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
Famous quotes containing the words key and/or generation:
“‘The key is in the window, the key is in the sunlight at the
window—I have the key—Get married Allen don’t take drugs—the key is in the bars, in the sunlight in the window.
Love,
your mother’”
—Allen Ginsberg (b. 1926)
“Through centuries he lived in poverty.
God only was his only elegance.
Then generation by generation he grew
Stronger and freer, a little better off.
He lived each life because, if it was bad,
He said a good life would be possible.”
—Wallace Stevens (1879–1955)