The deployment of integrated sensing and communication (ISAC) brings along unprecedented vulnerabilities to authorized sensing, necessitating the development of secure solutions. Sensing parameters are embedded within the target-reflected signal leaked to unauthorized passive radar sensing eavesdroppers (Eve), implying that they can silently extract sensory information without prior knowledge of the information data. To overcome this limitation, we propose a sensing-secure ISAC framework that ensures secure target detection and estimation for the legitimate system, while obfuscating unauthorized sensing without requiring any prior knowledge of Eve. By introducing artificial imperfections into the ambiguity function (AF) of ISAC signals, we introduce artificial targets into Eve's range profile which increase its range estimation ambiguity. In contrast, the legitimate sensing receiver (Alice) can suppress these AF artifacts using mismatched filtering, albeit at the expense of signal-to-noise ratio (SNR) loss. Employing an OFDM signal, a structured subcarrier power allocation scheme is designed to shape the secure autocorrelation function (ACF), inserting periodic peaks to mislead Eve's range estimation and degrade target detection performance. To quantify the sensing security, we introduce peak sidelobe level (PSL) and integrated sidelobe level (ISL) as key performance metrics. Then, we analyze the three-way trade-offs between communication, legitimate sensing, and sensing security, highlighting the impact of the proposed sensing-secure ISAC signaling on system performance. We formulate a convex optimization problem to maximize ISAC performance while guaranteeing a certain sensing security level. Numerical results validate the effectiveness of the proposed sensing-secure ISAC signaling, demonstrating its ability to degrade Eve's target estimation while preserving Alice's performance.