Security Notions Zoo

A taxonomy of cryptographic security notions, focusing on Fully Homomorphic Encryption (FHE).

Because most FHE constructions rely on lattices, interesting things happen due to ciphertext malleability and inherent noise. This has led to the definition of a wide variety of specialized attacks and security notions. The relationship map below illustrates this landscape of alternative security definitions tailored for FHE. Directed arrows indicate theoretical implications (A → B means A implies B, i.e. that A is (usually) a strictly stronger notion than B). Click on any notion in the graph or the list below for more information.

For more information on the different game variations, see the flavors page, which describes the differences between security games such as IND, KR, and others for the same security notion. If you are new to provable security, the security primer introduces the core vocabulary: PPT adversaries, negligible functions, game-based definitions, reductions, and hybrid arguments.