Even though it is not clear when (or if) quantum computers will be built, the theoretical existence of quantum computing has potentially far-reaching consequences for the future of cryptography. This thesis aims to provide an in-depth analysis of the security of existing (non-quantum) symmetric encryption schemes against an attacker with quantum capabilities. Here, formal security models will be developed and justified in the provable security framework. Our results add to existing efforts in post-quantum cryptography by providing security proofs for cryptographic schemes within the concrete security paradigm. In practice, this is more relevant than the asymptotic security paradigm that is usually assumed in post-quantum cryptography. We begin by exploring how existing classical confidentiality notions translate into a security model, where a quantum adversary is only allowed to make classical queries. Then we give a formal analysis of the security of encryption schemes, such as Counter mode, in this model. Next we turn our attention to another natural and conservative security model where a quantum adversary is permitted to make quantum queries. To demonstrate the quantum adversary’s power in this model, we show how it can break the security of block ciphers such as the Even-Mansour scheme. We further discuss the security of existing symmetric encryptions by defining security notions for confidentiality in this model. Specifically, we give a formal definition of the security of symmetric encryption schemes under both a quantum superposition chosen plaintext attack and a quantum superposition chosen ciphertext attack. Attention is also given to semantic security in this model.
|1 Sept 2015
|Unpublished - 2015