Multiplying Not-So-Big Integers with FFTs

Sat, 04 Jul 2026 00:00:00 +0000

This first-author research project, Finding and Pushing the Crossover on Large Modern OoO ARM CPUs, studies where NTT-based multiplication becomes practical for not-so-big integer sizes. The paper is available as and was accepted for presentation at the CHES 2026 Poster Session.

The project develops two generations of constant-time NTT-based multiplication for Cortex-A76. The second generation targets smaller operand sizes through tighter range bounds, redesigned 256/512-point NTT organization, fused reconstruction, and shorter carry and instruction-dependency chains.

Key Features

NEON-optimized NTT kernels: Developed constant-time fused NTT kernels in AArch64 assembly using ARM NEON instructions.
Multiplication pipeline: Combined Barrett and Montgomery arithmetic, Good’s trick, CRT reconstruction, and chunking and dechunking.
Crossover result: The second-generation two-unknown-input multiplier outperforms target-tuned variable-time GMP by 6.25% at 5,632 bits and 16.66% at 8,448 bits, placing the observed crossover at or below 5,632 bits.
Montgomery multiplication: The one-known-input implementation improves over OpenSSL’s Neon path by 5.19%-44.40% across the evaluated 5,120-10,240-bit sizes.
OpenSSL integration: End-to-end RSA verification and encryption improve by 15.98%-51.58% across RSA-5120, RSA-6144, RSA-8192, and RSA-10240.
Formal verification: Verified optimized assembly kernels with CryptoLine for algebraic correctness, range safety, and equivalence after Slothy scheduling, then used HOL Light to compose higher-level multiplication specifications.

Generative AI for High-Fidelity Side-Channel Trace Simulation

Fri, 03 Jul 2026 00:00:00 +0000

This research began through the NTU Global Connect Fellowship Program at Nanyang Technological University and continues as a remote collaboration, supervised by Gwee Bah Hwee and Juncheng Chen. A manuscript is in preparation.

The project studies how attack-relevant leakage emerges during diffusion-based side-channel trace generation and whether cryptanalytic utility develops at the same rate as waveform and distribution fidelity.

Experiments and Findings

Datasets: Developed conditional DDPM experiments on controlled synthetic traces and four measured AES datasets.
Reverse-trajectory evaluation: Evaluated predicted-clean traces across all 400 reverse-diffusion stages rather than only the final samples.
Attack-based evaluation: Measured CPA-based key-recovery complexity throughout the reverse trajectory.
Fidelity evaluation: Combined waveform and distribution distances with nearest-neighbor likelihood scoring.
Key observation: Found that attack-relevant leakage can emerge substantially earlier than full distributional fidelity.
Masked traces: Matching first-order marginals alone was insufficient to reproduce the cross-share dependence required for second-order attacks.

Research | David Shu-Yu Wu

Multiplying Not-So-Big Integers with FFTs

Key Features

Generative AI for High-Fidelity Side-Channel Trace Simulation

Experiments and Findings