Process for establishing a common cryptographic key for N subscribers
View Patent ↗A process is described which can be used to generate a cryptographic key for a group of subscribers whose number is subject to change. The process can further provide that even after the group key has been established, subscribers can be removed from or added to the key directory without great effort.
1. A process for secret transmission of a message by establishing a common cryptographic key for n subscribers using the Diffie-Hellman process, as recited in comprising:
assigning the n subscribers respective leaves of a binary-structured tree which has a root, n leaves, is of depth [log 2n] and has tree nodes;
for each one of the n subscribers, generating a respective secret, the respective secret being assigned to each one of the n leaves to which the one of the n subscribers is assigned; and
establishing secrets consecutively in a direction of the root of said tree for all k nodes of said tree starting from the n leaves of said tree across an entire hierarchy of said tree, wherein two already known secrets are combined using the Diffie-Hellman process to form a new common secret, the new common secret being allocated to a common node so that the common cryptographic key for all n subscribers is allocated to a last one of tree nodes, the last one of the tree nodes being the root of said tree;
adding a new subscriber to the n subscribers of said tree so that there are n+1 subscribers of said tree, the adding step including:
adding two new leaves as successors to a selected one of the n leaves of said tree so that a new binary-structure tree has n+1 leaves and is of depth [log 2(n+1)];
assigning the one of the n subscribers to whom the selected one of the n leaves is assigned one of the two new leaves and assigning the new subscriber to another one of the two new leaves, the selected one of the n leaves becoming the common node for the two new leaves; and
starting from the new leaves in the direction of the root of said tree, establishing new secrets only in those of the tree nodes which lie within a framework of said tree on a path from the two new leaves to the root of said tree.
2. A method of transmitting a message to a location, comprising:
establishing a common cryptographic key for n subscribers using Diffie-Hellman process;
encrypting the message with the common cryptographic key;
transmitting the encrypted message to the location,
wherein, the establishing the common cryptographic key includes:
assigning the n subscribers respective leaves of a binary-structured tree which has a root, n leaves, is of depth [log 2n] and has tree nodes;
for each one of the n subscribers, generating a respective secret, the respective secret being assigned to each one of the n leaves to which the one of the n subscribers is assigned; and
establishing secrets consecutively in a direction of the root of said tree for all k nodes of said tree starting from the n leaves of said tree across an entire hierarchy of said tree, wherein two already known secrets are combined using the Diffie-Hellman process to form a new common secret, the new common secret being allocated to a common node so that the common cryptographic key for all n subscribers is allocated to a last one of tree nodes, the last one of the tree nodes being the root of said tree;
adding a new subscriber to the n subscribers of said tree so that there are n+1 subscribers of said tree, the adding step including:
adding two new leaves as successors to a selected one of the n leaves of said tree so that a new binary-structure tree has n+1 leaves and is of depth [log 2(n+1)];
assigning the one of the n subscribers to whom the selected one of the n leaves is assigned one of the two new leaves and assigning the new subscriber to another one of the two new leaves, the selected one of the n leaves becoming the common node for the two new leaves; and
starting from the new leaves in the direction of the root of said tree, establishing new secrets only in those of the tree nodes which lie within a framework of said tree on a path from the two new leaves to the root of said tree.
3. The method as recited in claim 2 , further comprising:
excluding a selected one of the n subscribers from said tree, the excluding steps including:
removing a first one of the n leaves of said tree to which the selected one of the n subscribers is assigned;
removing a second one of the n leaves, the second one of the n leaves sharing a common node with the first one of the n leaves, the common node with the first one of the n leaves becoming a new leaf assigned to the one of the n subscribers to which the second one of the n leaves is assigned; and
starting from the new leaf of said tree in the direction of the root of said tree, establishing new secrets only in those of the tree nodes which lie within a framework of said tree on a path from the new leaf to the root of said tree.