Welcome to the resource topic for 2021/277
Title:
On the Integer Polynomial Learning with Errors Problem
Authors: Julien Devevey, Amin Sakzad, Damien Stehlé, Ron Steinfeld
Abstract:Several recent proposals of efficient public-key encryption are based on variants of the polynomial learning with errors problem (\mathsf{PLWE}^f) in which the underlying polynomial ring \mathbb{Z}_q[x]/f \ is replaced with the (related) modular integer ring \mathbb{Z}_{f(q)}; the corresponding problem is known as Integer Polynomial Learning with Errors (\mathsf{I-PLWE}^f). Cryptosystems based on \mathsf{I-PLWE}^f and its variants can exploit optimised big-integer arithmetic to achieve good practical performance, as exhibited by the \mathsf{ThreeBears} cryptosystem. Unfortunately, the average-case hardness of \mathsf{I-PLWE}^f and its relation to more established lattice problems have to date remained unclear. We describe the first polynomial-time average-case reductions for the search variant of \mathsf{I-PLWE}^f, proving its computational equivalence with the search variant of its counterpart problem \mathsf{PLWE}^f. Our reductions apply to a large class of defining polynomials f. To obtain our results, we employ a careful adaptation of Rényi divergence analysis techniques to bound the impact of the integer ring arithmetic carries on the error distributions. As an application, we present a deterministic public-key cryptosystem over integer rings. Our cryptosystem, which resembles \mathsf{ThreeBears}, enjoys one-way (OW-CPA) security provably based on the search variant of \mathsf{I-PLWE}^f.
ePrint: https://eprint.iacr.org/2021/277
Talk: https://www.youtube.com/watch?v=IPzfVQndvpg
Slides: https://iacr.org/submit/files/slides/2021/pkc/pkc2021/181/slides.pdf
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