# Functions: Utils¶

There are several helper methods available that abstract Bitcoin internals away in the main function implementation.

## sha256d¶

Bitcoin uses a double SHA256 hash to protect against “length-extension” attacks.

Note

Bitcoin uses little endian representations when sending hashes across the network and for storing values internally. For more details, see the documentation. The output of the SHA256 function is big endian by default.

*Function Signature*

`sha256d(data)`

*Parameters*

`data`

: bytes encoded input.

*Returns*

`hash`

: the double SHA256 hash encodes as a bytes from`data`

.

### Function Sequence¶

- Hash
`data`

with sha256. - Hash the result of step 1 with sha256.
- Return
`hash`

.

## concatSha256d¶

A function that computes a parent hash from two child nodes. This function is used in the reconstruction of the Merkle tree.

*Function Signature*

`concatSha256d(left, right)`

*Parameters*

`left`

: 32 bytes of input data that are added first.`right`

: 32 bytes of input data that are added second.

*Returns*

`hash`

: the double sha256 hash encoded as a bytes from`left`

and`right`

.

## nBitsToTarget¶

This function calculates the PoW difficulty target from a compressed nBits representation. See the Bitcoin documentation for further details. The computation for the difficulty is as follows:

*Function Signature*

`nBitsToTarget(nBits)`

*Parameters*

`nBits`

: 4 bytes compressed PoW target representation.

*Returns*

`target`

: PoW difficulty target computed from nBits.

### Function Sequence¶

- Extract the
*exponent*by shifting the`nBits`

to the right by 24. - Extract the
*significand*by taking the first three bytes of`nBits`

. - Calculate the
`target`

via the equation above and using 2 as the*base*(as we use the U256 type). - Return
`target`

.

## checkCorrectTarget¶

Verifies the currently submitted block header has the correct difficulty target.

*Function Signature*

`checkCorrectTarget(hashPrevBlock, blockHeight, target)`

*Parameters*

`hashPrevBlock`

: 32 bytes previous block hash (necessary to retrieve previous target).`blockHeight`

: height of the current block submission.`target`

: PoW difficulty target computed from nBits.

*Returns*

`True`

: if the difficulty target is set correctly.`False`

: otherwise.

### Function Sequence¶

Retrieve the previous block header with the

`hashPrevBlock`

from the`BlockHeaders`

storage and the difficulty target (`prevTarget`

) of this (previous) block.Check if the

`prevTarget`

difficulty should be adjusted at this`blockHeight`

.If the difficulty should not be adjusted, check if the

`target`

of the submitted block matches the`prevTarget`

of the previous block and check that`prevTarget``is not ``0`

. Return false if either of these checks fails.The difficulty should be adjusted. Calculate the new expected target by calling the computeNewTarget function and passing the timestamp of the previous block (get using

`hashPrevBlock`

key in`BlockHeaders`

), the timestamp of the last re-target (get block hash from`Chains`

using`blockHeight - 2016`

as key, then query`BlockHeaders`

) and the target of the previous block (get using`hashPrevBlock`

key in`BlockHeaders`

) as parameters. Check that the new target matches the`target`

of the current block (i.e., the block’s target was set correctly).- If the newly calculated target difficulty matches
`target`

, return`True`

. - Otherwise, return
`False`

.

- If the newly calculated target difficulty matches

## computeNewTarget¶

Computes the new difficulty target based on the given parameters, as implemented in the Bitcoin core client.

*Function Signature*

`computeNewTarget(prevTime, startTime, prevTarget)`

*Parameters*

`prevTime`

: timestamp of previous block.`startTime`

: timestamp of last re-target.`prevTarget`

: PoW difficulty target of the previous block.

*Returns*

`newTarget`

: PoW difficulty target of the current block.

### Function Sequence¶

- Compute the actual time span between
`prevTime`

and`startTime`

. - Compare if the actual time span is smaller than the target interval divided by 4 (default target interval in Bitcoin is two weeks). If true, set the actual time span to the target interval divided by 4.
- Compare if the actual time span is greater than the target interval multiplied by 4. If true, set the actual time span to the target interval multiplied by 4.
- Calculate the
`newTarget`

by multiplying the actual time span with the`prevTarget`

and dividing by the target time span (2 weeks for Bitcoin). - If the
`newTarget`

is greater than the maximum target in Bitcoin, set the`newTarget`

to the maximum target (Bitcoin maximum target is \(2^{224}-1\)). - Return the
`newTarget`

.

