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

Jung Hee Cheon; Keewoo Lee

Paper 2021/1033

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

Jung Hee Cheon and 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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: A major revision of an IACR publication in EUROCRYPT 2022
Keywords: Packing method Homomorphic encryption Multi-party computation Reverse multiplication-friendly embedding
Contact author(s): activecondor @ snu ac kr
History: 2022-03-01: last of 2 revisions; 2021-08-16: received; See all versions
Short URL: https://ia.cr/2021/1033
License: CC BY

BibTeX

@misc{cryptoeprint:2021/1033,
      author = {Jung Hee Cheon and Keewoo Lee},
      title = {Limits of Polynomial Packings for $\mathbb{Z}_{p^k}$ and $\mathbb{F}_{p^k}$},
      howpublished = {Cryptology {ePrint} Archive, Paper 2021/1033},
      year = {2021},
      url = {https://eprint.iacr.org/2021/1033}
}