Matematicka Analiza Merkle 19pdf Top __hot__ -

Thus, Merkle trees achieve (information-theoretically optimal) proof size up to constant factors. 4. Security Analysis: Collision Resistance and Binding 4.1 Formal Security Model Let ( H : 0,1^* \to 0,1^m ) be a cryptographic hash function (assumed collision-resistant).

Proof: Without ( \log_2 n ) independent digests, the adversary can simulate missing branches with arbitrary hashes and find collisions. This is a combinatorial argument based on the pigeonhole principle on hash chains. matematicka analiza merkle 19pdf top

If ( H ) is ( \epsilon )-collision-resistant (max probability ( \epsilon ) of finding collision in time ( t )), then the Merkle tree is ( \epsilon' )-binding where ( \epsilon' \leq \epsilon ) (and verification time ( O(\log n) )). 4.2 Inclusion Proof Security Probability a random forgery succeeds: Without access to preimages, the adversary must guess a sibling hash that recomputes to ( R ). This is as hard as finding a second preimage for ( H ). Proof: Without ( \log_2 n ) independent digests,

Proof size = ( O(\log n) ) still holds, but path pruning reduces storage. For append-only logs without fixed ( n ), Merkle Mountain Ranges (MMRs) allow dynamic insertion with ( O(\log n) ) proof updates. The structure is a set of perfect binary trees (peaks). but path pruning reduces storage.