Paper 2019/594

Cryptanalysis of Ring Homomorphic Encryption Schemes

Mugurel Barcau and Vicentiu Pasol

Abstract

We analyze the structure of finite commutative rings with respect to its idempotent and nilpotent elements. Based on this analysis we provide a quantum-classical IND-CCA^1 attack for ring homomorphic encryption schemes. Moreover, when the plaintext space is a finite reduced ring, i.e. a product of finite fields, we present a key-recovery attack based on representation problem in black-box finite fields. In particular, if the ciphertext space has smooth characteristic the key-recovery attack is effectively computable. We also extend the work of Maurer and Raub on representation problem in black-box finite fields to the case of a black-box product of finite fields of equal characteristic.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. Minor revision.
Keywords
homomorphic encryption schemesquantum computingkey-recovery attackblack-box rings
Contact author(s)
mugurel barcau @ imar ro
vicentiu pasol @ imar ro
History
2019-06-02: received
Short URL
https://ia.cr/2019/594
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2019/594,
      author = {Mugurel Barcau and Vicentiu Pasol},
      title = {Cryptanalysis of Ring Homomorphic Encryption Schemes},
      howpublished = {Cryptology ePrint Archive, Paper 2019/594},
      year = {2019},
      note = {\url{https://eprint.iacr.org/2019/594}},
      url = {https://eprint.iacr.org/2019/594}
}
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