Identify the Intended Covert Value Among an Adversary in a (t, n) Threshold Setup

In safeguarding daily communications over open networks, ensuring data confidentiality is paramount to prevent sensitive information from reaching unintended recipients. Secret sharing techniques facilitate secure private key exchanges for data transmission over public networks. This paper introduces a two-phase protocol that allows honest participants to detect and counter malicious activities by reconstructing the intended covert value, even in presence of an unknown adversary who is one of the legitimate participants. A trusted Dealer, in a (t, n) threshold setup, generates and distributes shares using a randomly derived polynomial. Polynomial reconstruction is incorporated to help retrieve the original secret securely. The proposed methods employ hash-based mechanisms to ensure information security and integrity, with the second approach introducing additional randomness to enhance protection against insider attacks. Comprehensive security analysis underscores the protocol's resilience, demonstrating its effectiveness in maintaining confidentiality.