Perhaps it’s Destiny!

We at Mathschool worked today 28th July 2015 as a mark of respect to that great soul who was my inspiration in many ways.

My research years were so memorable mostly because of these events that always circled about this one great personality!

It was the first conference on “Number Theory for Secure Communications” organized by SASTRA Kumbakonam. It was inaugurated on 20th December 2003 by His Excellency, Dr. A.P.J. Abdul Kalam, President of India.

I was seated in the audience when he gave his speech.

“Dream, Dream, Dream,
Dreams transform into thoughts,
And thoughts result in action.”

All of us repeated it after him.

And then we were all taken to the house of Srinivasa Ramanujam, purchased and renovated by SASTRA that was also inaugurated by His Excellency.

The last day of the conference, a pamphlet was handed over to me, and the phrase that I caught sight of was “brainchild of Abdul Kalam”. Having known about the organisation only few months ago I was excited. Set that as my goal.

Then came in December the Indocrypt 2004

I was again one among the audience totally charmed by his absolute simplicity. We were asked to give our questions to the President. My question was accepted and the second in line out of the ten.

” What are the measures taken by the Centre in the area of cryptographic e-voting techniques? ”

I heard my voice reverberate in the IMSc auditorium. The thoughts that ran through my mind….

Am I actually talking to The President ??
I wish my mom were here. She would be smiling from way up there. Just wait until my dad hears about this and the rest of the folks at home. Would they believe me?

Atleast I didn’t faint! And then after sometime it seemed like he was nodding his head. Just took the cue as the end of the answer, Said a thank you, handed over the microphone and sat down. Now was that embarrassing?! I don’t even vaguely remember what he said. Not then and not now! Who cares!! I still did get the attention of The President. And the after effects were a lot more interesting…”Hey! that’s the girl who spoke to the President!”

I had to carry this news home. And the next day there it was in the news: The Hindu

Well it was all so inspiring and I wrote out this article for The Hindu Sci-Tech page hoping that it will be published on time for many to know that we were hosts to the Asiacrypt in 2005.

Much to my disappointment this was what was published (that too after the conference ended)
Cryptography in eVoting

instead of this:

Cryptography in eVoting

The greatest challenge in eVoting is to develop a fully secure system that preserves the anonymity of the voter and the vote and also provides a universally verifiable process for tallying and verifying the proof of correctness of the votes. This would improve the integrity of the system and increase public confidence in the process of voting. As a result eVoting systems in recent years have shown an increasing trend towards the use of the science of cryptography. The popularity in the use of Cryptography in eVoting was evident in the use of the Diebold Electronic Voting Machines for the 2004 U.S.Elections. But it was Brazil that set an example to the entire world by the accelerated pace at which they replaced their legacy systems with fully computerized eBalloting in their 2000 elections.

Cryptography in eVoting

Cryptography is the science of disguising messages using either a single key or a public-private key pair. The system where a single key is used to encrypt as well as decrypt the message is called a Symmetric Key Cryptosystem and that which uses a pair of keys, one for encryption and another for decryption is called the Public Key Cryptosystem. The key that is public knowledge is called the public key and the key that is kept secret is called the private key. eVoting systems can be made public key cryptosystems where their security depends on the hardness of mathematical problems such as the discrete log problem in Elliptic Curve groups.

Fully secure eVoting systems recommended by Cryptographers are the Mixnets, the Homomorphic Encryption and Threshold cryptosystems. The Mixnets are multiparty computation and communication protocol where the encrypted ballots are shuffled so that they cannot be traced to their respective voters. But this can be done only after all votes are cast and involves exorbitant computations and time delay. Homomorphic Encryption is a classic method that binds the voter to the vote. In this scheme, it is possible to tally the votes without decrypting the individual vote. This preserves the secrecy of the eBallot. If the election official is dishonest the individual votes can be revealed. To reduce this risk the decryption key may be shared among several election officials that can be combined later using a Threshold Cryptosystem.

However, difficulties in translating social policies into computer procedures have seen the implementation of other systems of evoting called the Receipt System. A device that resembles a small cash register printer generates a printout that consists of information on the candidate voted for, the party affiliation etc. But these schemes violate the secrecy of the eBallot.


Now which of the above eVoting systems will suit our nation is for the experts to decide Our progress in the area of Cryptology has been tremendous in the last few years under the guidance and unrelenting effort of the Cryptology Research Society of India. Chennai plays a key role as the headquarters of the Society for Electronic Transactions and Security (SETS). The International Conference on Cryptology – Asiacrypt 2005, is also to be held in the first week of December at Chennai. The availability of in-house expertise and IT manpower is an advantage. The step towards a progressive and transparent democracy should begin here.


K.P.Vidya, Research Scholar, Department of Mathematics, Madras Christian College, Chennai

Well, am I glad that I can now put up the unedited version for all to read. [Needless to say my faith in humans dipped low soon after that and little did I know that that particular incident was just the beginning.]

Even during my visits to present papers at other conferences,  there would definitely be atleast one person in the crowd who would stand up and let the audience know how much he or she admired Dr.A.P.J.A.Kalam. and how they dreamed of India 2020.

