Internet-Draft MMRIVER October 2024
Bryce Expires 24 April 2025 [Page]
Workgroup:
COSE
Internet-Draft:
draft-bryce-cose-merkle-mountain-range-proofs-00
Published:
Intended Status:
Experimental
Expires:
Author:
R. Bryce
DataTrails

Merkle Mountain Range for Immediately Verifiable and Replicable Commitments

Abstract

This specification describes the COSE encoding of proofs for post-order traversal binary Merkle trees, also known as history trees and Merkle mountain ranges. Proving and verifying are defined in terms of the cryptographic asynchronous accumulator described by ReyzinYakoubov. The technical advantages of post-order traversal binary Merkle trees are discussed in CrosbyWallachStorage and PostOrderTlog.

Status of This Memo

This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79.

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This Internet-Draft will expire on 24 April 2025.

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Table of Contents

1. Introduction

A post ordered binary merkle tree is, logically, the unique series of perfect binary merkle trees required to commit its leaves.

Example,

   6
 2   5
0 1 3 4 7

This illustrates MMR(8), which is comprised of two perfect trees rooted at 6 and 7. 7 is the root of a tree comprised of a single element.

The peaks of the perfect trees form the accumulator.

The storage of a tree maintained in this way is addressed as a linear array, and additions to the tree are always appends.

2. Conventions and Definitions

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here.

In this specification, all numbers are unsigned 64 bit integers. The maximum height of a single tree is 64 (which will have g=63 for its peak).

3. Verifiable Data Structure

The integer identifier for this Verifiable Data Structure is 2.

4. Inclusion Proof

The CBOR representation of an inclusion proof is

inclusion-proof = bstr .cbor [

  ; zero based index of a tree node
  index: uint

  ; path proving the node's inclusion
  inclusion-path: [ + bstr ]
]

Note that the inclusion path for the index leads to a single permanent node in the tree. This node will initially be a peak in the accumulator, as the tree grows it will eventually be "buried" by a new peak.

4.1. inclusion_proof_path

inclusion_proof_path(i, c) is used to produce the verification paths for inclusion proofs and consistency proofs.

Given:

  • c the index of the last node in any tree which contains i.

  • i the index of the mmr node whose verification path is required.

And the methods:

And the constraints:

  • i <= c

We define inclusion_proof_path as

  def inclusion_proof_path(i, c):

    path = []

    g = index_height(i)

    while True:

      # The sibling of i is at i +/- 2^(g+1)
      siblingoffset = (2 << g)

      # If the index after i is higher, it is the left parent,
      # and i is the right sibling
      if index_height(i+1) > g:

        # The witness to the right sibling is offset behind i
        isibling = i - siblingoffset + 1

        # The parent of a right sibling is stored immediately
        # after
        i += 1
      else:

        # The witness to a left sibling is offset ahead of i
        isibling = i + siblingoffset - 1

        # The parent of a left sibling is stored immediately after
        # its right sibling
        i += siblingoffset

      # When the computed sibling exceedes the range of MMR(C+1),
      # we have completed the path
      if isibling > c:
          return path

      path.append(isibling)

      # Set g to the height of the next item in the path.
      g += 1

5. Receipt of Inclusion

The cbor representation of an inclusion proof is:

protected-header-map = {
  &(alg: 1) => int
  &(vds: 395) => 2
  * cose-label => cose-value
}

The unprotected header for an inclusion proof signature is:

inclusion-proofs = [ + inclusion-proof ]

verifiable-proofs = {
  &(inclusion-proof: -1) => inclusion-proofs
}

unprotected-header-map = {
  &(vdp: 396) => verifiable-proofs
  * cose-label => cose-value
}

The payload of an MMRIVER inclusion proof signature is the tree peak committing to the nodes inclusion, or the node itself where the proof path is empty. The algorithm included_root (Section 5.2) obtains this value.

The payload MUST be detached. Detaching the payload forces verifiers to recompute the root from the inclusion proof, this protects against implementation errors where the signature is verified but the payload merkle root does not match the inclusion proof.

5.1. Verifying the Receipt of inclusion

The inclusion proof and signature are verified in order. First the verifiers applies the inclusion proof to a possible entry (set member) bytes. If this process fails, the inclusion proof may have been tampered with. If this process succeeds, the result is a merkle root, which in the attached as the COSE Sign1 payload. Second the verifier checks the signature of the COSE Sign1. If the resulting signature verifies, the Receipt has proved inclusion of the entry in the verifiable data structure. If the resulting signature does not verify, the signature may have been tampered with.

It is recommended that implementations return a single boolean result for Receipt verification operations, to reduce the chance of accepting a valid signature over an invalid inclusion proof.

