A quantum secret sharing scheme is a method to share a quantum secret among participants in such a way that only certain specified subsets of the set of participants can combine to recover the secret. A quantum evolving secret sharing scheme is a recently introduced variant of secret sharing schemes where the sets of participants is not fixed and an unbounded and unspecified number of participants arrive one by one with time. The number of participants can be potentially infinite and and a quantum secret is shared and protected among the participants. The existing construction has some major drawbacks such as 1) the exponential quantum memory requirement and 2) the very high dimensions of the shares which makes the scheme difficult to implement. In this paper we overcome these drawbacks by constructing a scheme which uses quantum memory linear in the number of participants and significantly improves on the dimensions of the shares of the participants. This construction uses quantum secret redistribution and trap codes. The construction is flexible and can be modified to different types of access structures(subsets of participants which can recover the secret). Certain ramp properties can also be incorporated in the scheme.
A quantum secret sharing scheme is a method to share a quantum secret among participants in such a way that only certain specified subsets of the set of participants can combine to recover the secret. A quantum evolving secret sharing scheme is a recently introduced variant of secret sharing schemes where the sets of participants is not fixed and an unbounded and unspecified number of participants arrive one by one with time. The number of participants can be potentially infinite and and a quantum secret is shared and protected among the participants. The existing construction has some major drawbacks such as 1) the exponential quantum memory requirement and 2) the very high dimensions of the shares which makes the scheme difficult to implement. In this paper we overcome these drawbacks by constructing a scheme which uses quantum memory linear in the number of participants and significantly improves on the dimensions of the shares of the participants. This construction uses quantum secret redistribution and trap codes. The construction is flexible and can be modified to different types of access structures(subsets of participants which can recover the secret). Certain ramp properties can also be incorporated in the scheme.
We propose the concept ofQuantum Anamorphic Evolving Secret-Sharing(QAESS), combining two different cryptographic primitives in this paper. In QAESS, we have theanamorphic property, allowing alternate secrets to be embedded within the primary secret-sharing framework, accessible only under specific constraints, and theevolvingproperty ofsecret-sharing(ESS) where the scheme can dynamically adapt by accommodating potentially an infinite number of new parties without reinitialization. To achieve this, the major hurdles we encounter are 1) the large dimensions of shares and the requirement of huge quantum memory, and 2) the system breakdown by inserting a spy. In our first construction, we present a QAESS scheme, and in the second construction, we use secret redistribution to mitigate the above challenges. Our constructions extensively use quantum trap codes, random permutations, and data structure techniques. We analyze the schemes’ efficiency, scalability, and robustness through theoretical proofs and complexity estimates. This integration of quantum anamorphism and evolving properties finds potential application in several Internet of Things (IoT) and other practical scenarios. We close the paper by discussing several advantages of our constructions and some interesting problems for further study.
Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties in such a way that certain authorized subsets can reconstruct the secret, while unauthorized subsets obtain no information about it. Previous works on QSS for general access structures focused solely on the existence of perfectly secure schemes, and the share size of the known schemes is necessarily exponential even in cases where the access structure is computed by polynomial size monotone circuits. This stands in stark contrast to the classical setting, where polynomial-time computationally-secure secret sharing schemes have been long known for all access structures computed by polynomial-size monotone circuits under standard hardness assumptions, and one can even obtain shares which are much shorter than the secret (which is impossible with perfect security). While QSS was introduced over twenty years ago, previous works only considered information-theoretic privacy. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes, just as in the classical case. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time computationally-secure QSS schemes under standard hardness assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS necessarily required exponential share size. In fact, we can go even further: We construct QSS schemes for which the size of the quantum shares is significantly smaller than the size of the secret. As in the classical setting, this is impossible with perfect security. We also apply our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of n-party access structures to 1.5^{n+o(n)}, improving upon best known schemes and matching the best known result for general access structures in the classical setting. Finally, among other things, we study the class of access structures which can be efficiently implemented when the quantum secret sharing scheme has access to a given number of copies of the secret, including all such functions in 𝖯 and NP.
Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties so that certain subsets can reconstruct the secret, while unauthorized subsets obtain no information. While QSS was introduced over twenty years ago, previous works focused only on existence of perfectly secure schemes, and the share size of the known schemes is exponential even for access structures computed by polynomial size monotone circuits. This stands in contrast to the classical case, where efficient computationally-secure schemes have been long known for all access structures in monotoneP, and one can even obtain shares which are much shorter than the secret which is impossible with perfect security. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time QSS schemes under standard assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS required exponential share size. We also construct QSS schemes for which the size of the shares is significantly smaller than the size of the secret. As in the classical case, this is impossible with perfect security. We also use our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of access structures to 1.5n+o(n), improving upon best known schemes and matching the best known result for general access structures in the classical case. Finally, we show construct efficient schemes for all access structures in P and NP when the quantum secret sharing scheme is given multiple of copies of the secret.
Quantum secret sharing is an important branch of quantum cryptography, and secure multi-party quantum key distribution protocols can be constructed using quantum secret sharing. In this paper, we construct a quantum secret sharing scheme built on a constrained (t, n ) threshold access structure, where n is the number of participants and t is the threshold number of participants and the distributor. Participants from two different sets perform the corresponding phase shift operations on two particles in the GHZ state passed to them, and then t−1 participants with the distributor can recover the key, where the participant recovering the key measures the particles received by himself and finally obtains the key through the collaboration of the distributors. Security analysis shows that this protocol can be resistant to direct measurement attacks, interception retransmission attacks, and entanglement measurement attacks. This protocol is more secure, flexible, and efficient compared with similar existing protocols, which can save more quantum resources.
A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a collection of secret recovery functions.The study of schemes using arbitrary probability spaces and unbounded number of participants allows us to investigate their abstract properties, to connect the topic to other branches of mathematics, and to discover new design paradigms.A scheme is perfect if unqualified subsets have no information on the secret, that is, their total share is independent of the secret.By relaxing this security requirement, three other scheme types are defined.Our first result is that every (infinite) access structure can be realized by a perfect scheme where the recovery functions are non-measurable.The construction is based on a paradoxical pair of independent random variables which determine each other.Restricting the recovery functions to be measurable ones, we give a complete characterization of access structures realizable by each type of the schemes.In addition, either a vector-space or a Hilbert-space based scheme is constructed realizing the access structure.While the former one uses the traditional uniform distributions, the latter one uses Gaussian distributions, leading to a new design paradigm.
Quantum secret sharing (QSS) is a process in which the state of a quantum system is partitioned into multiple shares, allowing only specific subsets of shareholders to reconstruct the state, while others gain no information about its identity. In this work, we propose a variant of QSS, called ``helper QSS,'' which designates a special shareholder whose participation with any other group of parties is sufficient for recovering the state. We present different families of helper codes that function for an arbitrary number of parties and system sizes. As an application, we introduce the idea of a programmable access structure in QSS, which allows for a third-party programmer to independently choose the access structure of the code even after the shares are delivered to all the shareholders. This choice is made blindly, meaning that the programmer has no information about the secret being encoded, and it is implemented using the nonlocal process of quantum steering.