[Resource Topic] 2021/1033: Limits of Polynomial Packings for $\mathbb{Z}_{p^k}$ and $\mathbb{F}_{p^k}$

Welcome to the resource topic for 2021/1033

Title:
Limits of Polynomial Packings for \mathbb{Z}_{p^k} and \mathbb{F}_{p^k}

Authors: Jung Hee Cheon, Keewoo Lee

Abstract:

We formally define polynomial packing methods and initiate a unified study of related concepts in various contexts of cryptography. This includes homomorphic encryption (HE) packing and reverse multiplication-friendly embedding (RMFE) in information-theoretically secure multi-party computation (MPC). We prove several upper bounds and impossibility results on packing methods for \mathbb{Z}_{p^k} or \mathbb{F}_{p^k}-messages into \mathbb{Z}_{p^t}[x]/f(x) in terms of (i) packing density, (ii) level-consistency, and (iii) surjectivity. These results have implications on recent development of HE-based MPC over \mathbb{Z}_{2^k} secure against actively corrupted majority and provide new proofs for upper bounds on RMFE.

ePrint: https://eprint.iacr.org/2021/1033

Talk: https://www.youtube.com/watch?v=5sQyNshWu3g

Slides: https://iacr.org/submit/files/slides/2022/eurocrypt/eurocrypt2022/216/slides.pdf

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