The Secure Sockets Layer (SSL) is the main protocol used to secure Internet traffic and cloud computing. It relies on the computation-intensive RSA cryptography, which primarily limits the throughput of the handshake process. In this paper, we design and implement an OpenSSL library, termed PhiOpenSSL, which targets the Intel Xeon Phi (KNC) coprocessor, and utilizes Intel Phi's SIMD and multi-threading capability to reduce the SSL computation latency. In particular, PhiOpenSSL vectorizes all big integer multiplications and Montgomery operations involved in RSA calculations and employs theChinese Remainder Theorem and fixed-window exponentiation in its customized library. In an experiment involving the computation of Montgomery exponentiation, PhiOpenSSL was as much as 15.3 times faster than the two other reference libcrypto libraries, one from the Intel Many-core Platform Software Stack (MPSS) and the other from the default OpenSSL. Our RSA private key cryptography routines in PhiOpenSSL are 1.6-5.7 times faster than those in these two reference systems.