Cryptology ePrint Archive: Report 2018/1172

The impact of error dependencies on Ring/Mod-LWE/LWR based schemes

Jan-Pieter D'Anvers and Frederik Vercauteren and Ingrid Verbauwhede

Abstract: Current estimation techniques for the probability of decryption failures in Ring/Mod-LWE/LWR based schemes assume independence of the failures in individual bits of the transmitted message to calculate the full failure rate of the scheme. In this paper we disprove this assumption both theoretically and practically for schemes based on Ring/Mod-Learning with Errors/Rounding. We provide a method to estimate the decryption failure probability, taking into account the bit failure dependency. We show that the independence assumption is suitable for schemes without error correction, but that it might lead to underestimating the failure probability of algorithms using error correcting codes. In the worst case, for LAC-128, the failure rate is $2^{48}$ times bigger than estimated under the assumption of independence. This higher-than-expected failure rate could lead to more efficient cryptanalysis of the scheme through decryption failure attacks.

Category / Keywords: public-key cryptography / Lattice cryptography, Ring-LWE, Error Correcting Codes, Decryption Failures

Date: received 30 Nov 2018, last revised 7 Dec 2018

Contact author: janpieter danvers at esat kuleuven be

Available format(s): PDF | BibTeX Citation

Version: 20181207:085447 (All versions of this report)

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