A Practical Adaptive Key Recovery Attack on the LGM (GSW-like) Cryptosystem

Authors	P. Fauzi, M. N. Hovd and H. Raddum
Editors	T. J. P. C. J.H.
Title	A Practical Adaptive Key Recovery Attack on the LGM (GSW-like) Cryptosystem
Afilliation	Cryptography
Project(s)	Simula UiB
Status	Published
Publication Type	Proceedings, refereed
Year of Publication	2021
Conference Name	International Conference on Post-Quantum Cryptography
Volume	12841
Pagination	483-498
Date Published	07/2021
Publisher	Springer
ISBN Number	978-3-030-81292-8
Keywords	GSW, Key recovery, Somewhat homomorphic encryption, Statistical attack
Abstract	We present an adaptive key recovery attack on the leveled homomorphic encryption scheme suggested by Li, Galbraith and Ma (Provsec 2016), which itself is a modification of the GSW cryptosystem designed to resist key recovery attacks by using a different linear combination of secret keys for each decryption. We were able to efficiently recover the secret key for a realistic choice of parameters using a statistical attack. In particular, this means that the Li, Galbraith and Ma strategy does not prevent adaptive key recovery attacks.
URL	https://link.springer.com/chapter/10.1007/978-3-030-81293-5_25
DOI	10.1007/978-3-030-81293-5_25
Citation Key	27900

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