A method and system is provided for implementing a multilateral authorization quorum in a computer network. The authorization quorum comprises a total number of stakeholders out of which a threshold number of stakeholders can provide a multilateral authorization. To implement this multilateral authorization quorum, one or more access sets is first determined, each containing the threshold number of stakeholders. Since the stakeholders split a quorum private key, the shares of the quorum private key for each stakeholder in all access sets are determined. The shares of the private key held by the stakeholders in any one access set add up to a number directly related to the private key. One or more secret keys of the stakeholders are further determined for each access set. One or more polynomials for the access sets are then generated by using the shares of the private key and the secret keys thereof, wherein the private key is thus split among the stakeholders of the multilateral authorization quorum. Such a multilateral authorization quorum is ready to be used for making approvals for predetermined transactions.