Abstract
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