[Resource Topic] 2019/594: Cryptanalysis of Ring Homomorphic Encryption Schemes

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Title:
Cryptanalysis of Ring Homomorphic Encryption Schemes

Authors: Mugurel Barcau, 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.

ePrint: https://eprint.iacr.org/2019/594

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