Integrated Sensing and Communication (ISAC) has been identified as a promising candidate for 6th Generation networks. However, one of the key challenges with ISAC systems is the potential for communication information to be intercepted by malicious sensing targets, which raises concerns about the security of the transmitted data. In this context, the concept of Reconfigurable Intelligent Surfaces (RIS) offers a novel solution, as it can dynamically manipulate the wireless environment, thereby assisting in improving the physical layer security of ISAC systems. This study focuses on the RIS-assisted ISAC system, which is responsible for both communicating with several legitimate users and detecting various malicious sensing targets. Maximizing the sum secrecy rate of the system is achieved through the optimization of both the transmitting beamforming matrix at the base station (BS) and the phase shift matrix of the RIS, subject to constraints on the gain of the sensing beampattern, the attainable sum-rate for communication users, power restrictions of BS, and the reflection coefficients of the RIS. To effectively address this intricate optimization task, an alternating optimization method is applied, which integrates semi-definite relaxation with successive convex approximation techniques. The results from simulations demonstrate that the approach based on RIS significantly enhances security performance in comparison to random RIS scheme and without RIS scheme.