nim-eth/eth/ssz/merkleization.nim

# ssz_serialization
# Copyright (c) 2018-2021 Status Research & Development GmbH
# Licensed and distributed under either of
#   * MIT license (license terms in the root directory or at https://opensource.org/licenses/MIT).
#   * Apache v2 license (license terms in the root directory or at https://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.

# This module contains the parts necessary to create a merkle hash from the core
# SSZ types outlined in the spec:
# https://github.com/ethereum/eth2.0-specs/blob/v1.0.1/ssz/simple-serialize.md#merkleization

{.push raises: [Defect].}

import
  math, sequtils,
  stew/[bitops2, endians2, ptrops],
  stew/ranges/ptr_arith, nimcrypto/[hash, sha2],
  serialization/testing/tracing,
  "."/[bitseqs, types]

export
  types

when hasSerializationTracing:
  import stew/byteutils, typetraits

const
  zero64 = default array[64, byte]
  bitsPerChunk = bytesPerChunk * 8

func binaryTreeHeight*(totalElements: Limit): int =
  bitWidth nextPow2(uint64 totalElements)

type
  SszMerkleizerImpl = object
    combinedChunks: ptr UncheckedArray[Digest]
    totalChunks: uint64
    topIndex: int

  SszMerkleizer*[limit: static[Limit]] = object
    combinedChunks: ref array[binaryTreeHeight limit, Digest]
    impl: SszMerkleizerImpl

template chunks*(m: SszMerkleizerImpl): openArray[Digest] =
  m.combinedChunks.toOpenArray(0, m.topIndex)

template getChunkCount*(m: SszMerkleizer): uint64 =
  m.impl.totalChunks

template getCombinedChunks*(m: SszMerkleizer): openArray[Digest] =
  toOpenArray(m.impl.combinedChunks, 0, m.impl.topIndex)

type DigestCtx* = sha2.sha256

template computeDigest*(body: untyped): Digest =
  ## This little helper will init the hash function and return the sliced
  ## hash:
  ## let hashOfData = withHash: h.update(data)
  when nimvm:
    # In SSZ, computeZeroHashes require compile-time SHA256
    block:
      var h {.inject.}: sha256
      init(h)
      body
      finish(h)
  else:
    block:
      var h  {.inject, noInit.}: DigestCtx
      init(h)
      body
      finish(h)

func digest(a: openArray[byte]): Digest =
  result = computeDigest:
    h.update(a)

func digest(a, b: openArray[byte]): Digest =
  result = computeDigest:
    trs "DIGESTING ARRAYS ", toHex(a), " ", toHex(b)
    trs toHex(a)
    trs toHex(b)

    h.update a
    h.update b
  trs "HASH RESULT ", result

func digest(a, b, c: openArray[byte]): Digest =
  result = computeDigest:
    trs "DIGESTING ARRAYS ", toHex(a), " ", toHex(b), " ", toHex(c)

    h.update a
    h.update b
    h.update c
  trs "HASH RESULT ", result

func mergeBranches(existing: Digest, newData: openArray[byte]): Digest =
  trs "MERGING BRANCHES OPEN ARRAY"

  let paddingBytes = bytesPerChunk - newData.len
  digest(existing.data, newData, zero64.toOpenArray(0, paddingBytes - 1))

template mergeBranches(existing: Digest, newData: array[32, byte]): Digest =
  trs "MERGING BRANCHES ARRAY"
  digest(existing.data, newData)

template mergeBranches*(a, b: Digest): Digest =
  trs "MERGING BRANCHES DIGEST"
  digest(a.data, b.data)

func computeZeroHashes: array[sizeof(Limit) * 8, Digest] =
  result[0] = Digest()
  for i in 1 .. result.high:
    result[i] = mergeBranches(result[i - 1], result[i - 1])

const zeroHashes* = computeZeroHashes()

func addChunk*(merkleizer: var SszMerkleizerImpl, data: openArray[byte]) =
  doAssert data.len > 0 and data.len <= bytesPerChunk

  if getBitLE(merkleizer.totalChunks, 0):
    var hash = mergeBranches(merkleizer.combinedChunks[0], data)

