A concrete security treatment of symmetric encryption in a quantum computing world

James Bartusek, Eli Goldin

In this note, we consider the setting of uncloneable encryption satisfying uncloneable indistinguishability, a form of symmetric key encryption that prevents the cloning of ciphertexts in a very strong sense. Our goal is to minimize the assumptions under which (many-time secure) uncloneable encryption is known to exist, assuming the existence of an information-theoretic "uncloneable bit", i.e. a one-time secure uncloneable encryption scheme for one-bit messages. We observe that if a t -> t' uncloneable bit exists, then the following implications hold. 1. If many-time secure symmetric key encryption exists, then many-time secure t -> t' uncloneable encryption for arbitrary-length messages exists. Since many-time secure uncloneable encryption implies many-time secure symmetric key encryption, this result is tight. 2. If pseudorandom unitaries exist, then many-time secure t -> t' uncloneable encryption for arbitrary-length messages with identical copy security exists. These results together show that many-time secure uncloneable encryption may follow from concrete assumptions in "microcrypt", the world of unstructured quantum cryptography that plausibly exists even if P = NP.

David Garvin, Oleksiy Kondratyev, Alexander Lipton +1 more

Shahram Mossayebi, Rüdiger Schack

In 2013, Boneh and Zhandry introduced the notion of indistinguishability (IND) in chosen plaintext (CPA) and chosen ciphertext (CCA) attacks by a quantum adversary which is given superposition access to an oracle for encryption and decryption queries but is restricted to classical queries in the challenge phase. In this paper we define IND-CPA and IND-CCA notions for symmetric encryption schemes where the adversary has full quantum superposition access to the oracle, and give constructions that achieve these security notions. Our results are formulated in the concrete security framework.

Gorjan Alagic, Anne Broadbent, Bill Fefferman +3 more

Virgil D. Gligor, Jonathan I. Katz, Omer Horvitz

The computational treatment of cryptography, and indeed any scientific treatment of a problem, is marked by its definitional side and by it constructive side. Results in this thesis better our understanding of both: on one side, they characterize the extent to which computational definitions capture the security of the basic task of symmetric encryption; on the other, they provide explicit bounds on the efficiency of commitment and secure two-party computation constructions. Specifically: (1) We relate the formal and computational treatments of symmetric encryption, obtaining a precise characterization of computational schemes whose computational semantics imply their formal semantics. We prove that this characterization is strictly weaker than previously-identified notions, and show how it may be realized in a simpler, more efficient manner. (2) We provide lower-bounds on the number of times a one-way permutation needs to be invoked (as a black-box) in order to construct statistically-binding commitments. Our bounds are tight for the case of perfectly-binding schemes. (3) We show that the secure computation of any two-party functionality can be performed in an optimal two rounds of communication even in a setting that accounts for concurrent execution with other protocols (i.e., the Universal Composability framework). Here, we rely on the assumption that parties have access to a common reference string; some sort of setup is known to be necessary.

Céline Chevalier, Ehsan Ebrahimi, Quoc-Huy Vu