Or Sattath

In this work, we focus on the following question: what are the cryptographic implications of having access to an oracle that provides a single Haar random quantum state? We show, perhaps surprisingly, that such an oracle is sufficient to construct quantum pseudorandomness. Pseudorandom states (PRS) are a family of states for which it is hard to distinguish between polynomially many copies of either a state sampled uniformly from the family or a Haar random state. A weaker notion, called single-copy pseudorandom states (1PRS), satisfies this property with respect to a single copy. Our main result is that 1PRS (as well as bit-commitments) exist relative to an oracle that provides a single Haar random state. We build on this result to show the existence of an oracle relative to which 1PRS exist, but PRS do not. This provides one of the first black-box separations between different forms of quantum pseudorandomness.

Two fundamental properties of quantum states that quantum information theory explores are pseudorandomness and provability of destruction. We introduce the notion of quantum pseudorandom states with proofs of destruction (PRSPD) that combines both these properties. Like standard pseudorandom states (PRS), these are efficiently generated quantum states that are indistinguishable from random, but they can also be measured to create a classical string. This string is verifiable (given the secret key) and certifies that the state has been destructed. We show that, similarly to PRS, PRSPD can be constructed from any post-quantum one-way function. As far as the authors are aware, this is the first construction of a family of states that satisfies both pseudorandomness and provability of destruction. We show that many cryptographic applications that were shown based on PRS variants using quantum communication can be based on (variants of) PRSPD using only classical communication. This includes symmetric encryption, message authentication, one-time signatures, commitments, and classically verifiable private quantum coins.

Abstract In a quantum money scheme, a bank can issue money that users cannot counterfeit. Similar to bills of paper money, most quantum money schemes assign a unique serial number to each money state, thus potentially compromising the privacy of the users of quantum money. However in a quantum coins scheme, just like the traditional currency coin scheme, all the money states are exact copies of each other, providing a better level of privacy for the users. A quantum money scheme can be private, i.e., only the bank can verify the money states, or public, meaning anyone can verify. In this work, we propose a way to lift any private quantum coin scheme -- which is known to exist based on the existence of one-way functions by Ji, Liu, and Song (CRYPTO'18) -- to a scheme that closely resembles a public quantum coin scheme. Verification of a new coin is done by comparing it to the coins the user already possesses, by using a projector on to the symmetric subspace. No public coin scheme was known prior to this work. It is also the first construction that is close to a public quantum money scheme and is provably secure based on standard assumptions. The lifting technique when instantiated with the private quantum coins scheme by Mosca and Stebila (2010) gives rise to the first construction that is close to an inefficient unconditionally secure public quantum money scheme.

We put forward the idea that classical blockchains and smart contracts are potentially useful primitives not only for classical cryptography, but for quantum cryptography as well. Abstractly, a smart contract is a functionality that allows parties to deposit funds, and release them upon fulfillment of algorithmically checkable conditions, and can thus be employed as a formal tool to enforce monetary incentives. In this work, we give the first example of the use of smart contracts in a quantum setting. We describe a simple hybrid classical-quantum payment system whose main ingredients are a classical blockchain capable of handling stateful smart contracts, and quantum lightning, a strengthening of public-key quantum money introduced by Zhandry (Eurocrypt'19). Our hybrid payment system employs quantum states as banknotes and a classical blockchain to settle disputes and to keep track of the valid serial numbers. It has several desirable properties: it is decentralized, requiring no trust in any single entity; payments are as quick as quantum communication, regardless of the total number of users; when a quantum banknote is damaged or lost, the rightful owner can recover the lost value.

Different flavors of quantum pseudorandomness have proven useful for various cryptographic applications, with the compelling feature that these primitives are potentially weaker than post-quantum one-way functions. Ananth, Lin, and Yuen (2023) have shown that logarithmic pseudorandom states can be used to construct a pseudo-deterministic PRG: informally, for a fixed seed, the output is the same with 1 − 1/poly probability. In this work, we introduce new definitions for ⊥-PRG and ⊥-PRF. The correctness guarantees are that, for a fixed seed, except with negligible probability, the output is either the same (with probability 1 − 1/poly) or recognizable abort, denoted ⊥. Our approach admits a natural definition of multi-time PRG security, as well as the adaptive security of a PRF. We construct a ⊥-PRG from any pseudo-deterministic PRG and, from that, a ⊥-PRF. Even though most mini-crypt primitives, such as symmetric key encryption, commitments, MAC, and length-restricted one-time digital signatures, have been shown based on various quantum pseudorandomness assumptions, digital signatures remained elusive. Our main application is a (quantum) digital signature scheme with classical public keys and signatures, thereby addressing a previously unresolved question posed in Morimae and Yamakawa’s work (Crypto, 2022). Additionally, we construct CPA secure public-key encryption with tamper-resilient quantum public keys.

Message Authentication Code or MAC, is a well-studied cryptographic primitive that is used in order to authenticate communication between two parties sharing a secret key. A Tokenized MAC or TMAC is a related cryptographic primitive, introduced by Ben-David & Sattath (QCrypt'17) which allows to delegate limited signing authority to third parties via the use of single-use quantum signing tokens. These tokens can be issued using the secret key, such that each token can be used to sign at most one document. We provide an elementary construction for TMAC based on BB84 states. Our construction can tolerate up to 14% noise, making it the first noise-tolerant TMAC construction. The simplicity of the quantum states required for our construction combined with the noise-tolerance, makes it practically more feasible than the previous TMAC construction. The TMAC is existentially unforgeable against adversaries with signing and verification oracles (i.e., analogous to EUF-CMA security for MAC), assuming post-quantum collision-resistant hash functions exist.

In a quantum money scheme, a bank can issue money that users cannot counterfeit. Similar to bills of paper money, most quantum money schemes assign a unique serial number to each money state, thus potentially compromising the privacy of the users of quantum money. However in a quantum coins scheme, just like the traditional currency coin scheme, all the money states are exact copies of each other, providing a better level of privacy for the users. A quantum money scheme can be private, i.e., only the bank can verify the money states, or public, meaning anyone can verify. In this work, we propose a way to lift any private quantum coin scheme -- which is known to exist based on the existence of one-way functions, due to Ji, Liu, and Song (CRYPTO'18) -- to a scheme that closely resembles a public quantum coin scheme. Verification of a new coin is done by comparing it to the coins the user already possesses, by using a projector on to the symmetric subspace. No public coin scheme was known prior to this work. It is also the first construction that is very close to a public quantum money scheme and is provably secure based on standard assumptions. The lifting technique when instantiated with the private quantum coins scheme, due to Mosca and Stebila 2010, gives rise to the first construction that is very close to an inefficient unconditionally secure public quantum money scheme.

Quantum money allows a bank to mint quantum money states that can later be verified and cannot be forged. Usually, this requires a quantum communication infrastructure to transfer quantum states between the user and the bank. This work combines the notion of classical verification -- introduced by Gavinsky (CCC 2012) -- with the notion of user-generated money -- introduced here -- to introduce Semi-Quantum Money, the first quantum money scheme to require only classical communication with the (entirely classical) bank. This work features constructions for both a public memory-dependent semi-quantum money scheme, based on the works of Zhandry and Coladangelo, and for a private memoryless semi-quantum money scheme, based on the notion of Noisy Trapdoor Claw Free Functions (NTCF) introduced by Brakerski et al. (FOCS 2018). In terms of technique, our main contribution is a strong parallel repetition theorem for NTCF.