Welcome to the resource topic for
**2023/1841**

**Title:**

Unclonable Cryptography with Unbounded Collusions

**Authors:**
Alper Çakan, Vipul Goyal

**Abstract:**

Quantum no-cloning theorem gives rise to the intriguing possibility of quantum copy protection where we encode a program in a quantum state such that a user in possession of k such states cannot create k+1 working copies. Introduced by Aaronson (CCC’09) over a decade ago, copy protection has proven to be notoriously hard to achieve.

In this work, we construct public-key encryption and functional encryption schemes whose secret keys are copy-protected against unbounded collusions in the plain model (i.e. without any idealized oracles), assuming (post-quantum) subexponentially secure \mathcal{iO}, one-way functions and LWE. This resolves a long-standing open question of constructing fully collusion-resistant copy-protected functionalities raised by multiple previous works.

Prior to our work, copy-protected functionalities were known only in restricted collusion models where either an a-priori bound on the collusion size was needed, in the plain model with the same assumptions as ours (Liu, Liu, Qian, Zhandry [TCC’22]), or adversary was only prevented from doubling their number of working programs, in a structured quantum oracle model (Aaronson [CCC’09]).

We obtain our results through a novel technique which uses identity-based encryption to construct unbounded collusion resistant copy-protection schemes from 1\to2 secure schemes. This is analogous to the technique of using digital signatures to construct full-fledged quantum money from single banknote schemes (Lutomirski et al. [ICS’09], Farhi et al. [ITCS’12], Aaronson and Christiano [STOC’12]). We believe our technique is of independent interest.

Along the way, we also construct a puncturable functional encryption scheme whose master secret key can be punctured at all functions f such that f(m_0) \neq f(m_1). This might also be of independent interest.

**ePrint:**
https://eprint.iacr.org/2023/1841

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