SPIP: A Cryptographic Primitive Symbolic And Chaotic Maps
Symbolic Path Inversion Issue
Symbolic Path Inversion challenge (SPIP) is a new computing challenge based on Chaotic Symbolic's complex dynamics. The chaotic evolution of symbolic pathways underpins it. Reversing these symbolic lines is the problem.
Cryptographic systems must survive quantum computers threats, hence a new issue is needed. Cryptographic methods sometimes depend on how difficult algebraic mathematical riddles are to solve. However, these algebraic structures may have flaws that advanced algorithms, especially quantum computer algorithms, can exploit. This issue is prompting scholars to investigate cryptography foundations based on systems without built-in symmetries.
Mohamed Aly Bouke and colleagues propose the SPIP, which eliminates algebraic structures like rings and vector spaces, to reduce vulnerability to such advanced attacks. SPIP is introduced in "Towards a Non-Algebraic Post-Quantum Hardness Assumption".
Iterated Function Systems (IFS) underpin SPIP. IFS has contraction mappings. These tweaks consistently move points closer. Repeating these mappings creates complicated fractal attractors. This system uses affine maps, which combine translation and linear transformation. The successively applied transformations, or affine maps, were retrieved from the IFS in the “symbolic paths” order. To complicate inversion and path reversal, bounded noise is added. The underlying difficulty of reversing these symbolic paths underpins SPIP's hardness assumption, experts say.
A key finding of SPIP is its resistance to Grover's approach. Grover's algorithm is a prominent quantum method for cryptographic algorithm quantum security. The researchers found Grover's technique to SPIP solution ineffective. Grover's algorithm's verification oracle, which confirms a solution's correctness, is unstable and unclear, which is why it resists.
The system's non-algebraic nature, chaotic symbolic evolution, and rounding-induced non-injectivity make it resistant to quantum attacks. A single output or symbolic trajectory segment might come from several beginning inputs or map sequences, which is called non-injectivity. This makes reverse engineering the exact route followed difficult, if not impossible. This uncertainty hinders Grover's approach and other algorithms that validate possible responses.
Formal research has determined SPIP's computational complexity. PSPACE-hard and #P-hard problems have been identified.
PSPACE-hardness means solving SPIP would require exponential memory or space relative to the problem instance.
It is computationally difficult to count all SPIP instance solutions with P-hardness (called “sharp P-hardness”). Counting alternative options shows how difficult it is to find a precise solution.
These theoretical SPIP hardness findings are well supported by the researchers' simulations. These simulations indicated an exponential growth in viable trajectories that could result in a given outcome, even with small symbolic sequences. The exponentially quick development in ambiguity makes it harder to invert or reverse the procedure to get the symbolic path.
This method is unique in post-quantum cryptography. Numerous PQC techniques in development, such as lattice-based ones, rely on algebraic mathematics issues. These structures are different from those vulnerable to current attacks, but SPIP takes a different approach. It proposes using dynamical systems' complexity and chaos to create encryption algorithms that are impervious to classical and quantum attacks.
SPIP research is still theoretical, despite its excellent theoretical foundations. More research is needed to turn these theoretical notions into viable cryptography algorithms. This requires a detailed review of their security guarantees in real-world settings, performance attributes, and feasibility of implementation.
Quantum Zeitgeist published these data. The website covers quantum computing and related technology. Alan, the Quantum News Hound, wrote it. The website disclaimer states that the content is from reliable sources but cannot guarantee its completeness, correctness, usage, efficacy, or accuracy. Quantum Zeitgeist notes that third-party information, including the scientific paper, has not been verified.
In conclusion
The Symbolic Path Inversion cryptographic challenge is based on the difficulty of reversing symbolic trajectories produced by chaotic iterated function systems with noise. It may withstand quantum computer attacks due to its non-algebraic nature. Data shows exponential ambiguity in possible solutions, supporting PSPACE-hard and #P-hard designations. The chaotic system's instability, ambiguity, and non-injectivity make SPIP explicitly resistant to Grover's technique. A clear and promising path for post-quantum cryptography is shown.