As the proof must be processed prior to signature verification the implementation SHOULD check the lengths of the proof paths are appropriate for the provided tree sizes.

5.2. included_root

The algorithm included_root calculates the accumulator peak for the provided proof and node value.

Given:

  • i is the index the nodeHash is to be shown at

  • nodehash the value whose inclusion is to be shown

  • proof is the path of sibling values committing i.

And the methods:

We define included_root as

  def included_root(i, nodehash, proof):

    root = nodehash

    g = index_height(i)

    for sibling in proof:

      # If the index after i is higher, it is the left parent,
      # and i is the right sibling

      if index_height(i + 1) > g:

        # The parent of a right sibling is stored immediately after

        i = i + 1

        # Set `root` to `H(i+1 || sibling || root)`
        root = hash_pospair64(i + 1, sibling, root)
      else:

        # The parent of a left sibling is stored immediately after
        # its right sibling.

        i = i + (2 << g)

        # Set `root` to `H(i+1 || root || sibling)`
        root = hash_pospair64(i + 1, root, sibling)

      # Set g to the height of the next item in the path.
      g = g + 1

    # If the path length was zero, the original nodehash is returned
    return root

6. Consistency Proof

A consistency proof shows that the accumulator, defined in ReyzinYakoubov, for tree-size-1 is a prefix of the accumulator for tree-size-2.

The signature is over the complete accumulator for tree-size-2 obtained using the proof and the, supplied, possibly empty, list of right-peaks which complete the accumulator for tree-size-2.

The receipt of consistency is defined so that a chain of cumulative consistency proofs can be verified together.

The cbor representation of a consistency proof is:

consistency-path = [ * bstr ]

consistency-proof =  bstr .cbor [

  ; previous tree size
  tree-size-1: uint

  ; latest tree size
  tree-size-2: uint

  ; the inclusion path from each accumulator peak in
  ; tree-size-1 to its new peak in tree-size-2.
  consistency-paths: [ + consistency-path ]

  ; the additional peaks that
  ; complete the accumulator for tree-size-2,
  ; when appended to those produced by the consistency paths
  right-peaks: [ *bstr ]
]

6.1. consistency_proof_path

Produces the verification paths for inclusion of the peaks of tree-size-1 under the peaks of tree-size-2.

right-peaks are obtained by invoking peaks(tree-size-2 - 1), and discarding length(proofs) from the left.

Given:

  • ifrom is the last index of tree-size-1

  • ito is the last index of tree-size-2

And the methods:

And the constraints:

  • ifrom <= ito

We define consistency_proof_paths as

  def consistency_proof_paths(ifrom, ito):

    proof = []

    for i in peaks(ifrom):
      proof.append(inclusion_proof_path(i, ito))

    return proof

7. Receipt of Consistency

The cbor representation of an inclusion proof for MMRIVER is:

protected-header-map = {
  &(alg: 1) => int
  &(vds: 395) => 2
  * cose-label => cose-value
}

The unprotected header for an inclusion proof signature is:

consistency-proofs = [ + consistency-proof ]

verifiable-proofs = {
  &(consistency-proof: -2) => consistency-proof
}

unprotected-header-map = {
  &(vdp: 396) => verifiable-proofs
  * cose-label => cose-value
}

The payload MUST be detached. Detaching the payload forces verifiers to recompute the roots from the consistency proofs. This protects against implementation errors where the signature is verified but the payload is not genuinely produced by the included proof.

7.1. Verifying the Receipt of consistency

Verification accommodates verifying the result of a cumulative series of consistency proofs.

Perform the following for each consistency-proof in the list, verifying the signature with the output of the last.

  1. Initialize current proof as the first consistency-proof.

  2. Initialize accumulatorfrom to the peaks of tree-size-1 in the current proof.

  3. Initialize ifrom to tree-size-1 - 1 from the current proof.

  4. Initialize proofs to the consistency-paths from the current proof.

  5. Apply the algorithm consistent_roots (Section 7.1.1)

  6. Apply the peaks algorithm to obtain the accumulator for tree-size-2

  7. From the peaks for tres-size-2, discard from the left the number of roots returned by consistent_roots.

  8. Create the consistent accumulator by appending the remaining peaks to the consistent roots.

  9. If there are no remaining proofs, use the consistent accumulator as the detached payload and verify the signature of the COSE Sign1.

It is recommended that implementations return a single boolean result for Receipt verification operations, to reduce the chance of accepting a valid signature over an invalid consistency proof.

As the proof must be processed prior to signature verification the implementation SHOULD check the lengths of the proof paths are appropriate for the provided tree sizes.

7.1.1. consistent_roots

consistent_roots returns the descending height ordered list of elements from the accumulator for the consistent future state.

Implementations MUST require that the number of peaks returned by Section 9.2(ifrom) equals the number of entries in accumulatorfrom.

