COSE R. Bryce Internet-Draft DataTrails Intended status: Experimental 21 October 2024 Expires: 24 April 2025 Merkle Mountain Range for Immediately Verifiable and Replicable Commitments draft-bryce-cose-merkle-mountain-range-proofs-00 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 (https://eprint.iacr.org/2015/718.pdf). The technical advantages of post-order traversal binary Merkle trees are discussed in CrosbyWallachStorage (https://static.usenix.org/event/sec09/tech/full_papers/crosby.pdf) and PostOrderTlog (https://research.swtch.com/tlog#appendix_a). Status of This Memo This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet- Drafts is at https://datatracker.ietf.org/drafts/current/. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." This Internet-Draft will expire on 24 April 2025. Copyright Notice Copyright (c) 2024 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (https://trustee.ietf.org/ license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights Bryce Expires 24 April 2025 [Page 1] Internet-Draft MMRIVER October 2024 and restrictions with respect to this document. Code Components extracted from this document must include Revised BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Revised BSD License. Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Conventions and Definitions . . . . . . . . . . . . . . . . . 3 3. Verifiable Data Structure . . . . . . . . . . . . . . . . . . 4 4. Inclusion Proof . . . . . . . . . . . . . . . . . . . . . . . 4 4.1. inclusion_proof_path . . . . . . . . . . . . . . . . . . 4 5. Receipt of Inclusion . . . . . . . . . . . . . . . . . . . . 5 5.1. Verifying the Receipt of inclusion . . . . . . . . . . . 6 5.2. included_root . . . . . . . . . . . . . . . . . . . . . . 7 6. Consistency Proof . . . . . . . . . . . . . . . . . . . . . . 8 6.1. consistency_proof_path . . . . . . . . . . . . . . . . . 9 7. Receipt of Consistency . . . . . . . . . . . . . . . . . . . 10 7.1. Verifying the Receipt of consistency . . . . . . . . . . 10 7.1.1. consistent_roots . . . . . . . . . . . . . . . . . . 11 8. Appending a leaf . . . . . . . . . . . . . . . . . . . . . . 12 8.1. add_leaf_hash . . . . . . . . . . . . . . . . . . . . . . 12 8.2. Implementation defined storage methods . . . . . . . . . 14 8.2.1. Get . . . . . . . . . . . . . . . . . . . . . . . . . 14 8.2.2. Append . . . . . . . . . . . . . . . . . . . . . . . 14 8.3. Node values . . . . . . . . . . . . . . . . . . . . . . . 14 8.3.1. hash_pospair64 . . . . . . . . . . . . . . . . . . . 14 9. Essential supporting algorithms . . . . . . . . . . . . . . . 15 9.1. index_height . . . . . . . . . . . . . . . . . . . . . . 15 9.2. peaks . . . . . . . . . . . . . . . . . . . . . . . . . . 16 10. Security Considerations . . . . . . . . . . . . . . . . . . . 16 11. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 16 11.1. Additions to Existing Registries . . . . . . . . . . . . 16 11.2. New Registries . . . . . . . . . . . . . . . . . . . . . 16 12. Normative References . . . . . . . . . . . . . . . . . . . . 16 Appendix A. References . . . . . . . . . . . . . . . . . . . . . 17 A.1. Informative References . . . . . . . . . . . . . . . . . 17 Appendix B. Assumed bit primitives . . . . . . . . . . . . . . . 17 B.1. log2floor . . . . . . . . . . . . . . . . . . . . . . . . 17 B.2. most_sig_bit . . . . . . . . . . . . . . . . . . . . . . 18 B.3. bit_length . . . . . . . . . . . . . . . . . . . . . . . 18 B.4. all_ones . . . . . . . . . . . . . . . . . . . . . . . . 18 B.5. ones_count . . . . . . . . . . . . . . . . . . . . . . . 18 B.6. trailing_zeros . . . . . . . . . . . . . . . . . . . . . 18 Appendix C. Implementation Status . . . . . . . . . . . . . . . 18 C.1. Implementers . . . . . . . . . . . . . . . . . . . . . . 19 C.1.1. DataTrails . . . . . . . . . . . . . . . . . . . . . 19 C.1.2. Robin Bryce (1) . . . . . . . . . . . . . . . . . . . 19 Bryce Expires 24 April 2025 [Page 2] Internet-Draft MMRIVER October 2024 C.1.3. Robin Bryce (2) . . . . . . . . . . . . . . . . . . . 20 C.1.4. Mimblewimble . . . . . . . . . . . . . . . . . . . . 20 C.1.5. Herodotus . . . . . . . . . . . . . . . . . . . . . 