    for i in 1 .. merkleizer.topIndex:
      trs "ITERATING"
      if getBitLE(merkleizer.totalChunks, i):
        trs "CALLING MERGE BRANCHES"
        hash = mergeBranches(merkleizer.combinedChunks[i], hash)
      else:
        trs "WRITING FRESH CHUNK AT ", i, " = ", hash
        merkleizer.combinedChunks[i] = hash
        break
  else:
    let paddingBytes = bytesPerChunk - data.len

    merkleizer.combinedChunks[0].data[0..<data.len] = data
    merkleizer.combinedChunks[0].data[data.len..<bytesPerChunk] =
      zero64.toOpenArray(0, paddingBytes - 1)

    trs "WROTE BASE CHUNK ",
      toHex(merkleizer.combinedChunks[0].data), " ", data.len

  inc merkleizer.totalChunks

template isOdd(x: SomeNumber): bool =
  (x and 1) != 0

func addChunkAndGenMerkleProof*(merkleizer: var SszMerkleizerImpl,
                                hash: Digest,
                                outProof: var openArray[Digest]) =
  var
    hashWrittenToMerkleizer = false
    hash = hash

  doAssert merkleizer.topIndex < outProof.len

  for level in 0 .. merkleizer.topIndex:
    if getBitLE(merkleizer.totalChunks, level):
      outProof[level] = merkleizer.combinedChunks[level]
      hash = mergeBranches(merkleizer.combinedChunks[level], hash)
    else:
      if not hashWrittenToMerkleizer:
        merkleizer.combinedChunks[level] = hash
        hashWrittenToMerkleizer = true
      outProof[level] = zeroHashes[level]
      hash = mergeBranches(hash, zeroHashes[level])

  merkleizer.totalChunks += 1

func completeStartedChunk(merkleizer: var SszMerkleizerImpl,
                          hash: Digest, atLevel: int) =
  when false:
    let
      insertedChunksCount = 1'u64 shl (atLevel - 1)
      chunksStateMask = (insertedChunksCount shl 1) - 1
    doAssert (merkleizer.totalChunks and chunksStateMask) == insertedChunksCount

  var hash = hash
  for i in atLevel .. merkleizer.topIndex:
    if getBitLE(merkleizer.totalChunks, i):
      hash = mergeBranches(merkleizer.combinedChunks[i], hash)
    else:
      merkleizer.combinedChunks[i] = hash
      break

func addChunksAndGenMerkleProofs*(merkleizer: var SszMerkleizerImpl,
                                  chunks: openArray[Digest]): seq[Digest] =
  doAssert chunks.len > 0 and merkleizer.topIndex > 0

  let proofHeight = merkleizer.topIndex + 1
  result = newSeq[Digest](chunks.len * proofHeight)

  if chunks.len == 1:
    merkleizer.addChunkAndGenMerkleProof(chunks[0], result)
    return

  let newTotalChunks = merkleizer.totalChunks + chunks.len.uint64

  var
    # A perfect binary tree will take either `chunks.len * 2` values if the
    # number of elements in the base layer is odd and `chunks.len * 2 - 1`
    # otherwise. Each row may also need a single extra element at most if
    # it must be combined with the existing values in the Merkleizer:
    merkleTree = newSeqOfCap[Digest](chunks.len + merkleizer.topIndex)
    inRowIdx = merkleizer.totalChunks
    postUpdateInRowIdx = newTotalChunks
    zeroMixed = false

  template writeResult(chunkIdx, level: int, chunk: Digest) =
    result[chunkIdx * proofHeight + level] = chunk

  # We'll start by generating the first row of the merkle tree.
  var currPairEnd = if inRowIdx.isOdd:
    # an odd chunk number means that we must combine the
    # hash with the existing pending sibling hash in the
    # merkleizer.
    writeResult(0, 0, merkleizer.combinedChunks[0])
    merkleTree.add mergeBranches(merkleizer.combinedChunks[0], chunks[0])