Given:

  • ifrom the last index in the complete MMR from which consistency was proven.

  • accumulatorfrom the node values corresponding to the peaks of the accumulator for tree-size-1

  • proofs the inclusion proofs for each node in accumulatorfrom for tree-size-2

And the methods:

We define consistent_roots as

  def consistent_roots(ifrom, accumulatorfrom, proofs):

    frompeaks = peaks(ifrom)

    # if length(frompeaks) != length(proofs) -> ERROR

    roots = []
    for i in range(len(accumulatorfrom)):
      root = included_root(
          frompeaks[i], accumulatorfrom[i], proofs[i])

      if roots and roots[-1] == root:
          continue
      roots.append(root)

    return roots

8. Appending a leaf

An algorithm for appending to a tree maintained in post order layout is provided. Implementation defined methods for interacting with storage are specified.

8.1. add_leaf_hash

When a new node is appended, if its height matches the height of its immediate predecessor, then the two equal height siblings MUST be merged. Merging is defined as the append of a new node which takes the adjacent peaks as its left and right children. This process MUST proceed until there are no more completable sub trees.

add_leaf_hash(f) adds the leaf hash value f to the tree.

Given:

  • f the leaf value resulting from H(x) for the caller defined leaf value x

  • db an interface supporting the Section 8.2.2 and Section 8.2.1 implementation defined storage methods.

And the methods:

We define add_leaf_hash as

  def add_leaf_hash(db, f: bytes):

    # Set g to 0, the height of the leaf item f
    g = 0

    # Set i to the result of invoking Append(f)
    i = db.append(f)

    # If index_height(i) is greater than g (#looptarget)
    while index_height(i) > g:

      # Set ileft to the index of the left child of i,
      # which is i - 2^(g+1)

      ileft = i - (2 << g)

      # Set iright to the index of the the right child of i,
      # which is i - 1

      iright = i - 1

      # Set v to H(i + 1 || Get(ileft) || Get(iright))
      # Set i to the result of invoking Append(v)

      i = db.append(
        hash_pospair64(i+1, db.get(ileft), db.get(iright)))

      # Set g to the height of the new i, which is g + 1
      g += 1

    return i

8.2. Implementation defined storage methods

The following methods are assumed to be available to the implementation. Very minimal requirements are specified.

Informally, the storage must be array like and have no gaps.

8.2.1. Get

Reads the value from the tree at the supplied index.

The read MUST be consistent with any other calls to Append or Get within the same algorithm invocation.

Get MAY fail for transient reasons.

8.2.2. Append

Appends new node to storage and returns the index that will be occupied by the node provided to the next call to append.

The implementation MUST guarantee that the results of Append are immediately available to Get calls in the same invocation of the algorithm.

Append MUST return the node i identifying the node location which comes next.

The implementation MAY defer commitment to underlying persistent storage.

Append MAY fail for transient reasons.

8.3. Node values

Interior nodes in the MUST prefix the value provided to H(x) with pos.

The value v for any interior node MUST be H(pos || Get(LEFT_CHILD) || Get(RIGHT_CHILD))

The algorithm for leaf addition is provided the result of H(x) directly.

8.3.1. hash_pospair64

Returns H(pos || a || b), which is the value for the node identified by index pos - 1

Editors note: How this draft accommodates hash alg agility is tbd.

Given:

  • pos the size of the MMR whose last node index is pos - 1

  • a the first value to include in the hash after pos

  • b the second value to include in the hash after pos

And the constraints:

  • pos < 2^64

  • a and b MUST be hashes produced by the appropriate hash alg.

We define hash_pospair64 as

  def hash_pospair64(pos, a, b):

    # Note: Hash algorithm agility is tbd, this example uses SHA-256
    h = hashlib.sha256()

    # Take the big endian representation of pos
    h.update(pos.to_bytes(8, byteorder="big", signed=False))
    h.update(a)
    h.update(b)
    return h.digest()

9. Essential supporting algorithms

9.1. index_height

index_height(i) returns the zero based height g of the node index i

Given:

  • i the index of any mmr node.

We define index_height as

  def index_height(i) -> int:
    pos = i + 1
    while not all_ones(pos):
      pos = pos - most_sig_bit(pos) + 1

    return bit_length(pos) - 1

9.2. peaks

peaks(i) returns the peak indices for MMR(i+1), which is also its accumulator.

Assumes MMR(i+1) is complete, implementations can check for this condition by testing the height of i+1

Given:

  • i the index of any mmr node.

