### A Cryptosystem based on Topological Space

#### Abstract

The study of surface is topology. This paper uses some characteristics of knot theory and develops a public key cryptosystem. A topologically, algebraically one way trapdoor function-based knot cryptography. A link is a set of one or more closed loops in three-dimensional space. The individual loops are called the components of the link. The loops can be twisted or knotted. If there is only one loop, the link is called knot. The knot theory becomes fruitful after the discovery of Jones Polynomial. These knots are represented by three-dimensional geometry and polynomials both. But here we took an example on those knots, which can be represented by two variables; this is known by HOMFLY polynomial. HOMFLY is the compact version of the first letter of its discoverer, Hoste, Ocneanu, Millette, Freyd, Lickorish, and Yetter. There are several types of knot polynomials. Our proposed cryptography is based on all those knot polynomials, which are fit on the machinery of topology.

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DOI: https://doi.org/10.37591/joces.v11i2.849

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