Hardware Acceleration of FHEW

The magic of Fully Homomorphic Encryption (FHE) is that it allows operations on encrypted data without decryption. Unfortunately, the slow computation time limits their adoption. The slow computation time results from the vast memory requirements (64Kbits per ciphertext), a bootstrapping key of 1.3 GB, and sizeable computational overhead (10240 NTTs, each NTT requiring 5120 32-bit multiplications). We accelerate the FHEW bootstrapping in hardware on a high-end U280 FPGA. To reduce the computational complexity, we propose a fast hardware NTT architecture modified from with support for negatively wrapped convolution. The IP module includes large I/O ports to the NTT accelerator and an index bit-reversal block. The total architecture requires less than 225000 LUTs and 1280 DSPs. Assuming that a fast interface to the FHEW bootstrapping key is available, the execution speed of FHEW bootstrapping can increase by at least 7.5 times

Hardware Acceleration of the Prime-Factor and Rader NTT for BGV Fully Homomorphic Encryption

Fully Homomorphic Encryption (FHE) enables computation on encrypted data, holding immense potential for enhancing data privacy and security in various applications. Presently, FHE adoption is hindered by slow computation times, caused by data being encrypted into large polynomials. Optimized FHE libraries and hardware acceleration are emerging to tackle this performance bottleneck. Often, these libraries implement the Number Theoretic Transform (NTT) algorithm for efficient polynomial multiplication. Existing implementations mostly focus on the case where the polynomials are defined over a power-of-two cyclotomic ring, allowing to make use of the simpler Cooley-Tukey NTT. However, generalized cyclotomics have several benefits in the BGV FHE scheme, including more SIMD plaintext slots and a simpler bootstrapping algorithm. We present a hardware architecture for the NTT targeting generalized cyclotomics within the context of the BGV FHE scheme. We explore different non-power-of-two NTT algorithms, including the Prime-Factor, Rader, and Bluestein NTTs. Our most efficient architecture targets the 21845-th cyclotomic polynomial --- a practical parameter for BGV --- with ideal properties for use with a combination of the Prime-Factor and Rader algorithms. The design achieves high throughput with optimized resource utilization, by leveraging parallel processing, pipelining, and reusing processing elements. Compared to Wu et al.\u27s VLSI architecture of the Bluestein NTT, our approach showcases 2$\times$ to 5$\times$ improved throughput and area efficiency. Simulation and implementation results on an AMD Alveo U250 FPGA demonstrate the feasibility of the proposed hardware design for FHE

Photoperiod Stress in Arabidopsis thaliana Induces a Transcriptional Response Resembling That of Pathogen Infection

Plants are exposed to regular diurnal rhythms of light and dark. Changes in the photoperiod by the prolongation of the light period cause photoperiod stress in short day-adapted Arabidopsis thaliana. Here, we report on the transcriptional response to photoperiod stress of wild-type A. thaliana and photoperiod stress-sensitive cytokinin signaling and clock mutants and identify a core set of photoperiod stress-responsive genes. Photoperiod stress caused altered expression of numerous reactive oxygen species (ROS)-related genes. Photoperiod stress-sensitive mutants displayed similar, but stronger transcriptomic changes than wild-type plants. The alterations showed a strong overlap with those occurring in response to ozone stress, pathogen attack and flagellin peptide (flg22)-induced PAMP triggered immunity (PTI), which have in common the induction of an apoplastic oxidative burst. Interestingly, photoperiod stress triggers transcriptional changes in jasmonic acid (JA) and salicylic acid (SA) biosynthesis and signaling and results in increased JA, SA and camalexin levels. These responses are typically observed after pathogen infections. Consequently, photoperiod stress increased the resistance of Arabidopsis plants to a subsequent infection by Pseudomonas syringae pv. tomato DC3000. In summary, we show that photoperiod stress causes transcriptional reprogramming resembling plant pathogen defense responses and induces systemic acquired resistance (SAR) in the absence of a pathogen