We define peaks

  def peaks(i):
    peak = 0
    peaks = []
    s = i+1
    while s != 0:
      # find the highest peak size in the current MMR(s)
      highest_size = (1 << log2floor(s+1)) - 1
      peak = peak + highest_size
      peaks.append(peak-1)
      s -= highest_size

    return peaks

10. Security Considerations

See the security considerations section of:

11. IANA Considerations

Editors note: Hash agility is desired. We can start with SHA-256. Two of the referenced implementations use BLAKE2b-256, We would like to add support for SHA3-256, SHA3-512, and possibly Keccak and Pedersen.

11.1. Additions to Existing Registries

Editors note: todo registry requests

12. Normative References

[RFC2119]
Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, , <https://www.rfc-editor.org/rfc/rfc2119>.
[RFC8174]
Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, , <https://www.rfc-editor.org/rfc/rfc8174>.
[RFC9053]
Schaad, J., "CBOR Object Signing and Encryption (COSE): Initial Algorithms", RFC 9053, DOI 10.17487/RFC9053, , <https://www.rfc-editor.org/rfc/rfc9053>.

Appendix A. References

Appendix B. Assumed bit primitives

B.1. log2floor

Returns the floor of log base 2 x

  def log2floor(x):
    return x.bit_length() - 1

B.2. most_sig_bit

Returns the mask for the the most significant bit in pos

  def most_sig_bit(pos) -> int:
    return 1 << (pos.bit_length() - 1)

The following primitives are assumed for working with bits as they commonly have library or hardware support.

B.3. bit_length

The minimum number of bits to represent pos. b011 would be 2, b010 would be 2, and b001 would be 1.

  def bit_length(pos):
    return pos.bit_length()

B.4. all_ones

Tests if all bits, from the most significant that is set, are 1, b0111 would be true, b0101 would be false.

  def all_ones(pos) -> bool:
    msb = most_sig_bit(pos)
    mask = (1 << (msb + 1)) - 1
    return pos == mask

B.5. ones_count

Count of set bits. For example ones_count(b101) is 2

B.6. trailing_zeros

The count of nodes above and to the left of pos

  (v & -v).bit_length() - 1

Appendix C. Implementation Status

Note to RFC Editor: Please remove this section as well as references to BCP205 before AUTH48.

This section records the status of known implementations of the protocol defined by this specification at the time of posting of this Internet-Draft, and is based on a proposal described in BCP205. The description of implementations in this section is intended to assist the IETF in its decision processes in progressing drafts to RFCs. Please note that the listing of any individual implementation here does not imply endorsement by the IETF. Furthermore, no effort has been spent to verify the information presented here that was supplied by IETF contributors. This is not intended as, and must not be construed to be, a catalog of available implementations or their features. Readers are advised to note that other implementations may exist.

According to BCP205, "this will allow reviewers and working groups to assign due consideration to documents that have the benefit of running code, which may serve as evidence of valuable experimentation and feedback that have made the implemented protocols more mature. It is up to the individual working groups to use this information as they see fit".

C.1. Implementers

C.1.1. DataTrails

An open-source implementation was initiated and is maintained by Data Trails Inc. - DataTrails.

Uses SHA-256 as the hash alg

C.1.1.1. Implementation Name

An application demonstrating the concepts is available at https://app.datatrails.ai/.

C.1.1.2. Implementation URL

An open-source implementation is available at:

  • https://github.com/datatrails/go-datatrails-merklelog

C.1.1.3. Maturity

Used in production. SEMVER unstable (no backwards compat declared yet)

C.1.2. Robin Bryce (1)

C.1.2.1. Implementation URL

A minimal reference implementation of this draft. Used to generate the test vectors in this draft, is available at:

  • https://github.com/robinbryce/merkle-mountain-range-proofs/blob/main/algorithms.py

C.1.2.2. Maturity

Reference only

C.1.3. Robin Bryce (2)

C.1.3.1. Implementation URL

A minimal tiled log implementation

  • https://github.com/robinbryce/mmriver-tiles-ts

C.1.4. Mimblewimble

Is specifically committing to positions as we describe, but is committing zero based indices, and uses BLAKE2B as the HASH-ALG. Accounting for those differences, their commitment trees would be compatible with this draft.

C.1.4.1. Implementation URL

An implementation is available here:

  • https://github.com/mimblewimble/grin/blob/master/doc/mmr.md (Grin is a rust implementation of the mimblewimble protocol)

  • https://github.com/BeamMW/beam/blob/master/core/merkle.cpp (Beam is a C++ implementation of the mimblewimble protocol)

C.1.5. Herodotus

C.1.5.1. Implementation URL

https://github.com/HerodotusDev/rust-accumulators

Production, supports keccak, posiedon & pedersen hash algs

Editors note: test vectors, based on a SHA256 instantiation, are currently provided in a separate document. (./test-vectors.md)

Acknowledgments

Author's Address

Robin Bryce
DataTrails