This paper addresses a critical trade-off in modern digital security: the lack of auditable data transit in standard, secure-by-design elliptic curve cryptography (ECC) primitives. While widely adopted commercial standards, such as NIST P-256 and Curve25519, exhibit high performance and robust privacy, their mathematical opacity prevents legitimate data monitoring without exposing the long-term private keys of the end-to-end communication nodes. To resolve this issue, we evaluate the feasibility of a malleable, trapdoored Naccache-Stern-type elliptic curve scheme defined over the ring Zn. By configuring a smooth group order, an authorized auditor holding the factorization of the modulus can bypass the Elliptic Curve Discrete Logarithm Problem (ECDLP) using a local Pohlig-Hellman reduction. We present a custom implementation in Python and perform a comparative analysis between the auditable Naccache-Stern setup and standard opaque curves in terms of computation time, memory payload, and theoretical security. Furthermore, we assess the vulnerability of these primitives in the post-quantum era by simulating Shor’s period-finding algorithm on noisy simulators and executing it on real 156-qubit physical IBM Quantum hardware (ibm marrakesh), analyzing how NISQ physical noise degrades quantum fidelity.