    # TODO: can we immediately write this out?
    merkleizer.completeStartedChunk(merkleTree[^1], 1)
    2
  else:
    1

  if postUpdateInRowIdx.isOdd:
    merkleizer.combinedChunks[0] = chunks[^1]

  while currPairEnd < chunks.len:
    writeResult(currPairEnd - 1, 0, chunks[currPairEnd])
    writeResult(currPairEnd, 0, chunks[currPairEnd - 1])
    merkleTree.add mergeBranches(chunks[currPairEnd - 1],
                                 chunks[currPairEnd])
    currPairEnd += 2

  if currPairEnd - 1 < chunks.len:
    zeroMixed = true
    writeResult(currPairEnd - 1, 0, zeroHashes[0])
    merkleTree.add mergeBranches(chunks[currPairEnd - 1],
                                 zeroHashes[0])
  var
    level = 0
    baseChunksPerElement = 1
    treeRowStart = 0
    rowLen = merkleTree.len

  template writeProofs(rowChunkIdx: int, hash: Digest) =
    let
      startAbsIdx = (inRowIdx.int + rowChunkIdx) * baseChunksPerElement
      endAbsIdx = startAbsIdx + baseChunksPerElement
      startResIdx = max(startAbsIdx - merkleizer.totalChunks.int, 0)
      endResIdx = min(endAbsIdx - merkleizer.totalChunks.int, chunks.len)

    for resultPos in startResIdx ..< endResIdx:
      writeResult(resultPos, level, hash)

  if rowLen > 1:
    while level < merkleizer.topIndex:
      inc level
      baseChunksPerElement *= 2
      inRowIdx = inRowIdx div 2
      postUpdateInRowIdx = postUpdateInRowIdx div 2

      var currPairEnd = if inRowIdx.isOdd:
        # an odd chunk number means that we must combine the
        # hash with the existing pending sibling hash in the
        # merkleizer.
        writeProofs(0, merkleizer.combinedChunks[level])
        merkleTree.add mergeBranches(merkleizer.combinedChunks[level],
                                     merkleTree[treeRowStart])

        # TODO: can we immediately write this out?
        merkleizer.completeStartedChunk(merkleTree[^1], level + 1)
        2
      else:
        1

      if postUpdateInRowIdx.isOdd:
        merkleizer.combinedChunks[level] = merkleTree[treeRowStart + rowLen -
                                                      ord(zeroMixed) - 1]
      while currPairEnd < rowLen:
        writeProofs(currPairEnd - 1, merkleTree[treeRowStart + currPairEnd])
        writeProofs(currPairEnd, merkleTree[treeRowStart + currPairEnd - 1])
        merkleTree.add mergeBranches(merkleTree[treeRowStart + currPairEnd - 1],
                                     merkleTree[treeRowStart + currPairEnd])
        currPairEnd += 2

      if currPairEnd - 1 < rowLen:
        zeroMixed = true
        writeProofs(currPairEnd - 1, zeroHashes[level])
        merkleTree.add mergeBranches(merkleTree[treeRowStart + currPairEnd - 1],
                                     zeroHashes[level])

      treeRowStart += rowLen
      rowLen = merkleTree.len - treeRowStart

      if rowLen == 1:
        break

  doAssert rowLen == 1

  if (inRowIdx and 2) != 0:
    merkleizer.completeStartedChunk(
      mergeBranches(merkleizer.combinedChunks[level + 1], merkleTree[^1]),
      level + 2)

  if (not zeroMixed) and (postUpdateInRowIdx and 2) != 0:
    merkleizer.combinedChunks[level + 1] = merkleTree[^1]

  while level < merkleizer.topIndex:
    inc level
    baseChunksPerElement *= 2
    inRowIdx = inRowIdx div 2

    let hash = if getBitLE(merkleizer.totalChunks, level):
      merkleizer.combinedChunks[level]
    else:
      zeroHashes[level]

    writeProofs(0, hash)

  merkleizer.totalChunks = newTotalChunks

proc init*(S: type SszMerkleizer): S =
  new result.combinedChunks
  result.impl = SszMerkleizerImpl(
    combinedChunks: cast[ptr UncheckedArray[Digest]](
      addr result.combinedChunks[][0]),
    topIndex: binaryTreeHeight(result.limit) - 1,
    totalChunks: 0)

proc init*(S: type SszMerkleizer,
           combinedChunks: openArray[Digest],
           totalChunks: uint64): S =
  new result.combinedChunks
  result.combinedChunks[][0 ..< combinedChunks.len] = combinedChunks
  result.impl = SszMerkleizerImpl(
    combinedChunks: cast[ptr UncheckedArray[Digest]](
      addr result.combinedChunks[][0]),
    topIndex: binaryTreeHeight(result.limit) - 1,
    totalChunks: totalChunks)

