A quantum public-key encryption scheme is presented in this paper. In the proposed scheme, ciphertext is described by quantum states and security of this scheme is based on the assumption that NP-complete (NP-C) problems are intractable against quantum (probabilistic) polynomial-time Turing machines (QPTM). One of the main properties of our scheme is that it is immune to off-line attack, in which the adversaries can copy all the ciphertext on channel and analyze them at a later time. We call this type of encryption scheme the computationally secure uncloneable encryption scheme. It is shown that the presented scheme can also be used to encrypt quantum states.
A quantum public-key encryption scheme is presented in this paper. In the proposed scheme, ciphertext is described by quantum states and security of this scheme is based on the assumption that NP-complete (NP-C) problems are intractable against quantum (probabilistic) polynomial-time Turing machines (QPTM). One of the main properties of our scheme is that it is immune to off-line attack, in which the adversaries can copy all the ciphertext on channel and analyze them at a later time. We call this type of encryption scheme the computationally secure uncloneable encryption scheme. It is shown that the presented scheme can also be used to encrypt quantum states.
Quantum states cannot be cloned. I show how to extend this property to classical messages encoded using quantum states, a task I call ``uncloneable encryption.'' An uncloneable encryption scheme has the property that an eavesdropper Eve not only cannot read the encrypted message, but she cannot copy it down for later decoding. She could steal it, but then the receiver Bob would not receive the message, and would thus be alerted that something was amiss. I prove that any authentication scheme for quantum states acts as a secure uncloneable encryption scheme. Uncloneable encryption is also closely related to quantum key distribution (QKD), demonstrating a close connection between cryptographic tasks for quantum states and for classical messages. Thus, studying uncloneable encryption and quantum authentication allows for some modest improvements in QKD protocols. While the main results apply to a one-time key with unconditional security, I also show uncloneable encryption remains secure with a pseudorandom key. In this case, to defeat the scheme, Eve must break the computational assumption behind the pseudorandom sequence before Bob receives the message, or her opportunity is lost. This means uncloneable encryption can be used in a non-interactive setting, where QKD is not available, allowing Alice and Bob to convert a temporary computational assumption into a permanently secure message.
Abstract. This paper presents a new paradigm of cryptography, quantum public-key cryptosystems. In quantum public-key cryptosystems, all parties including senders, receivers and adversaries are modeled as quantum (probabilistic) poly-time Turing (QPT) machines and only classical channels (i.e., no quantum channels) are employed. A quantum trapdoor one-way function, f, plays an essential role in our system, in which a QPT machine can compute f with high probability, any QPT machine can invert f with negligible probability, and a QPT machine with trapdoor data can invert f. This paper proposes a concrete scheme for quantum public-key cryptosystems: a quantum public-key encryption scheme or quantum trapdoor one-way function. The security of our schemes is based on the computational assumption (over QPT machines) that a class of subset-sum problems is intractable against any QPT machine. Our scheme is very efficient and practical if Shor’s discrete logarithm algorithm is efficiently realized on a quantum machine.
Uncloneable encryption is a cryptographic primitive which encrypts a classical message into a quantum ciphertext, such that two quantum adversaries are limited in their capacity of being able to simultaneously decrypt, given the key and quantum side-information produced from the ciphertext. Since its initial proposal and scheme in the random oracle model by Broadbent and Lord [TQC 2020], uncloneable encryption has developed into an important primitive at the foundation of quantum uncloneability for cryptographic primitives. Despite sustained efforts, however, the question of unconditional uncloneable encryption (and in particular of the simplest case, called an uncloneable bit) has remained elusive. Here, we propose a candidate for the unconditional uncloneable bit problem, and provide strong evidence that the adversary's success probability in the related security game converges quadratically as 1 / 2 + 1 / ( 2 K ) , where K represents the number of keys and 1 / 2 is trivially achievable. We prove this bound's validity for K ranging from 2 to 7 and demonstrate the validity up to K = 17 using computations based on the NPA hierarchy. We furthemore provide compelling heuristic evidence towards the general case. In addition, we prove an asymptotic upper bound of 5 / 8 and give a numerical upper bound of ∼ 0.5980 , which to our knowledge is the best-known value in the unconditional model.
