considerations in the cloud, but computational and memory overheads are preventing its adoption. TFHE is a promising Torus-based FHE scheme that relies on bootstrapping, the noise-removal tool invoked after each encrypted logical/arithmetical operation. We present FPT, a Fixed-Point FPGA accelerator for TFHE bootstrapping. FPT is the first hardware accelerator to exploit the inherent noise present in FHE calculations. Instead of double or single-precision floating-point arithmetic, it implements TFHE bootstrapping entirely with approximate fixed-point arithmetic. Using an in-depth analysis of noise propagation in bootstrapping FFT computations, FPT is able to use noise-trimmed fixed-point representations that are up to 50% smaller than prior implementations. FPT is built as a streaming processor inspired by traditional streaming DSPs: it instantiates directly cascaded high-throughput computational stages, with minimal control logic and routing networks. We explore throughput-balanced compositions of streaming kernels with a user-configurable streaming width in order to construct a full bootstrapping pipeline. Our approach allows 100% utilization of arithmetic units and requires only a small bootstrapping key cache, enabling an entirely compute-bound bootstrapping throughput of 1 BS / 35us. This is in stark contrast to the classical CPU approach to FHE bootstrapping acceleration, which is typically constrained by memory and bandwidth. FPT is implemented and evaluated as a bootstrapping FPGA kernel for an Alveo U280 datacenter accelerator card. FPT achieves two to three orders of magnitude higher bootstrapping throughput than existing CPU-based implementations, and 2.5x higher throughput compared to recent ASIC emulation experiments.Comment: ACM CCS 202

Faster Amortized FHEW bootstrapping using Ring Automorphisms

Amortized bootstrapping offers a way to simultaneously refresh many ciphertexts of a fully homomorphic encryption scheme, at a total cost comparable to that of refreshing a single ciphertext. An amortization method for FHEW-style cryptosystems was first proposed by (Micciancio and Sorrell, ICALP 2018), who showed that the amortized cost of bootstrapping n FHEW-style ciphertexts can be reduced from $O(n)$ basic cryptographic operations to just $O(n^{\epsilon})$, for any constant $\epsilon>0$. However, despite the promising asymptotic saving, the algorithm was rather inpractical due to a large constant (exponential in $1/\epsilon$) hidden in the asymptotic notation. In this work, we propose an alternative amortized boostrapping method with much smaller overhead, still achieving $O(n^\epsilon)$ asymptotic amortized cost, but with a hidden constant that is only linear in $1/\epsilon$, and with reduced noise growth. This is achieved following the general strategy of (Micciancio and Sorrell), but replacing their use of the Nussbaumer transform, with a much more practical Number Theoretic Transform, with multiplication by twiddle factors implemented using ring automorphisms. A key technical ingredient to do this is a new scheme switching technique proposed in this paper which may be of independent interest

OpenFHE: Open-Source Fully Homomorphic Encryption Library

Fully Homomorphic Encryption (FHE) is a powerful cryptographic primitive that enables performing computations over encrypted data without having access to the secret key. We introduce OpenFHE, a new open-source FHE software library that incorporates selected design ideas from prior FHE projects, such as PALISADE, HElib, and HEAAN, and includes several new design concepts and ideas. The main new design features can be summarized as follows: (1) we assume from the very beginning that all implemented FHE schemes will support bootstrapping and scheme switching; (2) OpenFHE supports multiple hardware acceleration backends using a standard Hardware Abstraction Layer (HAL); (3) OpenFHE includes both user-friendly modes, where all maintenance operations, such as modulus switching, key switching, and bootstrapping, are automatically invoked by the library, and compiler-friendly modes, where an external compiler makes these decisions. This paper focuses on high-level description of OpenFHE design, and the reader is pointed to external OpenFHE references for a more detailed/technical description of the software library