Exploring the Roots of Secure Communication: Indian Knowledge Systems and the Dawn of Number Theory in Cryptography

India has a centuries-long tradition of contribution to mathematics, particularly in the field of cryptography and number theory, and has been a crucible for the development of mathematics throughout the world. The first written record of the binary system was made by ancient Indian scholars based on their work on Sanskrit prosody (Chandahsastra) c. 200 BCE by Pingala; ultimately, it has culminated in our modern binary code employed in digital computation (Kak, 1998). The early work of Aryabhata (c. 5th century CE) utilized methods of modular arithmetic, now commonplace in cryptographic methods such as RSA (Plofker, 2009). Introduction In the Arthashastra of Kautilya (c. 3^rd century BCE), methods of coded communication and information hiding were described as weapons of statecraft, indicating early applications of cryptographic ideas (Rangarajan, 1992). In addition, the work on combinatorial logic and arithmetic by Bhaskara II is consonant with ideas employed today for error correction and secure key exchange (Joseph, 2011). The further investigation of these systems is also pertinent to the development of culturally grounded and mathematically sound models for the modern cryptographic setting.