### 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)
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

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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