20 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 21 Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 21 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. * A complete MMR(n) defines an mmr with n nodes where no equal height sibling trees exist. * i shall be the index of any node, including leaf nodes, in the MMR * g shall be the zero based height of a node in the tree. * H(x) shall be the SHA-256 digest of any value x * || shall mean concatenation of raw byte representations of the referenced values. Bryce Expires 24 April 2025 [Page 3] Internet-Draft MMRIVER October 2024 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: * index_height (Section 9.1) which obtains the zero based height g of any node. And the constraints: * i <= c We define inclusion_proof_path as Bryce Expires 24 April 2025 [Page 4] Internet-Draft MMRIVER October 2024 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: Bryce Expires 24 April 2025 [Page 5] Internet-Draft MMRIVER October 2024 protected-header-map = { &(alg: 1) => int &(vds: 395) => 2 * cose-label => cose-value } * alg (label: 1): REQUIRED. Signature algorithm identifier. Value type: int. * vds (label: 395): REQUIRED. verifiable data structure algorithm identifier. Value type: int. 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. Bryce Expires 24 April 2025 [Page 6] Internet-Draft MMRIVER October 2024 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: * index_height (Section 9.1) which obtains the zero based height g of any node. * hash_pospair64 (Section 8.3.1) which applies H to the new node position and its children. We define included_root as Bryce Expires 24 April 2025 [Page 7] Internet-Draft MMRIVER October 2024 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 (https://eprint.iacr.org/2015/718.pdf), 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. Bryce Expires 24 April 2025 [Page 8] Internet-Draft MMRIVER October 2024 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: * inclusion_proof_path (Section 4.1) * Section 9.2 And the constraints: * ifrom <= ito We define consistency_proof_paths as Bryce Expires 24 April 2025 [Page 9] Internet-Draft MMRIVER October 2024 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 } * alg (label: 1): REQUIRED. Signature algorithm identifier. Value type: int. * vds (label: 395): REQUIRED. verifiable data structure algorithm identifier. Value type: int. 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. Bryce Expires 24 April 2025 [Page 10] Internet-Draft MMRIVER October 2024 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. Bryce Expires 24 April 2025 [Page 11] Internet-Draft MMRIVER October 2024 * 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: * included_root (Section 5.2) * Section 9.2 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: Bryce Expires 24 April 2025 [Page 12] Internet-Draft MMRIVER October 2024 * 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: * index_height (Section 9.1) * Section 8.3.1 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 Bryce Expires 24 April 2025 [Page 13] Internet-Draft MMRIVER October 2024 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 Bryce Expires 24 April 2025 [Page 14] Internet-Draft MMRIVER October 2024 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 Bryce Expires 24 April 2025 [Page 15] Internet-Draft MMRIVER October 2024 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: * [RFC9053] 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 11.2. New Registries 12. Normative References Bryce Expires 24 April 2025 [Page 16] Internet-Draft MMRIVER October 2024 [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997, . [RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, May 2017, . [RFC9053] Schaad, J., "CBOR Object Signing and Encryption (COSE): Initial Algorithms", RFC 9053, DOI 10.17487/RFC9053, August 2022, . Appendix A. References A.1. Informative References * ReyzinYakoubov (https://eprint.iacr.org/2015/718.pdf) * CrosbyWallach (https://static.usenix.org/event/sec09/tech/full_papers/ crosby.pdf) * CrosbyWallachStorage (https://static.usenix.org/event/sec09/tech/full_papers/ crosby.pdf) 3.3 Storing the log on secondary storage * PostOrderTlog (https://research.swtch.com/tlog#appendix_a) * PeterTodd (https://lists.linuxfoundation.org/pipermail/bitcoin- dev/2016-May/012715.html) * KnuthTBT (https://www-cs-faculty.stanford.edu/~knuth/taocp.html) 2.3.1 Traversing Binary Trees * BNT (https://eprint.iacr.org/2021/038.pdf) Appendix B. Assumed bit primitives B.1. log2floor Returns the floor of log base 2 x def log2floor(x): return x.bit_length() - 1 Bryce Expires 24 April 2025 [Page 17] Internet-Draft MMRIVER October 2024 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. Bryce Expires 24 April 2025 [Page 18] Internet-Draft MMRIVER October 2024 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/ (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: Bryce Expires 24 April 2025 [Page 19] Internet-Draft MMRIVER October 2024 * 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.1.3.2. Maturity Prototype 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) Bryce Expires 24 April 2025 [Page 20] Internet-Draft MMRIVER October 2024 Acknowledgments Author's Address Robin Bryce DataTrails Email: robinbryce@gmail.com Bryce Expires 24 April 2025 [Page 21]