EHDSA: Elliptic Curve-Based Homomorphic Digital Signature Algorithm with Isomorphic Message

Elliptic curve-based cryptographic systems have established themselves as fundamental components of modern cryptography, providing both efficiency and security guarantees. In this paper, we propose EHDSA (Elliptic Curve Homomorphic Digital Signature Algorithm), which addresses the privacy limitations inherent in classical ECDSA by introducing a novel isomorphism ϕ from the elliptic curve group E(Fp) to the integer ring Zn. Our approach utilizes a secret parameter t ∈ Zn∗ to define a scalar mapping that effectively obfuscates ephemeral public key components while maintaining the algebraic and homomorphic properties essential for signature verification. This transformation provides enhanced unlinkability and signature indistinguishability while preserving the computational efficiency of ECDSA. We provide formal security proofs under standard cryptographic assumptions, demonstrate correctness, and analyze computational complexity, showing that EHDSA achieves security levels equivalent to ECDSA with minimal computational overhead.