ElGamal-based single round threshold signatures for adaptive configuration

Threshold signature schemes are essential for secure and fault-tolerant distributed systems, allowing a group of participants to collectively generate a digital signature such that any subset of at least t out of n signers can produce a valid signature, while smaller subsets learn nothing. In this work, we propose a novel threshold signature scheme based on the ElGamal cryptosystem. Unlike conventional threshold schemes that distribute shares of a single signing key, the proposed approach allows each participant to retain an independent key pair. Individual public keys are aggregated into a unified public key, enhancing efficiency and scalability and enabling the corresponding signature shares to be combined into a single compact signature, thereby reducing communication overhead and simplifying key management. Additionally, the scheme employs a smart signer selection mechanism, SmartSelectNode, which dynamically determines the next participant in the signing process based on contextual factors such as energy availability or proximity, ensuring efficient and balanced resource utilization in distributed settings. Our scheme supports adaptive threshold configuration, allowing flexible t-of-n settings without modifying the protocol, and achieves single-round signing to minimize interaction overhead. We present a formal description of the protocol, prove its correctness and unforgeability, and evaluate its performance compared to existing threshold signature schemes.