Uncloneable decryptors are encryption schemes (with classical plaintexts and ciphertexts) with the added functionality of deriving uncloneable quantum states, called decryptors, which could be used to decrypt ciphers without knowledge of the secret key (Georgiou and Zhandry, IACR'20). We study uncloneable decryptors in the computational setting and provide increasingly strong security notions which extend the various indistinguishable security notions of symmetric encryption. We show that CPA secure uncloneable bit decryptors could be instantiated from a copy protection scheme (Aaronson, CCC'09) for any balanced binary function. We introduce a new notion of flip detection security for copy protection schemes inspired by the notions of left or right security for encryption schemes, and show that it could be used to instantiate CPA secure uncloneable decryptors for messages of unrestricted length. We then show how to strengthen the CPA security of uncloneable decryptors to CCA2 security using strong EUF-CMA secure digital signatures. We show that our constructions could be instantiated relative to either the quantum oracle used in [Aar09] or the classical oracle used in (Aaronson et al., CRYPTO'21) to instantiate copy protection schemes. Our constructions are the first to achieve CPA or CCA2 security in the symmetric setting.
In this note, we consider the setting of uncloneable encryption satisfying uncloneable indistinguishability, a form of symmetric key encryption that prevents the cloning of ciphertexts in a very strong sense. Our goal is to minimize the assumptions under which (many-time secure) uncloneable encryption is known to exist, assuming the existence of an information-theoretic "uncloneable bit", i.e. a one-time secure uncloneable encryption scheme for one-bit messages. We observe that if a t -> t' uncloneable bit exists, then the following implications hold.
1. If many-time secure symmetric key encryption exists, then many-time secure t -> t' uncloneable encryption for arbitrary-length messages exists. Since many-time secure uncloneable encryption implies many-time secure symmetric key encryption, this result is tight.
2. If pseudorandom unitaries exist, then many-time secure t -> t' uncloneable encryption for arbitrary-length messages with identical copy security exists.
These results together show that many-time secure uncloneable encryption may follow from concrete assumptions in "microcrypt", the world of unstructured quantum cryptography that plausibly exists even if P = NP.
Public-key cryptography is a key technology for making the Internet and other IT infrastructures secure. The security of the established public-key cryptosystems relies on the difficulty of factoring large composite integers or computing discrete logarithms. However, it is unclear whether these computational problems remain intractable in the future. For example, Shor showed in 1994 that quantum computers can be used to factor integers and to compute discrete logarithms in polynomial time. It is therefore necessary to develop alternative public-key cryptosystems which do not rely on the difficulty of factoring or computing discrete logarithms and which are secure even against quantum computer attacks. We call such cryptosystems quantum-immune. To prove the security of these quantum-immune cryptosystems, appropriate security models have to be used. Since quantum computers are able to solve problems in polynomial time which are supposed to be intractable for classical computers, the existing security models are inadequate in the presence of quantum adversaries. Therefore, new security models have to be developed to capture quantum adversaries. Properties of these new security models have to be investigated. On a more practical level, the quantum-immune cryptosystems have to be implemented in a way that they can seamlessly replace established cryptosystems. The implementations have to be efficient and suitable for resource-constrained devices. They must easily integrate into existing public-key infrastructures. This thesis contributes to both the theory and practice of quantum-immune cryptography, addressing the above-mentioned challenges. In the theoretical part, we concentrate on the quantum zero-knowledge property of interactive proof systems. We show for the first time that the quantum statistical, perfect, and computational zero-knowledge properties are preserved under sequential composition of interactive proof systems. In the practical part, we provide implementations of the most important quantum-immune cryptosystems. We present efficiency improvements of some of the alternative cryptosystems. The implementations are very efficient and easily integrate into existing public-key infrastructures. We present comprehensive timings that show that the alternative cryptosystems are competitive or even superior compared to established cryptosystems. Finally, we present a new cryptographic API that is particularly well-suited for resource-constrained devices like mobile phones and PDAs. With this API, the alternative cryptosystems can also be used with these devices.