About this artifact

This artifact accompanies our paper Multiplying Polynomials without Powerful Multiplication Instructions (Long Paper) accepted at TCHES 2025, Issue 1. Our paper aims at the following lattice-based schemes

• Dilithium
• Saber

on the following platforms:

• ARM Cortex-M3
• AVR

For Dilithium, the artifact targets a certain Round 3 version. There are several modifications after the publication of FIPS 204. This artifact doesn't apply those changes as they were not available at the time of the submission. We explicitly include the target Dilithium Round 3 implementation in this artifact for the functionality tests and will modify the implementations in compliance with FIPS 204 in the future.

Introduction

We outline the following contributions of our paper:

• Dilithium:
  • Dilithium NTT/iNTT on Cortex-M3 and AVR: We generalize Barrett multiplication that is suitable for multi-limb arithmetic. The resulting modular multiplication is used in Dilithium NTT/iNTT modulo the Dilithium prime $2^{23} - 2^{13} + 1$.
  • Fermat number transform for challenge polynomial multiplication $c \boldsymbol{s}_1, c \boldsymbol{s}_2$ on Cortex-M3: We follow AHKS22 and apply Fermat number transform for dilithium2 and dilithium5.
  • Nussbaumer + TMVP for challenge polynomial multiplication $c \boldsymbol{t}_0$ on Cortex-M3.
• Saber:
  • Nussbaumer + TMVP for matrix-vector multiplication and inner product on Cortex-M4.
  • Striding Toom--Cook for matrix-vector multiplication and inner product on AVR.

Requirements

• C compiler: This is for running the examples, the version doesn't matter as the performance numbers do not rely on the C compiler targeting the host machine.

Cortex-M3

Reproducing benchmark

• Board nucleo-f207zg: The target hardware.
• openocd: A tool for flashing the binary files to the board. Our version:

Open On-Chip Debugger 0.12.0

• libopencm3: For generating and compiling various platform-related files. Commit 9545471e4861090a77f79c4458eb19ec771e23d9 of libopencm3.
• python3 with argparse, pyserial, numpy, filecmp for reading from the serial port and parsing the data. We use Python 3.13.0.
• arm-none-eabi-gcc. Cross-compiler We use arm-none-eabi-gcc (GNU Arm Embedded Toolchain 10.3-2021.10) 10.3.1 20210824 (release). You can download it from Arm GNU Toolchain Downloads.

Testing correctness with emulation

This part varies between host machines.

• A cross-compiler targeting armv7-m, armv7-a, or armv7.
• A host machine with a qemu.

We tested with below:

• Ubuntu LTS 22.04.1, x86_64 GNU/Linux
• gcc-arm-linux-gnueabi or gcc-arm-linux-gnueabihf.
  • arm-linux-gnueabi-gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0
  • arm-linux-gnueabi-gcc-12 (Ubuntu 12.3.0-1ubuntu1~22.04) 12.3.0
  • arm-linux-gnueabihf-gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0
• qemu-user. We use 1:6.2+dfsg-2ubuntu6.24.

See cortex-m3.md for detailed instructions.

AVR

• IAR Embedded Workbench for AVR : We developed our AVR code in IAR Embedded Workbench AVR.
  • One can get a one week trial to run the artifact at the link.
  • [IAR Embedded Workbench for AVR] is a Windows-only software (544.5MB).

See avr.md for detailed instructions.

Examples of Toom--Cook, TMVP, and Nussbaumer

In the folder examples, we give the C programs implementing our Nussbaumer + TMVP over $Z_{1, 2, 4, ..., 2^{24}}$ used in Dilithium and Saber. One only needs a C compiler for running the examples. Please follow the instructions in examples/README.md

Generating the tables of constants

In the folder gen_constant_table, we include the C programs generating the tables of constants in our Dilithium NTT/iNTT and FNT for Dilithium. One only needs a C compiler for generating the constants. Please follow the instructions in gen_constant_table/README.md

Experimental range analysis

In the folder range, we include the C programs reporting the range of Dilithium NTT with random inputs as requested by reviewers. The numbers might differ for different randomness. One only needs a C compiler for deriving the experimental range. Please follow the instructions in range/README.md

Licenses

The following files are third-party materials licensed under GPL-3.0 / LGPL-3.0

• [every folder in this directory]/libopencm3
• m3_util/devices.data
• m3_util/genlink.py
• m3_util/linker.ld.S Other files are licensed under CC0 1.0 Universal.