Security-mediated cryptography was first introduced by Boneh et al. in 2001. The main motivation behind security-mediated cryptography was the capability to allow instant revocation of a user's secret key by necessitating the cooperation of a security mediator in any given transaction. Subsequently in 2003, Boneh et al. showed how to convert a RSA-based security-mediated encryption scheme from a traditional public key setting to an identity-based one, where certificates would no longer be required. Following these two pioneering papers, other cryptographic primitives that utilize a security-mediated approach began to surface. However, the security-mediated identity-based identification scheme (SM-IBI) was not introduced until Chin et al. in 2013 with a scheme built on bilinear pairings. In this paper, we improve on the efficiency results for SM-IBI schemes by proposing two schemes that are pairing-free and are based on well-studied complexity assumptions: the RSA and discrete logarithm assumptions.