@article {43114,
	title = {On the IND-CCA1 Security of FHE Schemes},
	journal = {MDPI Cryptography},
	volume = {6},
	number = {13},
	year = {2022},
	month = {03/2022},
	publisher = {MDPI},
	address = {Online},
	abstract = {Fully homomorphic encryption (FHE) is a powerful tool in cryptography that allows one to perform arbitrary computations on encrypted material without having to decrypt it first. There are numerous FHE schemes, all of which are expanded from somewhat homomorphic encryption (SHE) schemes, and some of which are considered viable in practice. However, while these FHE schemes are semantically (IND-CPA) secure, the question of their IND-CCA1 security is much less studied, and we therefore provide an overview of the IND-CCA1 security of all acknowledged FHE schemes in this paper. To give this overview, we group SHE schemes into broad categories based on their similarities and underlying hardness problems. For each category, we show that the SHE schemes are susceptible to either known adaptive key recovery attacks, a natural extension of known attacks, or our proposed attacks. Finally, we discuss the known techniques to achieve IND-CCA1 secure FHE and SHE schemes. We conclude that none of the proposed schemes are IND-CCA1 secure, and that the known general constructions all have their shortcomings.},
	keywords = {Cryptanalysis, FHE schemes, IND-CCA1},
	issn = {2410-387X},
	doi = {10.3390/cryptography6010013},
	url = {https://www.mdpi.com/2410-387X/6/1/13},
	author = {Martha Norberg {Hovd} and Raddum, H{\r a}vard and Fauzi, Prastudy}
}
@phdthesis {43135,
	title = {Studies on the Security of Selected Advanced Asymmetric Cryptographic Primitives},
	volume = {PhD},
	year = {2022},
	author = {Martha Norberg {Hovd}}
}
@inproceedings {27900,
	title = {A Practical Adaptive Key Recovery Attack on the LGM (GSW-like) Cryptosystem},
	journal = {International Conference on Post-Quantum Cryptography},
	volume = {12841},
	year = {2021},
	month = {07/2021},
	pages = {483-498},
	publisher = { Springer},
	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.},
	keywords = {GSW, Key recovery, Somewhat homomorphic encryption, Statistical attack},
	isbn = {978-3-030-81292-8},
	doi = {https://doi.org/10.1007/978-3-030-81293-5_25},
	url = {https://link.springer.com/chapter/10.1007/978-3-030-81293-5_25},
	author = {Fauzi, Prastudy and Martha Norberg {Hovd} and Raddum, H{\r a}vard},
	editor = {Tillich JP. Cheon {J.H.}}
}
@inproceedings {DBLP:conf/indocrypt/HovdS20,
	title = {Vetted Encryption},
	journal = {Progress in Cryptology - INDOCRYPT 2020 - 21st International Conference on Cryptology in India},
	volume = {12578},
	year = {2020},
	pages = {488{\textendash}507},
	publisher = {Springer},
	doi = {10.1007/978-3-030-65277-7_22},
	url = {https://doi.org/10.1007/978-3-030-65277-7_22},
	author = {Martha Norberg {Hovd} and Stam, Martijn},
	editor = {Bhargavan, Karthikeyan and Oswald, Elisabeth and Prabhakaran, Manoj}
}
