On Quantum Money and Evasive Obfuscation

Tzu-Hsiang Huang, Wei-Hsiang Hung, Shota Yamada

The evasive learning with errors (evasive LWE) assumption is a new assumption recently introduced by Wee [Wee22] and Tsabary [Tsa22] independently, as a significant strengthening of the standard LWE assumption. While the assumption is known to imply various strong primitives including witness encryption [Tsa22, VWW22], the assumption in the most general case (i.e., the private coin variant) is considered quite implausible due to the obfuscation based attack mentioned in [Wee22]. This obfuscation based attack is then later formalized by Vaikuntanathan, Wee, and Wichs [VWW22]. In this note, we revisit their attack and show that the attack actually does not work by showing a concrete counterexample. While various attacks against private-coin evasive LWE are now known, the attack of [VWW22] is the only one that applies in the setting where the sampler is oblivious to the LWE secret, which we call the S-oblivious regime. Therefore, our refutation closes the only known avenue for attacking the assumption in the S-oblivious regime. To complement the above refutation of this attack, we also present a variant of the counterexample assuming the existence of instance-hiding witness encryption. However, our sampler is not S-oblivious, and thus we do not fully recover the attack considered in [VWW22]. Taken together, these results indicate that the security of private-coin evasive LWE in the S-oblivious regime remains open.

Bhaskar Roberts

Gorjan Alagic, Bill Fefferman

Encryption of data is fundamental to secure communication in the modern world. Beyond encryption of data lies obfuscation, i.e., encryption of functionality. It is well-known that the most powerful means of obfuscating classical programs, so-called ``black-box obfuscation',' is provably impossible [Barak et al '12]. However, several recent results have yielded candidate schemes that satisfy a definition weaker than black-box, and yet still have numerous applications. In this work, we initialize the rigorous study of obfuscating programs via quantum-mechanical means. We define notions of quantum obfuscation which encompass several natural variants. The input to the obfuscator can describe classical or quantum functionality, and the output can be a circuit description or a quantum state. The obfuscator can also satisfy one of a number of obfuscation conditions: black-box, information-theoretic black-box, indistinguishability, and best possible; the last two conditions come in three variants: perfect, statistical, and computational. We discuss many applications, including CPA-secure quantum encryption, quantum fully-homomorphic encryption, and public-key quantum money. We then prove several impossibility results, extending a number of foundational papers on classical obfuscation to the quantum setting. We prove that quantum black-box obfuscation is impossible in a setting where adversaries can possess more than one output of the obfuscator. In particular, generic transformation of quantum circuits into black-box-obfuscated quantum circuits is impossible. We also show that statistical indistinguishability obfuscation is impossible, up to an unlikely complexity-theoretic collapse. Our proofs involve a new tool: chosen-ciphertext-secure encryption of quantum data, which was recently shown to be possible assuming quantum-secure one-way functions exist [Alagic et al '16].

Andriyan Bilyk, Javad Doliskani, Zhiyong Gong

Tao Shang, Jianwei Liu

Alper Çakan, Vipul Goyal, Takashi Yamakawa

Quantum information allows us to build quantum money schemes, where a bank can issue banknotes in the form of authenticatable quantum states that cannot be cloned or counterfeited. Similar to paper banknotes, in existing quantum money schemes, a banknote consists of an unclonable quantum state and a classical serial number, signed by bank. Thus, they lack one of the most fundamental properties cryptographers look for in a currency scheme: privacy. In this work, we first further develop the formal definitions of privacy for quantum money schemes. Then, we construct the first public-key quantum money schemes that satisfy these security notions. Namely, - Assuming existence of indistinguishability obfuscation (iO) and hardness of Learning with Errors (LWE), we construct a public-key quantum money scheme with anonymity against users and traceability by authorities. Since it is a policy choice whether authorities should be able to track banknotes or not, we also construct an untraceable money scheme from the same cryptographic assumptions, where no one (not even the authorities) can track banknotes. Further, we show that the no-cloning principle, a result of quantum mechanics, allows us to construct schemes, with security guarantees that are classically impossible, for a seemingly unrelated application: voting! - Assuming iO and LWE, we construct a universally verifiable quantum voting scheme with classical votes. Finally, as a technical tool, we introduce the notion of publicly rerandomizable encryption with strong correctness, where no adversary is able to produce a malicious ciphertext and a malicious randomness such that the ciphertext before and after rerandomization decrypts to different values! We believe this might be of independent interest. - Assuming LWE, we construct a (post-quantum) classical publicly rerandomizable encryption scheme with strong correctness.