I want to present to you an abstract provided after asking ChatGPT to synthesize specific ideas and concepts. I will present my additions in italics and I hope that after reading, you could envision the background of such a system of locks.

Abstract

In this proposal, we present a novel cryptographic communication system leveraging dynamic prime sets for secure information encoding and decoding. The system comprises two primary sets: primes and non-primes, each defined by specific intervals, both having equal cardinalities and dynamic sizes known only to authorized parties.


Key Components:

Security Measures:

Summarily:

The cryptographic system, based on dynamic prime sets and cyclic ciphers, offers a unique approach to secure communication. Incorporation of dynamic intervals and cyclic transitions adds layers of complexity, and positional symbols allow for a structured and secure information exchange. The proposal outlines a robust framework open for further exploration and refinement in practical secure communication systems.


Operational Details

First Iteration:

Possible Complexities:

Overall Security Measures:

Summarily:

Mathematical Model

Set Representation:

Cyclic Cipher:


Set Transition:

Positional Significance:

Pattern Recognition:

Security Measures:

Limitations:

Sample Operation

First Iteration:

Iterating by 3:

Limitations:

Security Measures in Mathematical Terms:


Conclusion

The mathematical model provides a formal representation of the cryptographic system, incorporating set intervals, cyclic transitions, and operational details. The use of algebraic expressions and mathematical conditions ensures precision and clarity in defining the system's behavior and security measures. This mathematical view lays the foundation for rigorous analysis and potential optimizations of the proposed cryptographic system.”-Chat GPT