### Efficient Ring-LWE Encryption on 8-bit AVR Processors

Zhe Liu, Hwajeong Seo, Sujoy Sinha Roy, Johann Großschädl, Howon Kim, and Ingrid Verbauwhede

##### Abstract

Public-key cryptography based on the ring-variant'' of the Learning with Errors (ring-LWE) problem is both efficient and believed to remain secure in a post-quantum world. In this paper, we introduce a carefully-optimized implementation of a ring-LWE encryption scheme for 8-bit AVR processors like the ATxmega128. Our research contributions include several optimizations for the Number Theoretic Transform (NTT) used for polynomial multiplication. More concretely, we describe the Move-and-Add (MA) and the Shift-Add-Multiply-Subtract-Subtract (SAMS2) technique to speed up the performance-critical multiplication and modular reduction of coefficients, respectively. We take advantage of incompletely-reduced intermediate results to minimize the total number of reduction operations and use a special coefficient-storage method to decrease the RAM footprint of NTT multiplications. In addition, we propose a byte-wise scanning strategy to improve the performance of a discrete Gaussian sampler based on the Knuth-Yao random walk algorithm. For medium-term security, our ring-LWE implementation needs 590k, 672k, and 276k clock cycles for key-generation, encryption, and decryption, respectively. On the other hand, for long-term security, the execution time of key-generation, encryption, and decryption amount to 2.2M, 2.6M, and 686k cycles, respectively. These results set new speed records for ring-LWE encryption on an 8-bit processor and outperform related RSA and ECC implementations by an order of magnitude.

Available format(s)
Publication info
Keywords
Implementation - Quantum cryptography
Contact author(s)
zhe liu @ uni lu
History
2015-09-20: last of 3 revisions
See all versions
Short URL
https://ia.cr/2015/410

CC BY

BibTeX

@misc{cryptoeprint:2015/410,
author = {Zhe Liu and Hwajeong Seo and Sujoy Sinha Roy and Johann Großschädl and Howon Kim and Ingrid Verbauwhede},
title = {Efficient Ring-LWE Encryption on 8-bit AVR Processors},
howpublished = {Cryptology ePrint Archive, Paper 2015/410},
year = {2015},
note = {\url{https://eprint.iacr.org/2015/410}},
url = {https://eprint.iacr.org/2015/410}
}

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