## computeMerkle¶

The computeMerkle function calculates the root of the Merkle tree of transactions in a Bitcoin block. Further details are included in the Bitcoin developer reference.

*Function Signature*

`computeMerkle(txId, txIndex, merkleProof)`

*Parameters*

`txId`

: the hash identifier of the transaction.`txIndex`

: index of transaction in the block’s transaction Merkle tree.`merkleProof`

: Merkle tree path (concatenated LE sha256 hashes).

*Returns*

`merkleRoot`

: the hash of the Merkle root.

*Errors*

`ERR_INVALID_MERKLE_PROOF = "Invalid Merkle Proof structure"`

: raise an exception if the Merkle proof is malformed.

### Function Sequence¶

Check if the length of the Merkle proof is 32 bytes long.

- If true, only the coinbase transaction is included in the block and the Merkle proof is the
`merkleRoot`

. Return the`merkleRoot`

. - If false, continue function execution.

- If true, only the coinbase transaction is included in the block and the Merkle proof is the
Check if the length of the Merkle proof is greater or equal to 64 and if it is a power of 2.

- If true, continue function execution.
- If false, raise
`ERR_INVALID_MERKLE_PROOF`

.

Calculate the

`merkleRoot`

. For each 32 bytes long hash in the Merkle proof:- Determine the position of transaction hash (or the last resulting hash) at either
`0`

or`1`

. - Slice the next 32 bytes from the Merkle proof.
- Concatenate the transaction hash (or last resulting hash) with the 32 bytes of the Merkle proof in the right order (depending on the transaction/last calculated hash position).
- Calculate the double SHA256 hash of the concatenated input with the concatSha256d function.
- Repeat until there are no more hashes in the
`merkleProof`

.

- Determine the position of transaction hash (or the last resulting hash) at either
The last resulting hash from step 3 is the

`merkleRoot`

. Return`merkleRoot`

.

### Example¶

Assume we have the following input:

- txId:
`330dbbc15169c538583073fd0a7708d8de2d3dc155d75b361cbf5c24b73f3586`

- txIndex:
`0`

- merkleProof:
`86353fb7245cbf1c365bd755c13d2dded808770afd73305838c56951c1bb0d33b635f586cf6c4763f3fc98b99daf8ac14ce1146dc775777c2cd2c4290578ef2e`

The `computeMerkle`

function would go past step 1 as our proof is longer than 32 bytes. Next, step 2 would also be passed as the proof length is equal to 64 bytes and a power of 2. Last, we calculate the Merkle root in step 3 as shown below.

## calculateDifficulty¶

Given the `target`

, calculates the Proof-of-Work `difficulty`

value, as defined in the Bitcoin wiki.

*Function Signature*

`calculateDifficulty(target)`

*Parameters*

`target`

: target as specified in a Bitcoin block header.

*Returns*

`difficulty`

: difficulty calculated from given`target`

.

### Function Sequence¶

- Return
`0xffff0000000000000000000000000000000000000000000000000000`

(max. possible target, also referred to as “difficulty 1”) divided by`target`

.

## getForkIdByBlockHash¶

Helper function allowing to query the list of tracked forks (`Forks`

) for the identifier of a fork given its last submitted (“highest”) block hash.

### Specification¶

*Function Signature*

`getForkIdByBlockHash(blockHash)`

*Parameters*

`blockHash`

: block hash of the last submitted block to a fork.

*Returns*

`forkId`

: if there exists a fork with`blockHash`

as latest submitted block in`forkHashes`

.`ERR_FORK_ID_NOT_FOUND`

: otherwise.

*Errors*

`ERR_FORK_ID_NOT_FOUND = Fork ID not found for specified block hash."`

: return this error if there exists no`forkId`

for the given`blockHash`

.

### Function Sequence¶

Loop over all entries in

`Forks`

and check if`forkHashes[forkHashes.length -1] == blockhash`

- If
`True`

: return the corresponding`forkId`

.

- If
Return

`ERR_FORK_ID_NOT_FOUND`

otherwise.