Problem: Enhanced Cryptographic Merkle Tree Functions

The problem involves building a secure Merkle tree system for transactions, integrating enhanced cryptographic hashing, transaction leaf generation, optimal tree level computation, and root derivation to produce robust, verifiable tree structures for data integrity and blockchain applications.

Background: ### Industry & Mathematical Background Knowledge for Code Reproduction
This set of functions implements an enhanced, secure Merkle tree system optimized for integrity verification, post-quantum resistance, and performance—common requirements in blockchain, secure data storage, and tamper-proof audit systems. Below is the critical domain knowledge to reproduce the code:

#### 1. Cryptographic Hash Enhancements (for `mock_hash`)
- **SHA-256 Foundation**: A NIST-standard cryptographic hash function used globally for data integrity. The code extends it with post-quantum and confusion/diffusion transformations.
- **Safe Primes & Modular Exponentiation**: Safe primes (primes `p` where `(p-1)/2` is also prime) are core to post-quantum lattice-based cryptography. The 256-bit NIST-approved safe prime used enables modular squaring operations that resist quantum factorization attacks.
- **AES-style S-box Substitution**: Non-linear substitution tables (S-boxes) introduce "confusion"—making input-output relationships non-trivial to reverse. The simplified AES S-box in the code increases cryptographic complexity.
- **MDS Matrix Diffusion**: Maximum Distance Separable (MDS) matrices ensure every output bit depends on every input bit (diffusion), a standard in AES/SHA-3. The 4x4 MDS matrix over GF(256) spreads byte influence across the hash.
- **Feedback Hashing Rounds**: Multi-round hashing with XOR feedback follows the Merkle-Damgård construction, compounding security to resist collision/preimage attacks.

#### 2. Merkle Leaf Generation (for `hash_leaves`)
- **Context-Bound Leaf Hashes**: Leaves bind transactions to their position in the tree using polynomial evaluation, preventing leaf-swapping attacks.
- **PBKDF2 Key Derivation**: A NIST-standard function that uses SHA-256 with 100k iterations to derive per-transaction keys from a master key and salt. This avoids key reuse and resists brute-force attacks.
- **HMAC Authentication**: HMAC-SHA256 verifies transaction integrity/authenticity before hashing into leaves, ensuring only valid transaction data contributes to the tree.
- **Parallel Processing**: `ThreadPoolExecutor` optimizes leaf computation for large transaction batches, a standard practice in high-throughput systems like blockchain nodes.
- **Secure Salting**: Cryptographically random salts (`secrets.token_bytes`) prevent precomputation attacks on leaf hashes.

#### 3. Optimized Merkle Tree Level Construction (for `compute_next_level`)
- **Odd-Length Padding**: Duplicating the last node for odd-length levels ensures balanced tree construction, a requirement for standard Merkle tree traversal.
- **Similarity-Based Greedy Pairing**: Nodes are paired by minimizing Hamming distance (differing bits in hashes) to optimize tree entropy—useful for zero-knowledge proofs and efficient updates.
- **Vector Normalization**: Lists/numpy arrays are scaled to the [0,1] range before hashing, enabling support for structured data (e.g., ML models) in Merkle trees.
- **Salted Pair Combination**: Random salts when combining pairs prevent precomputation of internal node hashes, adding another layer of security.

#### 4. Merkle Root Calculation (for `get_merkle_root`)
- **Dual Hash XOR**: Combining SHA-256 and Blake2b hashes via XOR provides redundancy—if one hash is compromised, the result remains secure. Blake2b is a fast, modern alternative to SHA-256.
- **Prefix Separation**: Distinct prefixes (0x00 for leaves, 0x01 for internal nodes) prevent collision attacks where leaf and internal node hashes could be confused, a standard in blockchain Merkle trees (e.g., Bitcoin).
- **Iterative Level Reduction**: The code iteratively reduces tree levels to compute the root efficiently, minimizing memory usage for large transaction sets.

#### Required Library Context
- `hashlib`: Implements standard cryptographic hash functions (SHA-256, Blake2b).
- `secrets`: Generates cryptographically secure random salts (critical for avoiding predictable hashes).
- `struct`: Packs/unpacks numerical data between bytes and integers for polynomial and key operations.
- `concurrent.futures.ThreadPoolExecutor`: Enables parallel processing for large-scale leaf generation.
- `numpy`: Handles vector data normalization and conversion for structured data inputs.
- `functools.lru_cache`: Caches intermediate results to optimize repeated hash computations in `mock_hash`.

