Signature Generation
To sign a message with the Merkle Signature Scheme, the message is signed with a one-time signature scheme, resulting in a signature, first. This is done, by using one of the public and private key pairs .
The corresponding leaf of the hash tree to a one-time public key is . We call the path in the hash tree from to the root . The path consists of nodes, with being the leaf and being the root of the tree. To compute this path, we need every child of the nodes . We know that is a child of . To calculate the next node of the path, we need to know both children of . So we need the brother node of . We call this node, so that . Hence, nodes are needed, to compute every node of the path . We now calculate and save these nodes .
These nodes, plus the one-time signature of is the signature of the Merkle Signature Scheme. An example of an authentication path is illustrated in the figure on the right.
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