proc copy*[L: static[Limit]](cloned: SszMerkleizer[L]): SszMerkleizer[L] =
  new result.combinedChunks
  result.combinedChunks[] = cloned.combinedChunks[]
  result.impl = SszMerkleizerImpl(
    combinedChunks: cast[ptr UncheckedArray[Digest]](
      addr result.combinedChunks[][0]),
    topIndex: binaryTreeHeight(L) - 1,
    totalChunks: cloned.totalChunks)

template addChunksAndGenMerkleProofs*(
    merkleizer: var SszMerkleizer,
    chunks: openArray[Digest]): seq[Digest] =
  addChunksAndGenMerkleProofs(merkleizer.impl, chunks)

template addChunk*(merkleizer: var SszMerkleizer, data: openArray[byte]) =
  addChunk(merkleizer.impl, data)

template totalChunks*(merkleizer: SszMerkleizer): uint64 =
  merkleizer.impl.totalChunks

template getFinalHash*(merkleizer: SszMerkleizer): Digest =
  merkleizer.impl.getFinalHash

template createMerkleizer*(totalElements: static Limit): SszMerkleizerImpl =
  trs "CREATING A MERKLEIZER FOR ", totalElements

  const treeHeight = binaryTreeHeight totalElements
  var combinedChunks {.noInit.}: array[treeHeight, Digest]
  
  let topIndex = treeHeight - 1
  
  SszMerkleizerImpl(
    combinedChunks: cast[ptr UncheckedArray[Digest]](addr combinedChunks),
    topIndex: if (topIndex < 0): 0 else: topIndex,
    totalChunks: 0)

func getFinalHash*(merkleizer: SszMerkleizerImpl): Digest =
  if merkleizer.totalChunks == 0:
    return zeroHashes[merkleizer.topIndex]

  let
    bottomHashIdx = firstOne(merkleizer.totalChunks) - 1
    submittedChunksHeight = bitWidth(merkleizer.totalChunks - 1)
    topHashIdx = merkleizer.topIndex

  trs "BOTTOM HASH ", bottomHashIdx
  trs "SUBMITTED HEIGHT ", submittedChunksHeight
  trs "TOP HASH IDX ", topHashIdx

  if bottomHashIdx != submittedChunksHeight:
    # Our tree is not finished. We must complete the work in progress
    # branches and then extend the tree to the right height.
    result = mergeBranches(merkleizer.combinedChunks[bottomHashIdx],
                           zeroHashes[bottomHashIdx])

    for i in bottomHashIdx + 1 ..< topHashIdx:
      if getBitLE(merkleizer.totalChunks, i):
        result = mergeBranches(merkleizer.combinedChunks[i], result)
        trs "COMBINED"
      else:
        result = mergeBranches(result, zeroHashes[i])
        trs "COMBINED WITH ZERO"

  elif bottomHashIdx == topHashIdx:
    # We have a perfect tree (chunks == 2**n) at just the right height!
    result = merkleizer.combinedChunks[bottomHashIdx]
  else:
    # We have a perfect tree of user chunks, but we have more work to
    # do - we must extend it to reach the desired height
    result = mergeBranches(merkleizer.combinedChunks[bottomHashIdx],
                           zeroHashes[bottomHashIdx])

    for i in bottomHashIdx + 1 ..< topHashIdx:
      result = mergeBranches(result, zeroHashes[i])

func mixInLength*(root: Digest, length: int): Digest =
  var dataLen: array[32, byte]
  dataLen[0..<8] = uint64(length).toBytesLE()
  mergeBranches(root, dataLen)

func hash_tree_root*(x: auto): Digest {.gcsafe, raises: [Defect].}

template merkleizeFields(totalElements: static Limit, body: untyped): Digest =
  var merkleizer {.inject.} = createMerkleizer(totalElements)

  template addField(field) =
    let hash = hash_tree_root(field)
    trs "MERKLEIZING FIELD ", astToStr(field), " = ", hash
    addChunk(merkleizer, hash.data)
    trs "CHUNK ADDED"

  body

  getFinalHash(merkleizer)

template writeBytesLE(chunk: var array[bytesPerChunk, byte], atParam: int,
                      val: SomeUnsignedInt) =
  let at = atParam
  chunk[at ..< at + sizeof(val)] = toBytesLE(val)

