An Application of Interior and Closure in General Topology: A Key Agreement Protocol

Abstract

In this paper, a new key agreement scheme is constructed using the notions of the interior of a set, the closure of a set, open function, closed function, continuous function in topological spaces. An implementation of this scheme is presented between the two parties and it is shown that they generate the common secret key.

Keywords

• closure
• interior
• cryptography
• key agreement

References

1. Douglas R Stinson. Cryptography: theory and practice. Chapman and Hall/CRC, 2005.
2. Ralph C Merkle. Secure communications over insecure channels. Communications of the ACM, 21(4):294–299, 1978.
3. Whitfield Diffie and Martin Hellman. New directions in cryptography. IEEE transactions on Information Theory, 22(6):644–654, 1976.
4. Juha Partala. Algebraic generalization of diffie–hellman key exchange. Journal of Mathematical Cryptology, 12(1):1–21, 2018.
5. Colin Conrad Adams and Robert David Franzosa. Introduction to topology: pure and applied. Pearson Prentice Hall Upper Saddle River, 2008.
6. John L Kelley. General topology. Courier Dover Publications, 2017.
7. James Munkres. Topology: Pearson New International Edition. Pearson, 2013.