arXiv subjects

George Alexakis

Publications and source records attributed to George Alexakis.

6 recordsLinked to original sources

arXiv2026

High-Performance NTT Accelerators for PQC leveraging Unified Redundant Arithmetic and Fine-Tuned Microarchitecture

Post-quantum cryptography and privacy-preserving technologies are expected to play a central role in future secure communication systems. Lattice-based PQC schemes such as ML-KEM (CRYSTALS-Kyber) and ML-DSA (CRYSTALS-Dilithium) rely heavily on large-degree polynomial arithmetic, making the Number Theoretic Transform (NTT) a key computational primitive. Although existing hardware accelerators exploit parallelism and pipelining to support both NTT and INTT, their efficiency is often limited by the overhead of modular reduction and correction steps, inverse-transform scaling operations, and suboptimal FPGA implementations. This work addresses these limitations by proposing parallel iterative NTT/INTT accelerators based on optimized unified butterfly units. We introduce a novel redundant number representation that eliminates conditional corrections for both Montgomery modulo multiplication and combined subtract-multiply operations, and integrate inverse-transform scaling into existing arithmetic hardware to avoid dedicated scaling units. Furthermore, we design hierarchical Montgomery multipliers that map efficiently onto FPGA DSP resources, reducing hardware cost while enabling high operating frequencies. FPGA-based experimental results demonstrate higher clock frequencies, reduced execution times, and competitive resource utilization, supporting efficient NTT acceleration for PQC and related privacy-preserving applications.

cs.AR↗

arXiv2026

Low-Cost Multi-Precision Systolic Arrays for Accelerating FHE NTTs on AI ASICs

Fully Homomorphic Encryption (FHE) ensures robust data privacy but suffers from prohibitive computational overhead. Accelerating FHE on AI hardware like Tensor Processing Units (TPUs) is promising, yet fundamentally limited by a precision mismatch: TPUs are optimized for 8-bit arithmetic, whereas FHE and its critical parts such as the Number Theoretic Transform (NTT), demand high precision. Current approaches bridge this gap using matrix decomposition to execute NTT computations on low-precision matrix engines. However, reconstructing the full-precision results requires shift-and-add accumulation that does not match the dataflow of matrix multiplication. This forces offloading full-precision reconstruction from matrix engines to vector processors that disrupts the matrix multiplication dataflow, creating significant performance bottleneck. To resolve this limitation, we propose a minimally modified multi-precision systolic array that performs full-precision output reconstruction natively within the array in sync with low-precision matrix multiplication under a uniform dataflow. Synthesized at 7nm with OpenRoad, our design incurs negligible hardware overhead. Cycle-accurate simulations using SCALE-Sim demonstrate that natively executing NTTs on the proposed architecture achieves at least 1.33x speedup, for transform sizes 2^12 to 2^16 on 128x128 matrix engines, successfully enabling standard AI hardware to support high-precision FHE acceleration.

cs.CR↗

arXiv2026

MPX: A Unified Systolic Array for Matrix and Polynomial Multiplication

Polynomial multiplication is a fundamental kernel in Fully Homomorphic Encryption (FHE) and post-quantum cryptography (PQC) and is commonly accelerated through Number Theoretic Transforms (NTTs). To avoid the cost of designing dedicated cryptographic accelerators, recent efforts have mapped NTT computations onto existing systolic matrix engines, enabling the reuse of AI hardware for cryptographic workloads. In this work, we take the opposite approach. We observe that the wavefront dataflow of systolic arrays naturally aligns with the accumulation pattern of polynomial multiplication and leverage this correspondence to design MPX, a dual-mode systolic array that supports both matrix multiplication and direct polynomial multiplication within the same hardware fabric. Experimental results show that extending a conventional systolic array with this dual-mode capability requires only 20% additional area and introduces negligible power overhead during matrix-multiplication execution. In polynomial-multiplication mode, MPX achieves more than 1.2x lower latency compared to NTT-based polynomial multiplication on systolic matrix engines.

