Related papers: Quantum Money from Abelian Group Actions
We present a new idea for a class of public key quantum money protocols where the bills are joint eigenstates of systems of commuting unitary operators. We show that this system is secure against black box attacks, and propose an…
Quantum money is the cryptographic application of the quantum no-cloning theorem. It has recently been instantiated by Montgomery and Sharif (Asiacrypt '24) from class group actions on elliptic curves. In this work, we propose a concrete…
We prove the security of quantum key distribution against the most general attacks which can be performed on the channel, by an eavesdropper who has unlimited computation abilities, and the full power allowed by the rules of classical and…
Forty years ago, Wiesner pointed out that quantum mechanics raises the striking possibility of money that cannot be counterfeited according to the laws of physics. We propose the first quantum money scheme that is (1) public-key, meaning…
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…
The construction of public key quantum money based on standard cryptographic assumptions is a longstanding open question. Here we introduce franchised quantum money, an alternative form of quantum money that is easier to construct.…
In a previous publication, we showed how group actions can be used to generate Bell inequalities. The group action yields a set of measurement probabilities whose sum is the basic element in the inequality. The sum has an upper bound if the…
Property testing has been extensively studied and its target is to determine whether a given object satisfies a certain property or it is far from the property. In this paper, we construct an efficient quantum algorithm which tests if a…
An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…
We propose a public-key quantum money scheme based on group actions and the Hartley transform. Our scheme adapts the quantum money scheme of Zhandry (2024), replacing the Fourier transform with the Hartley transform. This substitution…
A general mathematical framework for quantum key distribution based on the concepts of quantum channel and Turing machine is suggested. The security for its special case is proved. The assumption is that the adversary can perform only…
In this work we present a publicly verifiable quantum money protocol which assumes close to no quantum computational capabilities. We rely on one-time memories which in turn can be built from quantum conjugate coding and hardware-based…
The advent of large-scale quantum computers implies that our existing public-key cryptography infrastructure has become insecure. That means that the privacy of many mobile applications involving dynamic peer groups, such as multicast…
In this paper we consider a generalization of quantum hash functions for arbitrary groups. We show that quantum hash function exists for arbitrary abelian group. We construct a set of "good" automorphisms --- a key component of quantum hash…
Research on quantum technology spans multiple disciplines: physics, computer science, engineering, and mathematics. The objective of this manuscript is to provide an accessible introduction to this emerging field for economists that is…
Quantum networks connect and supply a large number of nodes with multi-party quantum resources for secure communication, networked quantum computing and distributed sensing. As these networks grow in size, certification tools will be…
Standard quantum key distribution protocols are provably secure against eavesdropping attacks, if quantum theory is correct. It is theoretically interesting to know if we need to assume the validity of quantum theory to prove the security…
Quantum key distribution allows two parties, traditionally known as Alice and Bob, to establish a secure random cryptographic key if, firstly, they have access to a quantum communication channel, and secondly, they can exchange classical…
A generalization of the original Diffie-Hellman key exchange in $(\Z/p\Z)^*$ found a new depth when Miller and Koblitz suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further…
Publicly-verifiable quantum money has been a central and challenging goal in quantum cryptography. To this day, no constructions exist based on standard assumptions. In this study, we propose an alternative notion called quantum cheques…