Paper 2024/732

Compact Encryption based on Module-NTRU problems

Shi Bai, Florida Atlantic University
Hansraj Jangir, Florida Atlantic University
Hao Lin, Delft University of Technology
Tran Ngo, Florida Atlantic University
Weiqiang Wen, Télécom ParisTech
Jinwei Zheng, Télécom ParisTech
Abstract

The Module-NTRU problem, introduced by Cheon, Kim, Kim, Son (IACR ePrint 2019/1468), and Chuengsatiansup, Prest, Stehlé, Wallet, Xagawa (ASIACCS ’20), generalizes the versatile NTRU assump- tion. One of its main advantages lies in its ability to offer greater flexibil- ity on parameters, such as the underlying ring dimension. In this work, we present several lattice-based encryption schemes, which are IND-CPA (or OW-CPA) secure in the standard model based on the Module-NTRU and Module-LWE problems. Leveraging the Fujisaki-Okamoto transfor- mations, one can obtain IND-CCA secure key encapsulation schemes. Our first encryption scheme is based on the Module-NTRU assumption, which uses the determinant of the secret matrix over the underlying ring for the decryption. Our second scheme is analogue to the Module-LWE encryption scheme, but uses only a matrix as the public key, based on a vectorial variant of the Module-NTRU problem. In the end, we conduct comprehensive analysis of known attacks and propose concrete parame- ters for the instantiations. In particular, our ciphertext size is about 614 (resp. 1228) bytes for NIST Level 1 (resp. Level 5) security and small decryption failure, placing it on par with the most recent schemes such as the one proposed by Zhang, Feng and Yan (ASIACRYPT ’23). We also present several competitive parameters for NIST Level 3, which has a ci- phertext size of 921 bytes. Moreover, our schemes do not require specific codes for plaintext encoding and decoding.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Published elsewhere. PQCrypto 2024
Keywords
Lattice-based cryptographyEncryptionEncapsulationModule- NTRU problem
Contact author(s)
shih bai @ gmail com
hjangir2020 @ fau edu
baronlin001 @ gmail com
tran tbngo @ gmail com
weiqiang wen @ telecom-paris fr
jinwei zheng @ telecom-paris fr
History
2024-06-11: last of 2 revisions
2024-05-13: received
See all versions
Short URL
https://ia.cr/2024/732
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2024/732,
      author = {Shi Bai and Hansraj Jangir and Hao Lin and Tran Ngo and Weiqiang Wen and Jinwei Zheng},
      title = {Compact Encryption based on Module-{NTRU} problems},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/732},
      year = {2024},
      url = {https://eprint.iacr.org/2024/732}
}
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