By Muhammed Shafin P
CC BY SA 4.0 LICENSED
Introduction
In modern encryption, security relies heavily on key secrecy, mathematical complexity, and diffusion mechanisms that prevent attackers from easily reversing the process. The custom encryption system described here introduces a novel method that combines prime-based data mapping, exponentiation, modular arithmetic, and avalanche effects. The core idea is that a single key can control the selection of multiple transformation parameters, making brute-force attacks practically impossible, while maintaining flexibility and high security.
Key Generation and Map Selection
The encryption begins with a master key, which is used to control all subsequent transformations. The key itself does not contain large primes or explicit operation details. Instead, it acts as a selector for one of thousands of predefined prime-mapping tables stored in the library. Each table provides a unique representation of input data - such as UTF‑8 characters - into large prime numbers.
Once the map is chosen, the key also indirectly determines the rules for exponentiation, multiplication, and modular arithmetic applied to each block of data. In addition, the modulus pattern itself is carried by the key, specifying the sequence of moduli to be used for each block. By selecting the map and operational rules, the key effectively governs the entire encryption workflow without needing to carry large numbers directly.
Data Mapping and Transformation
After selecting the map, each block of plaintext is converted into a prime-based numeric representation. This mapping ensures that even small changes in the input data produce significantly different numeric outputs when processed further.
Next, exponentiation is applied to each mapped number, raising it to a power determined by the key. To manage the rapid growth of numbers and introduce additional nonlinearity, a modulus is applied to the exponentiated value. The modulus values follow a pattern carried by the key - for example, the first few blocks might use 100, 56, and so on, repeating as necessary - creating structured yet unpredictable behavior in the ciphertext.
Optional multiplication or division steps can be incorporated, further enhancing the avalanche effect. This ensures that even minor changes in the input or key propagate throughout the ciphertext, making it nearly impossible to predict the result.
Multi-Map Security and Brute-Force Resistance
The system’s strength lies in the combination of thousands of predefined maps and key-derived transformation rules. An attacker attempting a brute-force attack must simultaneously:
- Guess the correct map from thousands of possibilities
- Determine the exponentiation and modular arithmetic rules for each block
- Reverse each prime-mapped block using the correct modular operations
This creates an astronomical number of possible combinations. Even with high-end computing resources, matching all points correctly is practically impossible.
Decryption Process
Decryption is simply the reverse process, guided entirely by the same key:
- The key selects the same prime map from the library
- Each block undergoes inverse modular exponentiation and other arithmetic operations as dictated by the key
- The prime numbers are mapped back to the original data using the selected map
Without the correct key, any attempt to decrypt will fail, as the map, modulus pattern, and exponentiation rules will all be unknown.
Advantages and Flexibility
This encryption system offers several distinct advantages:
- Single-key control - The key indirectly governs the map, modular pattern, and arithmetic operations
- Strong avalanche effect - Small changes in input or key produce large, unpredictable changes in output
- High brute-force resistance - Multi-map selection and per-block transformations make exhaustive attacks infeasible
- Customizable modulus patterns - Predefined patterns, carried by the key, allow for flexibility and additional diffusion
Moreover, this approach can be combined with standard symmetric algorithms for faster processing of large datasets or used independently for secure communication of smaller messages.
Conclusion
The custom prime-based encryption system introduces a novel method that merges prime mapping, key-driven operations, exponentiation, modular arithmetic, and modulus patterns carried by the key into a single, coherent encryption scheme. By leveraging thousands of maps and key-dependent transformations, it achieves high avalanche, strong diffusion, and formidable resistance to brute-force attacks. This concept demonstrates that with careful design, custom numeric-based encryption can be both secure and flexible for modern applications.
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