How does a blind know the other
person is blind or not? One of the toughest explorations of humankind is the
exploration for the truth. Human search for food ended with finding food. In
some way, it is parallel to what other living beings also do. Hunger for food
brings human beings, animal and plants on the same platform. They work towards
getting good, sometimes good food. As a rational animal, human beings went
further ahead. They searched for the truth behind it. They found that there is
much more in the truth.
Among the three types of living
beings, human beings and animals are superior to plants because of their
capacity to change their positions. They find better positions, in the face of
threats and sometimes for comfort. Hence we may say that plants live in the
first dimension. Human beings are
superior to animals because of their capacity to change their positions in
thinking. Though animals think, their thinking is a very static thinking. Hence,
we may say that animals live in the second dimension. They live according their
instinct. Human beings live in the third dimension. They have life. They can
move. They can remember the past and dream about the future. They can imagine.
Among the many capacities human
beings have, the most important one is the capacity to reason. Reason is the
reason for human beings to search for truth. Human beings, in general, are in
an incessant search for truth. Some search for the truth of life. Some others
search for the truth of the nature. There are some others who search for the
truth of the truth itself. This search for truth is the basis of recording and
documentation. Documentation is the backbone of all the developments in the
world. As human beings change their styles and modes of living, a continuous
progress is visible in the world. It is by encountering and polishing the
truths of the nature, the truths of the truths, human beings progress towards
better life. In this pursuit of
progress, the most important and precise recording is in the form of Mathematics.
Many say, “Mathematics is the
study of anything that has reason.” Mathematics is about recognizing patterns
in the world and contributing suggestions for its repetition and improving. In establishing the claims of what is right
and what is good, mathematicians use a technique called “Proof.” In fact,
everyone with rationality does proving, in many different ways. Hence, in
general everyone is a mathematician. However, academic mathematicians do more
documented proving. There are various methods of Proof.
One without the capacity to see
things using one’s own eyes is termed as a blind. Of course, blindness is not a
hindrance to reasoning. Hence, a blind person also does proving. But, can a
blind person use a visual proof? To be precise, we come back to the initial question,
“how does a blind know the other person is blind or not?” One can always bluff
the blind by pretending to be blind or not. Here comes a beautiful mathematical
proof method, named as “Zero Knowledge Proof.” It is illustrated in the case a
blind person (B) who tests the blindness of another (A).
B has two identical marbles of
different colours.
In modern cryptography, Zero
Knowledge Proof is efficiently utilized. It was initially conceived and
published by the trio Shafi Goldwasser, Silvio Micali and Charles Rackoff.* The
power of Zero Knowledge Proof is that the prover never passes the proof but a
verifier can always test the prover of the knowledge of the proof and be
satisfied.
