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HashX7 Algorithm Calculation

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6zip-online edited this page Jul 23, 2024 · 1 revision

Understanding the HashX7 Algorithm

To illustrate how the HashX7 Algorithm processes example data, we need to walk through the steps involved in hashing a block header using HashX7. This document provides a detailed step-by-step calculation and explanation of the process.

Data

Let's assume the following block header values:

  • nVersion: 1
  • hashPrevBlock: 0x0000000000000000000a1b2c3d4e5f67890abcdef1234567890abcdef123456 (256-bit hash, represented as a 64-character hex string)
  • hashMerkleRoot: 0xabcdef1234567890abcdef1234567890abcdef1234567890abcdef1234567890
  • nTime: 1633072800 (Unix timestamp)
  • nBits: 0x1d00fff0 (Difficulty target)
  • nNonce: 2083236893

Step-by-Step Calculation

1. Serialize the Block Header

The block header is serialized into a vector of bytes (vch). Here’s a simplified representation of the serialized data:

// Serialized data (example)
std::vector<unsigned char> vch = {
    // nVersion (4 bytes)
    0x01, 0x00, 0x00, 0x00,
    // hashPrevBlock (32 bytes)
    0x00, 0x00, 0x00, 0x00, /* ... more bytes ... */ 0xef, 0x12, 0x34,
    // hashMerkleRoot (32 bytes)
    0xab, 0xcd, 0xef, /* ... more bytes ... */ 0x90, 0x78, 0x56, 0x78,
    // nTime (4 bytes)
    0x00, 0x00, 0x4d, 0x3b,
    // nBits (4 bytes)
    0xff, 0x00, 0x1d, 0x00,
    // nNonce (4 bytes)
    0x15, 0x8b, 0x9d, 0x7d
};

## Step-by-Step Calculation 

### 2. Convert Timestamp

Let `prevTimestamp` (obtained from `GetBlockTime()`) be  `1633072800`.

### 3. Hash Calculation Using HashX7

The `HashX7` Algorithm processes this serialized data and timestamp as follows:

1. **Blake512 Hashing**

   - **Input Data**: `vch` concatenated with `timestamp`.
   - **Output Hash**: `H_0`

   Blake512 applies its hash function to the combined data of the serialized block header and timestamp. This produces the first intermediate hash value, `H_0`.

2. **BMW512 Hashing**

   - **Input Data**: `H_0`
   - **Output Hash**: `H_1`

   BMW512 then hashes `H_0`, yielding the second intermediate hash value, `H_1`.

3. **XOR Operation (First XOR)**

   - **XOR** `H_0` and `H_1`
   - **Result**: `X_0`

   Perform an XOR operation between `H_0` and `H_1`. This adds complexity and mixes the bits, resulting in `X_0`.

4. **Groestl512 Hashing**

   - **Input Data**: `X_0`
   - **Output Hash**: `H_2`

   Groestl512 hashes `X_0`, producing the next intermediate hash value, `H_2`.

5. **Skein512 Hashing**

   - **Input Data**: `H_2`
   - **Output Hash**: `H_3`

   Skein512 processes `H_2` to generate `H_3`.

6. **XOR Operation (Second XOR)**

   - **XOR** `H_2` and `H_3`
   - **Result**: `X_1`

   Perform another XOR operation between `H_2` and `H_3`, resulting in `X_1`.

7. **Keccak512 Hashing**

   - **Input Data**: `X_1`
   - **Output Hash**: `H_4`

   Keccak512 hashes `X_1`, producing `H_4`.

8. **Luffa512 Hashing**

   - **Input Data**: `H_4`
   - **Output Hash**: `H_5`

   Luffa512 hashes `H_4` to yield `H_5`.

9. **Echo512 Hashing**

   - **Input Data**: `H_5`
   - **Output Hash**: `H_6`

   Echo512 processes `H_5` to produce `H_6`.

10. **Final XOR Operation**

    - **XOR** `H_5` and `H_6`
    - **Result**: `X_2`

    Perform the final XOR operation between `H_5` and `H_6`, resulting in `X_2`.

11. **Return Final Hash**

    - **Trim** `X_2` to 256 bits if necessary.

    The result `X_2` is trimmed to 256 bits if it exceeds this size, providing the final hash output.

## Calculation with Real Data

Assuming you have an block header and timestamp, you can compute the hashes as follows:

1. **Initialize Blake512** with `vch` and `timestamp`.
   - **Result**: `H_0`

2. **Initialize BMW512** with `H_0`.
   - **Result**: `H_1`

3. **Compute XOR** of `H_0` and `H_1`.
   - **Result**: `X_0`

4. **Initialize Groestl512** with `X_0`.
   - **Result**: `H_2`

5. **Initialize Skein512** with `H_2`.
   - **Result**: `H_3`

6. **Compute XOR** of `H_2` and `H_3`.
   - **Result**: `X_1`

7. **Initialize Keccak512** with `X_1`.
   - **Result**: `H_4`

8. **Initialize Luffa512** with `H_4`.
   - **Result**: `H_5`

9. **Initialize Echo512** with `H_5`.
   - **Result**: `H_6`

10. **Compute XOR** of `H_5` and `H_6`.
    - **Result**: `X_2`

11. **Trim** `X_2` to 256 bits to get the final hash.

## Mathematical Illustration

For each step:

- **Hash Algorithm**: Each cryptographic hash algorithm applies complex transformations to its input data, generating a unique fixed-size output.
- **XOR Operations**: XOR combines the binary representations of two hash outputs, adding a layer of complexity and ensuring that the final hash depends on all intermediate values.

By combining multiple hashing algorithms and XOR operations, `HashX7` provides a robust and secure hash that is resistant to various types of cryptographic attacks. The final result ensures that every block header has a unique and tamper-proof identifier.

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