Identity-based linear homomorphic signature for a restricted combiners' group for e-commerce

As the volume of electronic transaction data increases and the demand for real-time processing grows, network coding techniques have become popular for improving performance. However, early implementations often overlooked critical data security issues, such as forgery and data leakage. While existing homomorphic signature schemes effectively ensure data integrity, they can unintentionally allow malicious actors to exploit intermediate signatures. This misuse can lead to unnecessary bandwidth consumption and hinder the verification processes for legitimate users. To address the problem of malicious combinations, we apply the Chinese Remainder theorem (CRT) to establish a layer of secret-sharing that restricts access to authorized users in conjunction with homomorphic signatures. Furthermore, we introduce a formal definition for an identity-based linear homomorphic signature for a restricted combiners' group (IBLHS-RCG). This framework integrates linear homomorphic signatures with the CRT within the context of e-commerce, enabling us to develop a specialized scheme for IBLHS-RCG. We demonstrate that our scheme is unforgeable against adaptive chosen-message attacks. Additionally, simulations conducted using the Python Pairing-based Cryptography Library (PYPBC) show that the signing and verification costs of our approach are low.