1. Group Theory Foundations

2. Finite Fields (Galois Fields)

3. Data Representation in

$GF(p^n)$

4. Encryption and Decryption Functions

5. Security Considerations

6. Logical Framework

7. Symbolic Logic Mapping

+---------------------------------------------+
|                                             |
|             System Boundary                 |
|                                             |
|  +-------------------+                      |
|  | Bio-Data Input    |                      |
|  | Module            |                      |
|  +---------+---------+                      |
|            |                                |
|            v                                |
|  +---------+---------+                      |
|  | Data Representation|                     |
|  | Module             |                     |
|  +---------+---------+                      |
|            |                                |
|            v                                |
|  +---------+---------+                      |
|  | Finite Field      |                      |
|  | Operations        |                      |
|  |  +-------------+  |                      |
|  |  | Encryption  |  |                      |
|  |  | Function    |  |                      |
|  |  +------+------|  |                      |
|  |         |         |                      |
|  |         v         |                      |
|  |  +------+------|  |                      |
|  |  | Decryption  |  |                      |
|  |  | Function    |  |                      |
|  |  +-------------+  |                      |
|  +---------+---------+                      |
|            |                                |
|            v                                |
|  +---------+---------+                      |
|  | Decryption Output |                      |
|  | Module            |                      |
|  +-------------------+                      |
|                                             |
+-----------------+---------------------------+
                  |
                  v
+-----------------+---------------------------+
| External Components                          |
|                                             |
|  +-------------------+  +-----------------+ |
|  | Key Management    |  | Encrypted Data  | |
|  | System (KMS)      |  | Storage         | |
|  +---------+---------+  +---------+-------+ |
|            |                      |         |
|            v                      v         |
|  +-------------------+  +-----------------+ |
|  | Communication     |  | Communication   | |
|  | Channel           |  | Channel         | |
|  +-------------------+  +-----------------+ |
|                                             |
+---------------------------------------------+