A Dynamic Multi-Secret Sharing Scheme with Cheater Detection using Recursive Bivariate Polynomials

Improving the Cheater Identification Capability of Threshold Secret Sharing Schemes

Secret sharing is an important cryptographic primitive by which any confidential information or secret is shared among a group of participants. Only authorized subsets of participants can recover the secret correctly, while unauthorized subsets of participants eventually get no information about the secret. Vulnerabilities arise in a secret sharing scheme due to a single or multiple dishonest participants. A single or multiple participants can collude to cheat by modifying their shares during the reconstruction of the secret. This enables them to recover the secret correctly for themselves by misleading the honest participants. The proposed scheme aims to detect such dishonest activity of the cheating participants and identify them. The detection mechanism utilizes the property of divided difference and identifies cheaters by checking the consistency of the inherent algebraic constraints across multiple subsets of shares arising from the divided difference structure. Further, the scheme does not rely on any cryptographic assumption and achieves an improved bound on the maximum number of identifiable cheaters while maintaining the share size equal to that of the secret. In addition, a lower bound on the minimum number of participants required for successful undetectable cooperative cheating is established.

A Code-Based ( k, n )-Threshold Secret Sharing Scheme with Integrity Verification

Construction of statistically optimal dynamic S-boxes for secure image encryption

Introducing innovative ways to generate dynamic substitution boxes (S-boxes) is essential in achieving the desired diffusion and confusion. One kind of algebraic S-box generators attain these two properties either by fixed degree irreducible polynomials or by an algebraic map, which limits the randomness and security in the resultant output. The other type use total orders to avoid these limitations, making the time complexity nonlinear. In this study, we present an S-box generator that integrates dynamic polynomial with its induced map to generate highly secure and dynamic outputs, and keep the time complexity flexible. The current scheme incorporates a polynomial as an injective mapping to increase its algebraic strength. We present two highly nonlinear S-boxes by the proposed method. To validate the effectiveness of our scheme, we conduct comprehensive comparative analyses regarding construction mechanism and standard cryptographic metrics, confirming the robustness of the proposed method. Statistical analyses are also performed to assess key sensitivity, correlation, fixed points, time and space complexity, ensuring that the scheme meets practical security requirements. Furthermore, we propose an image encryption by employing the generated S-boxes, and the rigorous analysis confirms their applicability in secure multimedia transmissions.

A method for constructing robust multisecret sharing schemes based on polynomial transformations over finite commutative principal ideal rings

This paper is devoted to the development of a method for constructing secret sharing schemes intended for registry management systems of the National Center for Backup of State Information Resources. Such schemes represent cryptographic protocols that enable cryptographic keys to be distributed among multiple participants and stored at different locations or by different participants, while allowing secret reconstruction only for predefined authorized coalitions. Registry management systems of the National Center require unconditionally secure multiple secret sharing schemes characterized by low computational complexity of share generation and secret reconstruction procedures, as well as robustness, i.e., unconditional resistance against attacks by dishonest participants who may substitute their own shares in order to corrupt the reconstructed secrets. Existing constructions of robust secret sharing schemes are mainly based on auxiliary transformations over finite fields and are applicable only to single-secret sharing schemes. The paper proposes a method for constructing robust multisecret sharing schemes based on vector secret sharing schemes for a single secret and polynomial transformations over finite commutative principal ideal rings. The proposed method generalizes a previously known approach for constructing robust secret sharing schemes for vector access structures over finite fields. At the same time, the resulting constructions generalize previously known multiple secret sharing schemes defined over residue rings modulo a natural number. An analytical upper bound on the probability of successful share substitution by participants of an arbitrary forbidden coalition is obtained, and conditions are established under which this probability can be made arbitrarily small. The proposed method can be applied to the construction of cryptographic protocols for distributed storage and processing of confidential information with enhanced resistance against dishonest participants, as well as to access control systems, distributed information systems, and collaborative data storage services requiring guaranteed integrity and correctness of secret reconstruction.

A Communication-Reduced Privacy-Preserving ViT Inference Framework for Distributed Edge Intelligence

SVIiT is described as communication-reduced relative to the evaluated MPC baselines rather than universally lightweight, and its present practical scope is primarily high-bandwidth LAN or provider-edge deployments.

A Maliciously Secure and Fully Decentralized Threshold FHE Scheme with Native RNS Acceleration

: Threshold fully homomorphic (ThFHE) encryption, as a communication encryption protocol, ensures that no third party participates in generating or knows any parameters. Compared to multi-key fully homomorphic encryption, it avoids excessive noise expansion caused by too many users participating in the calculation. However, current ThFHE algorithms focus on reducing computational overhead, thereby neglecting integrity verification of participating nodes’ behavior in distributed collaborative environments, leaving the system vulnerable to malicious actors. Without an effective verification mechanism, malicious nodes can manipulate the final result without breaking the protocol flow by injecting biased noise or providing forged partial decryption values, compromising data integrity. This research proposes an enhanced ThFHE encryption scheme based on a Full Remainder System (Full-RNS) architecture. This scheme integrates Distributed Key Generation (DKG) and Multi-Party Computation Relinearized Key (MPC RLK) techniques to achieve fully decentralized parameter initialization. To combat malicious attacks, we introduce a Non-Interactive Zero-Knowledge (NIZK) proof that incorporates smudging noise, ensuring that the computational trajectory at each stage can be publicly verified without leaking private key information. The results of the experiment show that this scheme maintains efficient homomorphic computation of the BFV algorithm while effectively resisting node fraud, providing more robust security for voting systems and medical privacy computations.