Key Generation
The Merkle Signature Scheme can only be used to sign a limited number of messages with one public key . The number of possible messages must be a power of two, so that we denote the possible number of messages as .
The first step of generating the public key is to generate the public keys and private keys of one-time signatures. For each public key, with, a hash value is computed. With these hash values a hash tree is built.
We call a node of the tree, where denotes the level of the node. The level of a node is defined by the distance from the node to a leaf. Hence, a leaf of the tree has level and the root has level . We number all nodes of one level from the left to the right, so that is the leftmost node of level .
In the Merkle Tree the hash values are the leaves of a binary tree, so that . Each inner node of the tree is the hash value of the concatenation of its two children. So and .
In this way, a tree with leaves and nodes is built. The root of the tree is the public key of the Merkle Signature Scheme.
Read more about this topic: Merkle Signature Scheme
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