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 methodHomomorphic encryptionMulti-party computationReverse 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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2021/1033}},
      url = {https://eprint.iacr.org/2021/1033}
}
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