RSA cryptography provides key functions for signing/verifying digital signatures and encrypting/decrypting shared secrets, and is broadly deployed to ensure secure end-to-end communications nowadays. However, the adoption of RSA-enabled applications is fairly limited mainly due to the large computation overheads, in particular, of cryptographic operations with the RSA private key. In this paper, we design and implement sRSA, a high speed RSA on the new Intel® Many Integrated Core (MIC) architecture. We introduce several optimization strategies to sRSA for the MIC architecture without jeopardizing the security level. For example, 1) sRSA explicitly and efficiently vectorizes the underlying cryptographic primitives with the 512-bit vector registers; 2) It also integrates the advanced algorithmic features of fast RSA variants and many other fine-grained implementations; 3) It is thoroughly designed to resist applicable RSA system attacks, i.e., the factoring attacks and the CRT exponent attack. In the end, we evaluate the performance of sRSA and compare it with the industry-standard OpenSSL. The benchmark result shows that sRSA retains a comparable latency with, but demonstrates a much higher throughput than OpenSSL on both CPU and MIC based Phi coprocessor.