A New Approach of Cryptographic Application via Unique Fixed Point Results in C* C^ ‐Algebra Valued b b ‐Metric Spaces

ABSTRACT In this paper, we study unique fixed‐point outcomes in ‐algebra valued metric space and their approach to constructing a chaotic system. We demonstrate some fixed‐point theorems without requiring the continuity of self‐mappings in the said space. In favor of our findings, we establish a nontrivial illustrative example to prove the uniqueness of fixed‐point. In addition to validating our results, we present a line graph based on numerical examples to verify the inequality of our single‐valued contraction condition in . Moreover, we construct a computationally efficient chaotic system for a cryptographic algorithm using a unique fixed‐point of a single‐valued contraction condition. However, a fixed‐point contraction itself can hardly fulfill chaotic phenomena. In this connection, we design a jumping algorithm for generating large‐scale chaotic data output around fixed‐point. Meanwhile, we validate the chaos feature of the proposed algorithm via Lyapunov and bifurcation representation.