A Quantum Evolving Secret Sharing Scheme

Shion Samadder Chaudhury

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.

Xu Shengwei

Shion Samadder Chaudhury, Sayantan Ganguly

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.

Ting-Ting Xu, Zhihui Li, Chen‐Ming Bai +1 more

Arpita Maitra, Goutam Paul

Kittiphop Phalakarn

Nowadays, computation becomes more advanced, and may require more than one parties to participate.Some examples include e-voting system and privacy-preserving data analytics.One of the main concerns here is privacy.Inputs of these systems must be kept secret.To address this concern, we can construct the systems by using secure multi-party protocols, where several parties with their secret inputs perform joint computations in oblivious ways.Many aspects of the protocols can be further improved towards the usage in reallife applications, considering operational requirements and trade-offs.These operational requirements include efficiency, functionality, security, scalability, and verifiability.This thesis consists of three parts; each part focuses on specific improvements.In the first part, we focus on improving security and efficiency.We consider a homomorphic secret sharing scheme, where a secret input from each party is divided into several shares, each share is sent to different computing server, and the servers can perform some computation locally to get shares of the result.It is obvious that homomorphic secret sharing schemes can be used as secure multi-party protocols with small communication.We found that the existing homomorphic secret sharing scheme with public key of Lai et al. (Asiacrypt 2018) is 1-secure, which means if more than one computing servers try to collude, the security of the system will be compromised.They also proposed a t-secure scheme, but it requires solving NP-hard problem.To improve their security level, we use the idea from the secret sharing scheme of Ito et al.Our scheme also supports any number of computing servers without solving NP-hard problem.Using hyper-graph representation of non-access structures, we prove the maximum polynomial degree that our scheme can support.In addition, we prove correctness and security of the scheme, and propose some possible further improvements.In the second part, we focus on improving scalability and efficiency.Most of the secret sharing schemes, including homomorphic secret sharing, require the number of parties to be fixed in advance.This causes an inconvenience if we want to add more parties later in order to change the security setting or improve availability of the system.One existing variant of secret sharing, called evolving secret sharing, allows any number of parties to join the system at any time.However, it is inefficient to perform computation on this kind of secret sharing.To address this problem, we propose the definition of evolving homomorphic secret sharing, which combines evolving and homomorphic properties together.The scheme iii then supports unbounded number of parties, and allows local computation on shares.In addition to the definition, we propose two concrete schemes.The first scheme realizes evolving disjunctive hierarchical access structure supporting multiplication.The second scheme realizes evolving partially disjunctive hierarchical access structure supporting lowdegree polynomial computation.In the third part, we focus on improving functionality, verifiability, and efficiency.We consider the problem of oblivious deterministic finite automata (DFA) evaluation protocol.In this problem, one party holds a secret string, and the other party holds a secret pattern.The goal of this protocol is to output whether the string matches with the pattern of not without revealing both secret inputs.Most of the existing protocols use several communication rounds and require public key primitives, which can be inefficient.As our contribution, we propose an oblivious conditional disclosure of secrets (CDS) scheme for DFA.It is the first CDS scheme that has a functionality of DFA evaluation.We then use the proposed oblivious CDS scheme as a building block to construct an oblivious DFA evaluation protocol, using a multi-client verifiable computation framework.As a result, our protocol is constant-round, verifiable, and does not require any public key primitives.We also propose a standard CDS scheme for DFA as an independent interest.This thesis is expected to be a step of secure multi-party protocols and secret sharing schemes enhancements towards real-life applications.High level ideas for more improvements are also suggested as future prospects.