An Analytical Approach to Understanding the Principles of Cryptography within the kaṭapayādi System as Reflected in the Works of Nemicandra

Abstract: The kaṭapayādi system is an alphabetic system of numeral notation developed in India. This paper aims to understand the ideas related to cryptography within the kaṭapayādi system, although this system was not developed to hide information. To do this, this paper studies the use of this system in the Gommaṭasāra-Jīvakāṇḍa and Trilokasāra of Nemicandra (981 CE) using an analytical approach. This paper finds that, like the Caesar cipher and Vigenère cipher, the ciphertext in this system is also a substitution cypher, but unlike them, the letters of the Sanskrit alphabet substitute the digits of a number in it with no shift. This system provides multiple ways to encrypt a number. It has symmetric encryption. Correctness property is ensured in it. In it, the writer is the one who encrypts the number into ciphertext, and the one who decrypts the ciphertext into a number is the reader. The key in this system was not a public key, although it was publicly available.