PPT FOR UNDERSTANDING MERKLE TREE

1. • Blockchain, definition, application, benefits
• All the imp terms
• Basics of cryptography---
• Block, definition, header body
• Mining process, consensus,

16. Merkle tree
• In blockchains, a Merkle tree is a data structure used to encode
blockchain data efficiently and securely.
• Transactions are passed through a hashing function to produce a
transaction hash.
• A block stores all transactions in the blockchain.
• These transactions in a block after being hashed pairs of
transactions are concatenated together to form a single hash.
• This process continues until there is a single hash for the whole
block of transactions.
• In the case there are an odd number of transactions, one will be
double hashed and its hash is concatenated with itself.
• A Merkle tree / binary hash tree is used to summarize and verify
the integrity of these transactions.
• These trees hold cryptographic hashes at their nodes and the tree
is usually displayed up-side-down whereby the root is at the top
and the leaves at the bottom.

17. Merkle Trees in Bitcoin.
• In Bitcoin, merkle trees are used to summarize all
transactions in a block to produce an overall digital
fingerprint of all transactions in the block.
• This process produces a hash such that if a
transaction in the block is mutated or removed, it
would result in a totally different hash rendering
the block invalid.
• The resulting hash is referred to as the Merkle
root and the hashing algorithm used is SHA-256.

18. • consider the case where we have four transactions, A,
B, C, and S.
• An even number of transactions. In this case, we will
have four leaves HA, HB, HC, and HD where;
HA = SHA-256(SHA-256(Transaction A))
•
To obtain the parent node HAB, we concatenate the
two hashes HA and HB to obtain a 64-byte string(32-
byte each).
• We then double hash the string to obtain the parent;
HAB = SHA-256(SHA-256(HA + HB))
• To obtain the parent node HCD, the process is
repeated;
HCD = SHA-256(SHA-256(HC + HD))

21. • This concept can be used to construct Merkle trees
of all sizes.
• In Bitcoin, a block is mined after every 10 minutes,
meaning it will contain transactions in the past 10
minutes.
• This number ranges from hundreds to thousands
of transactions in a block depending on the
network activity.
• This number of transactions is combined to form a
single hash, the root of the tree.
• The beauty of hash functions is that any size or
length of transaction passed through the hashing
function results in a fixed-length string(32-byte).

22. • Now, to make sure that a transaction is in a
block, a node produces log2(N) 32-byte hashes
that constitute if an authentication/Merkle
path that connects the transaction to the root.
• In this case, the base-2 logarithm increases
much more steadily as the number of
transaction increase.
• This enables the efficient production of 10-path
to 12-path hashes that provide proof that a
transaction exists within the tree.

24. • A node can prove that transaction K is in the
block by producing a 32-byte hash long
Merkle/authentication path consisting of four
hashes(HL, HIJ, HMNOP, and HABCDEFGH).
• With this path, any node can verify that a
transaction(HK) exists in a block by computing
four pair-wise hashes, HKL, HIJKL, HIJKLMNOP +
root.
• Note that, as the number of blocks and
transactions increases, the Merkle tree only gets
better and more efficient.
• The following image summarizes its efficiency;

26. • Merkle trees in Bitcoin allow nodes to just download
block headers and be able to know if a transaction
has been included in the block instead of storing the
whole copy of the blockchain.
• This is applicable in mobile wallets where there is
not enough space to store the full blockchain.
• In this case, the app will retrieve a small Merkle path
from a full node without the need to store or
transmit it.
•
These nodes are referred to as simplified payment
verification nodes.
• They use Merkle paths without having to download
and store the full blockchain copy.

30. Merkle Trees and SPVs.
• As mentioned SPV nodes don't store the full blockchain copy and therefore
don't have all transactions.
• They only download block headers.
• To verify a transaction is included in a block, they use
an authentication/Merkle path.
• For example, we have an SPV node that verifies payments to a wallet
address. It will establish a bloom filter on its peers.
• This filters the number of transactions that are received and results in only
those containing the wallet address.
•
When a transaction matches the filter, the node sends the block using
the merkleblock message.
• This message contains the block header and the merkle path linking the
transaction in question.
The node uses the path to connect the transaction to the block and verify its
inclusion in the block.
The block header is also used t link the block to the rest of the chain.
• These two links(transaction-block, block-blockchain) when combined are all
that is needed to prove a transaction is included in the blockchain.