Input/Output: The problem takes four inputs: 1) a UTF-8 encodable string for the mock_hash function; 2) an Iterable of transactions (each bytes or string) for hash_leaves; 3) a list (current_level) of strings, float-convertible lists, or float-convertible numpy arrays for compute_next_level; 4) an Iterable of transactions (each string, bytes, or numpy.ndarray if installed) for get_merkle_root. The problem generates four outputs: 1) a 64-character hexadecimal string from mock_hash (enhanced SHA-256 hash); 2) a list of bytes from hash_leaves (enhanced cryptographic leaves); 3) a list of SHA-256 hex strings from compute_next_level (next Merkle tree level); 4) a hexadecimal string from get_merkle_root (Merkle root of transactions). Each input undergoes validation and cryptographic operations (e.g., modular exponentiation, S-box substitution, parallel hashing, Merkle pairing) to produce the corresponding output.

Required dependencies:
import hashlib
from functools import lru_cache
import struct
from concurrent.futures import ThreadPoolExecutor
import secrets
import hmac
from typing import Iterable, Union, List, Any
import numpy as np

Sub-steps:
step_number: 1
step_description_prompt: Please write a Python function named mock_hash. It validates input string, encodes to UTF-8. Applies SHA-256 with modular exponentiation (safe prime), S-box substitution + bit reversal, linear transformation + MDS matrix, feedback hashing rounds, returns a 64-character hex string. Handle type and value errors appropriately.

function_header: def mock_hash(data_str):
test_cases: import hashlib
test_data_hash = [
    ("", "e93902d56da68b5a3b2fcca099960bc9159ee328d69a73dd484f5fb64323a2e0"),  # Updated: Enhanced hash with lattice-based operations
    ("a", "2ef8f3cd8bd78642f66975cf53a12f3b48353e98b4891d6badeeea164d496e7c"),  # Updated: Enhanced hash
    ("123", "7bc3f9cd0d38d07c2085b07dcdaed7ae3da623bf385dcf92957e724a7cc98c50")  # Updated: Enhanced hash
]
for data, expected in test_data_hash:
    assert mock_hash(data) == expected

step_number: 2
step_description_prompt: Please write a Python function named hash_leaves that takes an Iterable of transactions (bytes/str) and returns enhanced crypto leaves. Steps: validate/convet tx to bytes → derive master key and poly coefficients → parallel compute each leaf (salt, PBKDF2 key, HMAC, poly value at index+1 → hash combo). Handle empty tx, invalid types, crypto errors.
function_header: def hash_leaves(transactions):
test_cases: import hashlib
# Test skipped - hash_leaves uses random salt, results are non-deterministic
# test_data_leaves = [
#     (["a"], ["ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb"]),
#     (["a", "b"], ["ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb",
#                   "3e23e8160039594a33894f6564e1b1348bbd7a0088d42c4acb73eeaed59c009d"]),
#     ([], [])
# ]
# for txs, expected in test_data_leaves:
#     assert hash_leaves(txs) == expected

step_number: 3
step_description_prompt: Please write a Python function named compute_next_level. This function generates the next level of a Merkle tree from a list: validates input elements (str, list, numpy array), pads if odd length, computes SHA256 digests for each element, pairs optimally using similarity-based greedy matching, combines pairs with salt, and returns hashed next level.
function_header: def compute_next_level(current_level):
test_cases: import hashlib
h1 = "ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb" # hash of 'a'
h2 = "3e236511ba0309503096d8427367d130c25fdbef6705660888257002e230554c" # hash of 'b'
test_data_level = [
    ([h1, h2], 1),    # 偶数个节点：2个变为1个
    ([h1, h2, h1], 2), # 奇数个节点：3个变为2个 (末尾复制)
    ([h1], 1)          # 单个节点：1个变为1个 (复制自身再哈希)
]
for level, exp_len in test_data_level:
    res = compute_next_level(level[:]) # 传入副本防止修改原列表
    assert len(res) == exp_len
    # Note: compute_next_level uses random salt, so exact hash match is not possible
    # We only verify the length is correct

step_number: 4
step_description_prompt: Please write a Python function named get_merkle_root that takes an iterable of transactions (str, bytes, or numpy.ndarray if installed). Compute leaf hashes via SHA256 and Blake2b (prefix 0x00) XORed. Build Merkle tree: pair nodes, hash each pair (prefix0x01, same hash combo), repeat until root. Return root's hex string.
function_header: def get_merkle_root(transactions):
test_cases: import hashlib
test_data_root = [
    (["a"], "701e6157fb0a02465029b262b93eb76405bd9727352fcfea148f5f82d19a2fba"), # 单交易根即其哈希
    (["a", "b"], "af5b6ba057b8965d4f290f6d89732671d0f666260210412f14af9f2503cbc588"), # hash(hash(a)+hash(b))
    ([], "") # 空交易返回空字符串
]
for txs, expected in test_data_root:
    actual = get_merkle_root(txs)
    assert actual == expected

General solution:

General tests: