Tsvetan Dimitrov

Agenda

• Merkle Trees

  • Definition

  • Benefits

  • Use Cases

• Sparse Merkle Trees

• Cryptographic Hash Functions

• SHA-256

• Summary

Merkle Trees

Definition / 1

• Also called Binary Hash Tree.

• Leaves represent individual pieces of data, such as transactions in a blockchain.

Definition / 2

• Each internal node in the tree represents the hash of the concatenation of its two child nodes.

• This continues until a single root node is reached, which represents the root hash of the entire tree, called Merkle Root.

Definition / 3

• Data can be audited using the Merkle Root in O(log n) time to the number of leaves. This is called the Merkle Proof.

• The Merkle Path corresponds to recreating the branch containing the piece of data from the root to the piece of data being audited.

Benefits

• Validate data integrity.

• Take small amount of disk space.

• Small amount of information is sent across the network.

• Efficient data format enabling fast verification.

• Prove that giving tiny amounts of information across the network is all that is required for a transaction to be valid.

Use Cases in Blockchain

Other Use Cases

• Git

• Interplanetary File System, a peer-to-peer distributed protocol (Merkle DAG).

• It's part of the technique that generates verifiable certificate transparency logs.

• Amazon DynamoDB and Apache Cassandra use it during the data replication process to control discrepancies.

Sparse Merkle Trees

• A standard Merkle Tree, except the contained data is indexed, and each data point is placed at the leaf that corresponds to that data point’s index.

• Suitable for proving non-inclusion of a node in the tree.

• Acts as a key-value store inside of a Merkle Tree.

Definition

Space Complexity and Caching

• Efficient proofs of non-inclusion, but at the cost of huge trees (about 2²⁵⁶ hashes)

• Luckily, caching is possible because H(null) is a constant value and so is H(H(null)).

• A naive caching strategy could record every hash that is non-empty.

• The goal is to capture branches down to the leaves by a constant.

Cryptographic Hash Functions

Non Cryptographic Hash Functions / 1

Non Cryptographic Hash Functions / 2

Properties of CHF

CHF Algorithm Families

SHA-256

Definition

• Produces a fixed-size, 256-bit hash value.

• Part of the SHA-2 family of hash functions and designed by the National Security Agency (NSA).

• Built with a Merkle-Damgård structure derived from a one-way compression function.

• A brute-force attack would need to make 2²⁵⁶ attempts to generate the initial data.

Step 1: Padding Bits

• Bits are appended to the original input to make it compatible with the hash function.

• Total bits must always be 64 bits short of any multiple of 512.

• The first bit added is 1 and the rest are zeroes.

Original Message

Padding Bits

Step 2: Padding Length

• The length of the original message is padded to the result from step 1 and it is expressed in the form of 64 bits.

• The final data to be hashed will now be a multiple of 512 (used mostly to increase the complexity of the function).

Original Message

Padding Bits

Input Length

Step 3: Initialize Chaining Variables

• The entire message is broken down into blocks of 512 bits each (5 buffers of 32 bits each).

• They are 5 words named A, B, C, D, and E.

• The first iteration has fixed hex values.

Step 4.1: Process Each Block

• 512 bit block = 16 sub blocks * 32 bits each.

• 4 rounds of operations, utilizing the ABCDE register, the 512 bit block and a constant named K[t].

• Each round has 20 iterations: 4 * 20 = 80.

• K[t] is an array of 80 elements.

Step 4.2: Process Each Block

• On each iteration the following formula is calculated:

• P = Non Linear Logical Process that changes each round.

• S⁵ = Circular shift by 5 bits.

• W(t) = A 32 bit string derived from an existing sub block.

• K(t) = One of the 80 constants which change with every round.

Summary

• Merkle Trees and Sparse Merkle Trees - definitions, use cases, benefits and drawbacks.

• Differences between CHF and non CHF.

• SHA-256 definition and algorithm explanation.

Questions?