func chunkedHashTreeRootForBasicTypes[T](merkleizer: var SszMerkleizerImpl,
                                         arr: openArray[T]): Digest =
  static:
    doAssert T is BasicType

  if arr.len == 0:
    return getFinalHash(merkleizer)

  when T is byte:
    var
      remainingBytes = arr.len
      pos = cast[ptr byte](unsafeAddr arr[0])

    while remainingBytes >= bytesPerChunk:
      merkleizer.addChunk(makeOpenArray(pos, bytesPerChunk))
      pos = offset(pos, bytesPerChunk)
      remainingBytes -= bytesPerChunk

    if remainingBytes > 0:
      merkleizer.addChunk(makeOpenArray(pos, remainingBytes))

  elif T is bool or cpuEndian == littleEndian:
    let
      baseAddr = cast[ptr byte](unsafeAddr arr[0])
      len = arr.len * sizeof(T)
    return chunkedHashTreeRootForBasicTypes(merkleizer, makeOpenArray(baseAddr, len))

  else:
    static:
      doAssert T is UintN
      doAssert bytesPerChunk mod sizeof(Т) == 0

    const valuesPerChunk = bytesPerChunk div sizeof(Т)

    var writtenValues = 0

    var chunk: array[bytesPerChunk, byte]
    while writtenValues < arr.len - valuesPerChunk:
      for i in 0 ..< valuesPerChunk:
        chunk.writeBytesLE(i * sizeof(T), arr[writtenValues + i])
      merkleizer.addChunk chunk
      inc writtenValues, valuesPerChunk

    let remainingValues = arr.len - writtenValues
    if remainingValues > 0:
      var lastChunk: array[bytesPerChunk, byte]
      for i in 0 ..< remainingValues:
        chunk.writeBytesLE(i * sizeof(T), arr[writtenValues + i])
      merkleizer.addChunk lastChunk

  getFinalHash(merkleizer)

func bitListHashTreeRoot(merkleizer: var SszMerkleizerImpl, x: BitSeq): Digest =
  # TODO: Switch to a simpler BitList representation and
  #       replace this with `chunkedHashTreeRoot`
  var
    totalBytes = bytes(x).len
    lastCorrectedByte = bytes(x)[^1]

  if lastCorrectedByte == byte(1):
    if totalBytes == 1:
      # This is an empty bit list.
      # It should be hashed as a tree containing all zeros:
      return mergeBranches(zeroHashes[merkleizer.topIndex],
                           zeroHashes[0]) # this is the mixed length

    totalBytes -= 1
    lastCorrectedByte = bytes(x)[^2]
  else:
    let markerPos = log2trunc(lastCorrectedByte)
    lastCorrectedByte.clearBit(markerPos)

  var
    bytesInLastChunk = totalBytes mod bytesPerChunk
    fullChunks = totalBytes div bytesPerChunk

  if bytesInLastChunk == 0:
    fullChunks -= 1
    bytesInLastChunk = 32

  for i in 0 ..< fullChunks:
    let
      chunkStartPos = i * bytesPerChunk
      chunkEndPos = chunkStartPos + bytesPerChunk - 1

    merkleizer.addChunk bytes(x).toOpenArray(chunkStartPos, chunkEndPos)

  var
    lastChunk: array[bytesPerChunk, byte]
    chunkStartPos = fullChunks * bytesPerChunk

  for i in 0 .. bytesInLastChunk - 2:
    lastChunk[i] = bytes(x)[chunkStartPos + i]

  lastChunk[bytesInLastChunk - 1] = lastCorrectedByte

  merkleizer.addChunk lastChunk.toOpenArray(0, bytesInLastChunk - 1)
  let contentsHash = merkleizer.getFinalHash
  mixInLength contentsHash, x.len

func maxChunksCount(T: type, maxLen: Limit): Limit =
  when T is BitList|BitArray:
    (maxLen + bitsPerChunk - 1) div bitsPerChunk
  elif T is array|List:
    maxChunkIdx(ElemType(T), maxLen)
  else:
    unsupported T # This should never happen