cs.CR↗

arXiv2025

High-Performance Pipelined NTT Accelerators with Homogeneous Digit-Serial Modulo Arithmetic

The Number Theoretic Transform (NTT) is a fundamental operation in privacy-preserving technologies, particularly within fully homomorphic encryption (FHE). The efficiency of NTT computation directly impacts the overall performance of FHE, making hardware acceleration a critical technology that will enable realistic FHE applications. Custom accelerators, in FPGAs or ASICs, offer significant performance advantages due to their ability to exploit massive parallelism and specialized optimizations. However, the operation of NTT over large moduli requires large word-length modulo arithmetic that limits achievable clock frequencies in hardware and increases hardware area costs. To overcome such deficits, digit-serial arithmetic has been explored for modular multiplication and addition independently. The goal of this work is to leverage digit-serial modulo arithmetic combined with appropriate redundant data representation to design modular pipelined NTT accelerators that operate uniformly on arbitrary small digits, without the need for intermediate (de)serialization. The proposed architecture enables high clock frequencies through regular pipelining while maintaining parallelism. Experimental results demonstrate that the proposed approach outperforms state-of-the-art implementations and reduces hardware complexity under equal performance and input-output bandwidth constraints.

cs.AR↗

arXiv2025

Efficient Implementation of RISC-V Vector Permutation Instructions

RISC-V CPUs leverage the RVV (RISC-V Vector) extension to accelerate data-parallel workloads. In addition to arithmetic operations, RVV includes powerful permutation instructions that enable flexible element rearrangement within vector registers --critical for optimizing performance in tasks such as matrix operations and cryptographic computations. However, the diverse control mechanisms of these instructions complicate their execution within a unified datapath while maintaining the fixed-latency requirement of cryptographic accelerators. To address this, we propose a unified microarchitecture capable of executing all RVV permutation instructions efficiently, regardless of their control information structure. This approach minimizes area and hardware costs while ensuring single-cycle execution for short vector machines (up to 256 bits) and enabling efficient pipelining for longer vectors. The proposed design is integrated into an open-source RISC-V vector processor and implemented at 7 nm using the OpenRoad physical synthesis flow. Experimental results validate the efficiency of our unified vector permutation unit, demonstrating that it only incurs 1.5% area overhead to the total vector processor. Furthermore, this area overhead decreases to near-0% as the minimum supported element width for vector permutations increases.

cs.AR↗

arXiv2025

Register Dispersion: Reducing the Footprint of the Vector Register File in Vector Engines of Low-Cost RISC-V CPUs

The deployment of Machine Learning (ML) applications at the edge on resource-constrained devices has accentuated the need for efficient ML processing on low-cost processors. While traditional CPUs provide programming flexibility, their general-purpose architecture often lacks the throughput required for complex ML models. The augmentation of a RISC-V processor with a vector unit can provide substantial data-level parallelism. However, increasing the data-level parallelism supported by vector processing would make the Vector Register File (VRF) a major area consumer in ultra low-cost processors, since 32 vector registers are required for RISC-V Vector ISA compliance. This work leverages the insight that many ML vectorized kernels require a small number of active vector registers, and proposes the use of a physically smaller VRF that dynamically caches only the vector registers currently accessed by the application. This approach, called Register Dispersion, maps the architectural vector registers to a smaller set of physical registers. The proposed ISA-compliant VRF is significantly smaller than a full-size VRF and operates like a conventional cache, i.e., it only stores the most recently accessed vector registers. Essential registers remain readily accessible within the compact VRF, while the others are offloaded to the cache/memory sub-system. The compact VRF design is demonstrated to yield substantial area and power savings, as compared to using a full VRF, with no or minimal impact on performance. This effective trade-off renders the inclusion of vector units in low-cost processors feasible and practical.

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