MerkleLamport signatures Signatures from any oneway function - PowerPoint PPT Presentation
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MerkleLamport signatures Signatures from any oneway function
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The red parts are given out to sign green is public key. How ... A 'casual' approach requires O(n) work to compute a node, where n is the number of leaves... – PowerPoint PPT presentation
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Title: MerkleLamport signatures Signatures from any oneway function
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Merkle/Lamport signaturesSignatures from any
one-way function
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Recall What functions are hard?
DES/AES Stream ciphers Hash functions
RSA Factorization Discrete log
Speed action
Graphs
Size representation
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Public key
Called Lamport signature Problem uses up
public key!
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Avoid using up public key
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Avoid using up public key
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Avoid using up public key
Longer longer!
A Merkle signature
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Merkle signatures with a tree
The red parts are given out to sign green is
public key
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How is a signature verified?
Pair-wise hashing compare root with known value
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Avoiding birthday attacks
The input to each hash step is a counter and an
identifier
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Are all values stored?
- We can generate leaf values on the fly by
making the secret keys of these be outputs of a
Pseudo Random Generator that takes as input the
leaf position, the secret key index, and a secret
seed. - (But the interior nodes cannot be generated like
this.)
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How to maintain the tree?
- You can store it all (thats a lot of storage!)
- You can compute the nodes you want when you want
them (thats a lot of work!) - You can amortize the computation by storing a
part and computing a little each time. (JLMS, S)
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Goal and Metrics
- Output sequence of (leaf preimage,
authentication path) - Metrics minimize computation and storage
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Why is this difficult?
- The value of each interior node depends on all
its descendants - A casual approach requires O(n) work to compute
a node, where n is the number of leaves - or needs O(n) values to be stored
- We want to reduce both to poly-logarithmic!
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Static view of storage
Blue areas contain pebbles, storing the tree
values.
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Dynamic view of storage
- Existing subtrees in blue, desired subtrees in
grey
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Computation of desired subtrees
Blue pebbles where filled, tail hanging below.
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Three phases
- Key generation (other computer ok)
- Output (by weak computer)
- Verification (traditional)
- For a description of the algorithm, see paper.
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