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Lattice-based Threshold Signature Optimization for RAM Constrained Devices
Shapoval, Vladyslav ; Ricci, Sara
The DS2 scheme is a lattice-based (n, n)-threshold signature based on the standardized Dilithium signature. However, deploying DS2, as well as Dilithium, on microcontrollers is a challenge due to the memory limitations of these devices. While the decryption phase can be implemented relatively straightforwardly, the key generation and signing phases require the generation and manipulation of large matrices and vectors, which can quickly exhaust the available memory on the microcontroller. In this paper, we propose an optimization of the DS2 key generation and signing algorithms tailored for microcontrollers. Our approach focuses on minimizing memory consumption by generating large elements, such as the commitment key ck and the random commitment parameter r, on the fly from random and non-random seeds. This approach significantly reduces the overall size of the signature from 143 KB to less than 5 KB, depending on the number of signers involved. We also split the algorithms into two distinct components: a security-critical part and a non-security-critical part. The security-critical part contains operations that require secret knowledge and must be run on the microcontroller itself. Conversely, the non-critical part contains operations that do not require secret knowledge and can be performed on a connected, more powerful central host.
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Lattice-Based Cryptography on Constrained Devises
Shapoval, Vladyslav ; Dzurenda, Petr (oponent) ; Ricci, Sara (vedoucí práce)
This master’s thesis presents a modified software implementation of the module-lattice-based signature scheme Dilithium and its distributed variant DS2 for the ARM Cortex-M4 microcontroller. Dilithium is a part of the CRYSTALS suite and was selected by the NIST as a new post-quantum signature standard. This work is focused on reducing the memory footprint of both algorithms in order to make them more applicable to a wider spectrum of microcontrollers and constrained devices. Both signatures were optimized to run on the STM32 Cortex-M4 microcontroller. On one hand, Dilithium signature presented an already optimized implementation that can run on a microcontroller. Therefore, we focused on adding hardware acceleration support for AES for the generation of pseudo-random numbers during the generation of the signature. On the other hand, DS2 signature is more memory demanding and we proposed two microcontroller-tailored optimization approaches. These optimizations aim to reduce memory consumption while maintaining security strength. Experimental results and security analysis demonstrate the efficacy and practicality of our solutions. As a result of our work, we successfully developed new versions of both Dilithium and DS2 with memory consumption reduced by more than 50\% and 90\%, respectively, compared to the original.
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