Welcome to the resource topic for 2024/1822
Title:
Anonymous Public-Key Quantum Money and Quantum Voting
Authors: Alper Çakan, Vipul Goyal, Takashi Yamakawa
Abstract: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: a user in possession of k banknotes cannot produce k +1 banknotes. 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 and hardness of Learning with Errors, 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, where no one (not even the authorities) can track banknotes.
• Assuming existence of indistinguishability obfuscation and hardness of Learning with Er- rors, we construct a public-key quantum money scheme with untraceability.
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 existence of indistinguishability obfuscation and hardness of Learning with Errors, 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 random tape such that the ciphertext before and after rerandomization (with the malicious tape) decrypts to different values! We believe this might be of independent interest. • Assuming the (quantum) hardness of Learning with Errors, we construct a (post-quantum) classical publicly rerandomizable encryption scheme with strong correctness
ePrint: https://eprint.iacr.org/2024/1822
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