Studies on the Security of Selected Advanced Asymmetric Cryptographic Primitives
Doctoral thesis
Åpne
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https://hdl.handle.net/11250/2982028Utgivelsesdato
2022-03-11Metadata
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Sammendrag
The main goal of asymmetric cryptography is to provide confidential communication, which allows two parties to communicate securely even in the presence of adversaries. Ever since its invention in the seventies, asymmetric cryptography has been improved and developed further, and a formal security framework has been established around it. This framework includes different security goals, attack models, and security notions. As progress was made in the field, more advanced asymmetric cryptographic primitives were proposed, with other properties in addition to confidentiality. These new primitives also have their own definitions and notions of security.
This thesis consists of two parts, where the first relates to the security of fully homomorphic encryption and related primitives. The second part presents a novel cryptographic primitive, and defines what security goals the primitive should achieve.
The first part of the thesis consists of Article I, II, and III, which all pertain to the security of homomorphic encryption schemes in one respect or another. Article I demonstrates that a particular fully homomorphic encryption scheme is insecure in the sense that an adversary with access only to the public material can recover the secret key. It is also shown that this insecurity mainly stems from the operations necessary to make the scheme fully homomorphic. Article II presents an adaptive key recovery attack on a leveled homomorphic encryption scheme. The scheme in question claimed to withstand precisely such attacks, and was the only scheme of its kind to do so at the time. This part of the thesis culminates with Article III, which is an overview article on the IND-CCA1 security of all acknowledged homomorphic encryption schemes.
The second part of the thesis consists of Article IV, which presents Vetted Encryption (VE), a novel asymmetric cryptographic primitive. The primitive is designed to allow a recipient to vet who may send them messages, by setting up a public filter with a public verification key, and providing each vetted sender with their own encryption key. There are three different variants of VE, based on whether the sender is identifiable to the filter and/or the recipient. Security definitions, general constructions and comparisons to already existing cryptographic primitives are provided for all three variants.
Består av
Paper 1. Martha Norberg Hovd: A Successful Subfield Lattice Attack on a Fully Homomorphic Encryption Scheme. In Stig Frode Mjølsnes and Ragnar Soleng, editors, Proceedings of the 11th Norwegian Information Security Conference, September 2018. The article is available in the thesis.Paper 2. Prastudy Fauzi, Martha Norberg Hovd and Håvard Raddum. A Practical Adaptive Key Recovery Attack on the LGM (GSW-like) Cryptosystem. In Jung Hee Cheon and Jean-Pierre Tillich, editors, Post-Quantum Cryptography - 12th International Conference, PQCrypto 2021, pages 483-498, Springer, Cham, July 2021. The article is available in the thesis. The final publication is available at: https://doi.org/10.1007/978-3-030-81293-5_25
Paper 3. Prastudy Fauzi, Martha Norberg Hovd and Håvard Raddum. On the IND-CCA1 Security of FHE Schemes. Cryptology ePrint Archive, Report 2021/1624, 2021. The article is available in the thesis.
Paper 4. Martha Norberg Hovd and Martijn Stam. Vetted Encryption. In Karthikeyan Bhargavan, Elisabeth Oswald and Manoj Prabhakaran, editors, INDOCRYPT 2020, volume 12578 of LNCS, pages 488-507. Springer, Heidelberg, December 2020. The article is available in the thesis.