In this paper, a data structure to enhance remote authentication is proposed generalizing the concept of ISO/IEC 24761. Current technologies do not provide sufficient information on products which are used in the authentication process at the Claimant to the Verifier. As a result, the Verifier cannot sufficiently distinguish the authentication result executed with a trusted product from that without a trusted product. The difference is made clear if an evidence data of the execution of authentication process at the Claimant is generated by the trusted product and used for verification by the Verifier. Data structure for such a data is proposed in this paper as client Authentication Context (cAC) instance. Relation to other works and extension of the proposal are also described for further improvement of remote authentication. For this proposal to realize, standardization activities are to be taken as the next steps.