A system and method for establishing a secure communication agreement between an initiating unit 102 and a responding unit 104 through a channel 106 are provided. The method includes generating, using first set of local random numbers, multi-dimensional matrices by an initiating unit. The method includes computing a transcript by the initiating unit based on multi-dimensional matrices and communicating to the responding unit. The method includes determining response by selecting a subset of the transcript to communicate response to the initiating unit. The method includes iteratively generating, communicating a subsequent transcript and waiting for a subsequent response from the responding unit for one or more times. The method includes computing a secret key as a function of the first set of local random numbers, the second set of local numbers, the subsequent transcripts, the subsequent responses at each iteration, and the indices of the selected subset J.