Paper 2013/815 Original: eprint.iacr.org/2013/815 ↗
Iterated group products and leakage resilience against NC^1
Abstract
We show that if NC^1 \neq L, then for every element g of the alternating group A_t, circuits of depth O(log t) cannot distinguish between a uniform vector over (A_t)^t with product = g and one with product = identity. Combined with a recent construction by the author and Viola in the setting of leakage-resilient cryptography [STOC '13], this gives a compiler that produces circuits withstanding leakage from NC^1 (assuming NC^1 \neq L). For context, leakage from NC^1 breaks nearly all previous constructions, and security against leakage from P is impossible. We build on work by Cook and McKenzie [J.\ Algorithms '87] establishing the relationship between L = logarithmic space and the symmetric group S_t. Our techniques include a novel algorithmic use of commutators to manipulate the cycle structure of permutations in A_t.
Metadata
- Available format(s)
PDF- Publication info
- Preprint.
- History
- 2013-12-06: last updated
- 2013-12-06: published
- Short URL
- https://ia.cr/2013/815
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2013/815,
author = {Eric Miles},
title = {Iterated group products and leakage resilience against NC^1},
howpublished = {Cryptology {ePrint} Archive, Paper 2013/815},
year = {2013},
url = {https://eprint.iacr.org/2013/815}
}