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

Area of Science:

• Cryptography
• E-commerce Security
• Network Coding

Background:

• Increasing electronic transaction data volume necessitates real-time processing, driving adoption of network coding.
• Existing homomorphic signatures ensure data integrity but are vulnerable to malicious exploitation of intermediate signatures, causing bandwidth issues and hindering verification.
• Critical security issues like forgery and data leakage were overlooked in early network coding implementations.

Purpose of the Study:

• To address malicious combinations in homomorphic signatures by introducing a secret-sharing layer using the Chinese Remainder Theorem (CRT).
• To formally define an identity-based linear homomorphic signature for a restricted combiners' group (IBLHS-RCG).
• To develop a specialized e-commerce security scheme for IBLHS-RCG.

Main Methods:

• Applying the Chinese Remainder Theorem (CRT) for secret-sharing to restrict access to authorized users.
• Integrating linear homomorphic signatures with CRT for the IBLHS-RCG framework.
• Developing and demonstrating an unforgeable scheme against adaptive chosen-message attacks.

Main Results:

• The proposed scheme effectively restricts access to authorized users, mitigating malicious combinations.
• The developed IBLHS-RCG scheme is proven unforgeable against adaptive chosen-message attacks.
• Simulations using the Python Pairing-based Cryptography Library (PYPBC) indicate low signing and verification costs.

Conclusions:

• The novel IBLHS-RCG scheme enhances e-commerce security by combining homomorphic signatures with CRT-based secret-sharing.
• The scheme provides robust protection against data forgery and leakage while maintaining efficiency.
• This approach offers a secure and practical solution for real-time electronic transactions.