The Stream Control Transport Protocol (SCTP) is a new transport layer protocol that has been designed to provide reliable transport over the Internet. While the Transport Control Protocol (TCP) is the most popular transport protocol for the Internet, it falls short with regard to security, more specifically resilience to Denial-of-Service (DoS) attacks, such as SYN attacks. The need for resilience to DoS attacks is obvious, and SCTP provides for this resilience via its improved handshake mechanism and the Cookie feature. This paper discusses the SCTP simulation with particular emphasis on resilience to DoS attacks. As revealed by our detailed simulation study, the increased DoS resilience comes with increased overheads. While DoS resilience is extremely critical, reducing overheads in the resource-constrained wireless environment also assumes paramount importance. Hence we propose secure SCTP with an innovative Cookie mechanism using a combination of cache and INIT packet repetition to minimize the communication overhead and simultaneously to maximize security associated with SCTP's DoS resilience for wireless Internet.