What’s the undeniable link between modern-day quantum computing, Srinivasa Ramanujan’s mathematical brilliance, and Vedic scholar Vatsyayana?
On the face of it, there is none. But the common thread that ties all of these together is coding and decoding, encryption and decryption, which enables data transfer on the information highway, safe and sound, and at lightning speed.
Unravelling this deep link may provide a clue to Indian quantum thrust, even as China and the United States (US) battle it out for supremacy, bit by bit, all the way.
At a time when cyber wars and cyber security are the buzzwords, India’s itihasa of protecting information may provide the basis for our policy formulation and has a fighting chance to take on the quantum biggies globally.
One of the earliest mentions of a substitution cipher, the basic tenet of encryption and decryption techniques, can be traced to Vatsyayana, the Vedic scholar from the fourth century AD, who laid down the popularly-known mlecchita vikalpa. This technique was known only to amorous partners for the exchange of information in full secrecy. It is also regarded as the oldest form of encoding and decoding information, popular as the Kama Sutra cipher code.
At the heart of cryptography is a branch of mathematics called ‘number theory’ (sankhya siddhanta). It has its roots in the work of eminent mathematicians from ancient India, like Hemachandra, Brahmagupta, Aryabhatta, Pingala, and Panini. Sages and poets in ancient India developed mathematical and numerical knowledge to write poetry, compose music, and study all aspects of human existence. The concept of shunya or zero, for instance, can be traced to Aryabhatiya, a timeless mathematical and astronomical treatise by Aryabhatta, written around 500 CE.
Sanskrit poet Pingala is credited for innovation in the binary number system that laid the foundation for modern-day communication. This has been found in his work Chandahshastra, put together in the second century BCE.
Jain scholar Hemachandra wrote about a numerical series that later came to be known by the name of Italian mathematician Fibonacci. In 628 CE, Brahmagupta expounded on negative and positive numbers, the computation of square roots, and developed algebraic notations to solve quadratic equations. All of these mathematical concepts have led to computational advances in modern times.
Groundbreaking mathematical innovations in this field were carried out by none other than the genius mathematician of the twentieth century, Srinivasa Ramanujan. He made significant advances in mathematics that paved the way for innumerable innovations in cryptography. His works have become the bedrock of several advancements in modern mathematical and computing areas.
As Western countries and China make strides in quantum technologies, it would be useful for India to revisit Ramanujan’s mathematical concepts to catch up in quantum computing.
With the announcement to set up the National Mission on Quantum Technology and its Applications (NM-QTA) in the budget speech of 2020-21, India finally got a foot in the door in the realm of quantum technology.
Quantum technology, which finds its roots in quantum physics, will bring about a paradigm shift in the way we perceive technology today. Computational power will increase exponentially and problems that would take hundreds of years for a classical computer to solve will be addressed in seconds by a quantum computer.
Encryption and decryption will also undergo a sea change with the onset of quantum computers. These mega machines will disrupt the way we communicate. Researchers around the world believe that quantum computers will be able to hack into the strongest and most robust cryptographic algorithms, like RSA 2048-bit, in a matter of seconds, posing a challenge to safe exchange of critical information.
Since classical computers are not equipped to identify quantum-led cyber attacks, it will be difficult to mitigate such maliciousness in the future. Cyber security will be threatened and massive data breaches might become commonplace.
As quantum computers evolve to compromise encryption, the only way to counter it is to build quantum-resistant encryption standards. Alternatively, building on quantum principles, like entanglement and superposition, to develop encryption algorithms is another way.
While the latter will involve huge costs and infrastructure apart from a functional quantum computer, the former uses Ramanujan graphs for post-quantum cryptography. This can further be deployed to develop algorithms using classical computers.
In the last few decades, cryptology enthusiasts have applied number theory to fathom the depths of Ramanujan graphs. These are mathematical functions that have gained prominence for two major reasons: first, they have solved long-standing external problems in the field of communication and, secondly, for their aesthetic.
Researchers around the world are working on Ramanujan graphs for post-quantum cryptography; that is, developing this set of mathematical functions to roll out mechanisms in order to safeguard data and information from quantum-led cyber attacks. This can be achieved as India’s pursuit of developing quantum computers continues in parallel.
For countries like India that have just entered the race to quantum supremacy, a colossal amount of effort and investment will be necessary to compete with the US and China, which have already invested heavily in this frontier technology.
Needless to say, first-mover advantage can be exploited for technological advancement and to exploit vulnerabilities in existing communication systems of emerging economies.
Turning to her classics and her rich history in mathematics, linguistics, and poetic traditions may prove to be a clincher for India in building systems that can protect information, safeguard the privacy of her citizens, and find ways to uphold national security.
Prachi Mishra is a Tech Policy Fellow at the University of Chicago. She works in the areas of tech policy, quantum computing, meta-ethics, and national security. She also works as a consultant with the Delhi-based Centre for Integrated and Holistic Studies. She tweets at @mishra_praachi.
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