Result (512-bit Hash):
The hash will appear here...
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Operating Principles of the P-Hash Algorithm
The P-Hash algorithm is a cryptographic hash function whose behavior is not based on traditional Boolean operations or modular arithmetic, but on the evolution of a complex system derived from the P System. The digital fingerprint of data emerges from the chaotic but deterministic dynamics of the Selective Genealogical Algorithm (SGA), the generative engine of the P System.
Seeding Phase
The input (text or file) is read as a sequence of bytes. To ensure the system's self-sufficiency, the algorithm itself generates a deterministic list of prime numbers that serves as a universal mapping. Each byte of the input is mapped to a prime number from this list. The resulting sequence of primes is then composed with an internal structural constant and combined through an iterative process to produce a Compact Numerical Seed. This seed represents the input in a unique and ordered numerical form, ready to initialize the generative process.
Processing Phase (Propagation)
The Compact Numerical Seed is provided as an initial parameter to the Selective Genealogical Algorithm (SGA). The SGA executes a fixed number of 1,000,000 iterations. At each step of the process, the seed dynamically perturbs the calculation of future "jobs" within the SGA's Propagation Queue. This continuous perturbation, applied to an inherently non-linear system, creates a chaotic and unique evolutionary trajectory, extremely sensitive to the slightest variations in the initial seed (avalanche effect).
Harvesting Phase
At the end of the iterations, the final state of the SGA is analyzed. The Morphogenetic Signature of the P System (composed of the parameters delta, nu, phi, rho, omega) is calculated on the entire sequence of promoters that emerged during propagation. This signature, which captures the qualitative "history" of the evolution, is combined with the last 32 promoters generated. The set of this structured data is finally processed by a standard extraction function (SHA-512) to produce the final 512-bit hash in hexadecimal format.
Analysis and Features
Unlike algorithms such as SHA-256, whose security is based on the complexity of inverting Boolean logic functions, P-Hash security is based on a different principle: the computational difficulty of reversing the evolution of a complex and generative system. Instead of a single difficult mathematical function, P-Hash resistance is distributed across a million interdependent steps. Attempting to trace back to the original input from the final hash is like trying to calculate backward the exact path of a leaf in a hurricane, starting only from its final position.
- Generative Architecture: The hash function is the emergent result of a simulation process (the SGA), not a direct calculation.
- Source of Complexity: The chaoticity derives from the emergence dynamics of prime numbers, a behavior studied in number theory for its apparent randomness.
- Morphogenetic Signature: The use of the P System signature introduces a qualitative and structural analysis in the hashing process.
- Post-Quantum Potential: Based on a computational problem not linked to factorization or discrete logarithms, P-Hash is a candidate for post-quantum cryptography.
- Transparency: The algorithm is an open research project and its source code will be made available for public analysis.