func hashTreeRootAux[T](x: T): Digest =
  when T is bool|char:
    result.data[0] = byte(x)
  elif T is SomeUnsignedInt:
    when cpuEndian == bigEndian:
      result.data[0..<sizeof(x)] = toBytesLE(x)
    else:
      copyMem(addr result.data[0], unsafeAddr x, sizeof x)
  elif (when T is array: ElemType(T) is BasicType else: false):
    type E = ElemType(T)
    when sizeof(T) <= sizeof(result.data):
      when E is byte|bool or cpuEndian == littleEndian:
        copyMem(addr result.data[0], unsafeAddr x, sizeof x)
      else:
        var pos = 0
        for e in x:
          writeBytesLE(result.data, pos, e)
          pos += sizeof(E)
    else:
      trs "FIXED TYPE; USE CHUNK STREAM"
      var markleizer = createMerkleizer(maxChunksCount(T, Limit x.len))
      chunkedHashTreeRootForBasicTypes(markleizer, x)
  elif T is BitArray:
    hashTreeRootAux(x.bytes)
  elif T is array|object|tuple:
    trs "MERKLEIZING FIELDS"
    const totalFields = when T is array: len(x)
                        else: totalSerializedFields(T)
    merkleizeFields(Limit totalFields):
      x.enumerateSubFields(f):
        addField f
  #elif isCaseObject(T):
  #  # TODO implement this
  else:
    unsupported T

func hashTreeRootList(x: List|BitList): Digest =
  const maxLen = static(x.maxLen)
  type T = type(x)
  const limit = maxChunksCount(T, maxLen)
  var merkleizer = createMerkleizer(limit)

  when x is BitList:
    merkleizer.bitListHashTreeRoot(BitSeq x)
  else:
    type E = ElemType(T)
    let contentsHash = when E is BasicType:
      chunkedHashTreeRootForBasicTypes(merkleizer, asSeq x)
    else:
      for elem in x:
        let elemHash = hash_tree_root(elem)
        merkleizer.addChunk(elemHash.data)
      merkleizer.getFinalHash()
    mixInLength(contentsHash, x.len)

func hash_tree_root*(x: auto): Digest {.raises: [Defect].} =
  trs "STARTING HASH TREE ROOT FOR TYPE ", name(type(x))
  mixin toSszType

  result =
    when x is List|BitList:
      hashTreeRootList(x)
    else:
      hashTreeRootAux toSszType(x)

  trs "HASH TREE ROOT FOR ", name(type x), " = ", "0x", $result

# https://github.com/ethereum/eth2.0-specs/blob/dev/ssz/merkle-proofs.md#get_generalized_index_length
func getGeneralizedIndexLength(x: uint64): int =
  log2trunc(x)

# https://github.com/ethereum/eth2.0-specs/blob/dev/ssz/merkle-proofs.md#get_generalized_index_bit
func getGeneralizedIndexBit(index: uint64, position: uint64): bool =
  (index and (1'u64 shl position)) > 0

# validates merkle proof. Provided index should be a generalized index of leaf node
# as defined in: https://github.com/ethereum/eth2.0-specs/blob/dev/ssz/merkle-proofs.md#generalized-merkle-tree-index
func isValidProof*(leaf: Digest, proof: openArray[Digest],
                             index: uint64, root: Digest): bool =
  if len(proof) == getGeneralizedIndexLength(index):
    var
      value = leaf

    for i, digest in proof:
      value =
        if getGeneralizedIndexBit(index, uint64 i):
          mergeBranches(digest, value)
        else:
          mergeBranches(value, digest)

    value == root
  else:
    false

proc slice[T](x: openArray[T]): seq[T] = x.toSeq()

# Helper functions to get proof for any element of a list
proc getProofForAllListElements*(list: List): seq[Digest] = 
  type T = type(list)
  type E = ElemType(T)
  # basic types have different chunking rules
  static:
    doAssert (E is not BasicType)
  var digests: seq[Digest] = @[]
  for e in list:
    let root = hash_tree_root(e)
    digests.add(root)
  var merk = createMerkleizer(list.maxLen)
  merk.addChunksAndGenMerkleProofs(digests)

proc getProofWithIdx*(list: List, allProofs: seq[Digest], idx: int): seq[Digest] =
  let treeHeight = binaryTreeHeight(list.maxLen)
  let startPos = idx * treeHeight
  let endPos = startPos + treeHeight - 2
  slice(allProofs.toOpenArray(startPos, endPos))

proc generateAndGetProofWithIdx*(list: List, idx: int): seq[Digest] =
  let allProofs = getProofForAllListElements(list)
  getProofWithIdx(list, allProofs, idx)