Unclonable Encryption in the Haar Random Oracle Model

Abstract

We construct unclonable encryption (UE) in the Haar random oracle model, where all parties have query access to $U,U^\dagger,U^*,U^T$ for a Haar random unitary $U$. Our scheme satisfies the standard notion of unclonable indistinguishability security, supports reuse of the secret key, and can encrypt arbitrary-length messages. That is, we give the first evidence that (reusable) UE, which requires computational assumptions, exists in "micocrypt", a world where one-way functions may not exist. As one of our central technical contributions, we build on the recently introduced path recording framework to prove a natural ``unitary reprogramming lemma'', which may be of independent interest.

Figures (21)

• Figure : Hybrid $1$: The security game for uncloneable encryption
• Figure : Hybrid $3$: We split the Haar random unitary $U$ into two random unitaries: $U_1$ acting on a superset of the encryption randomness and $U_2$ acting on the orthogonal space.
• Figure : Hybrid $5$: We sample $V$, and then set $U_1$ to first apply $\widetilde{E}_k^{\vec{V}}$.
• Figure : Hybrid $0$: The game $FindSEnc(C)$.
• Figure : Hybrid $2$: Instead of sampling $U_1 \gets Haar(S_2)$, we sample each $\ket{\phi_s} = U_1 \ket{s}$ from $HaarSt(S_2)$.

Theorems & Definitions (98)

• Theorem 1.1: Informal
• Corollary 1.2
• Theorem 1.3: Informal
• Lemma 1.4: Informal: Unitary reprogramming lemma
• Definition 2.1
• Definition 2.2
• Definition 2.3
• Definition 2.4
• Definition 2.5: Diamond norm
• Theorem 2.6