Then came the interview in 2006. (Was it June or July?) Yep. I was sitting inside the boardroom of this organization, brainchild of Dr.Kalam. I had applied for a job and was called for the interview when one of the interviewers mentioned that many thought this office was the backdoor to the Rashtrapathi Bhavan. Now was it or was it not?!

emails sent to Rashtrapathi Bhavan might have hit the forward button yet there was positive change that cared for our nation.

If that burning desire to pursue research continued to exist in me then it was only because of this great soul who I am certain will light the path for many more new entrants in research.

A few years after receiving my Doctorate, I’d gifted my dad with Dr.Kalam’s “Wings of Fire” and the first line Dad said to me was “He’s my age.” and for Dr.Kalam too to take leave in the month of July, exactly two years after Dad, perhaps it was Destiny!

Great souls don’t just die. They scatter their energy to millions and those worthy of them acquire their qualities! RIP Dr.Kalam.


Cloning vs No Cloning

Okay, so its bits vs qubits.

Would you believe that it can actually prevent counterfeiting?!

Which can?



yep. They can’t be cloned! and a random sequence of qubits embedded in a currency note acts as a one time pad that cannot be duplicated without detection.

And the Banker of Banks is the authority that would claim responsibilty for cloning if there is any?

Well…, this is where theory doesn’t meet practice. Unless somebody comes up with a public key scheme.

Since the volume of info that needs to be stored regarding keys will be lower than what’s necessary if its a onetime pad. hmmmm…..Interesting.

But the digitisation of quantum money would happen only after quantum networks are deployed. Till then it would have to be only physical. The alternative is the use of Bitcoins. But the idea behind Bitcoins is to do away with the Central Authority.

yeah?! I would be sceptical about Bitcoins then. After witnessing the hype created in the growth of private financial institutions which were later forced to shut down only suggestive of a handful of trustee members to have siphoned off the funds; the stock market scam in the ’90s; and, when nationalised banks were showing NPAs.

Well, we do have reason to be cautious of course. Maybe a certain section of the community do look forward to alternate currency for a less cumbersome system to transfer funds, a system where the transaction can be carried out for a lesser fee or no fee at all.

So quantum money doesn’t really satisfy that.

Quantum money is more or less like cash. The mining authority is usually the Central bank where the transactions are traceless and the end-user holds on to anonymity.

That seems more sensible to me than pretend that the plastic tokens given to me by the vendor at the vegetable market in exchange for my real cash, is actually cash. The plastic tokens exchanged by the vendors in each stall in return for the vegetables is recognised for its worth based on the colour and the value engraved on it. The balance of tokens left behind after my shopping has to be exchanged back into real cash at the time of leaving the market. This is the sort of private network for alternate currency that people actually want?!!.                                                                                                                                                                                       Now this is where the hitch lies. I can exchange the plastic tokens only IF the vendor at the cash counter is still seated in office. When there is no accountability to the appointment or management and or functioning of such a role of a person in that position in the market then I will be left with only plastic trash! Don’t you think the barter system of the age old days was better?! Atleast the end user is left with a commodity that is equivalent in value to the cash given in exchange.

Have to agree with you now that it does occur to me that With Bitcoins we may be repeating the same mistake that happened during the rule of Muhammed bin Tughlaq…..the government placing its trust in the public to mint money.

It’s where Theory meets Practice

The Solution to it is of course encryption. Goals and assumptions are defined clearly followed by a rigorous justification of the claim that if these assumptions hold then the designed system meets the stated goals.

Okay, what about the adversary then?

It leads to an analysis of a situation where the environment may maintain state or not considering an adversary may manipulate the environment.

By that you mean follow the thoughts of an adversary? ;-))

The more wicked your imagination gets the higher the levels of security you obtain.

Then may I assume that its the possible goals and the various possible attack models that classify the definition of a secure encryption?

Yes. These are modern ways though where it’s all about enforcing trust or distributed trust in secure communication while Classical crypto was always only about  keeping information secret.

What would be the highest level of secrecy that one can expect?

For any simple encryption scheme, we can hope for what’s called Perfect Secrecy which is a one-time secure encryption where the key may be used only once and it is as large as the message itself.


Phillips Hughes

I’ve never been much of a cricket fan. A student of mine in seventh grade informs me he’ll miss his math class for cricket coaching and along with it he adds Phillip Hughes died. I just had to mention the name Douglas Jardine and he explains in detail about bodyline tactics and about the number of bouncers that can be bowled in an over…….

I Switched on the T.V. set this morning to catch up on the weather report only to watch Hughes funeral service.

To me it meant “Yet another cricketer dies in his twenties…..”

It brought back memories of this boy who I knew when he was eleven. It was a treat to watch a sixer off Dharma’s bat, a cartwheel of the stumps to his bowling or a diving catch that would turn the game. The team he was in, was always a sure winner until one morning many years later when I was shown this article in the newspaper

Couldn’t believe it. He was only 20 years. Even one who knows him well might only be able to assume Why he would go to such extremes. Probably a moment of acute depression after a loss. Adequate measures to help him cope with emotional distress, a little care and attention from the cricketing fraternity might have saved his life. Just a little care and attentionfrom the cricketing fraternity……. could have saved Phillip Hughes’s also.

Do we still have to rationalize our conduct under the guise of survival of the fittest? Like death always is, its an awakening. Foremost though is something that’s currently ignored and does need to be addressed which is true for any field and not just cricket.

As we grow into a more inclusive society, competition gets ugly and it certainly is destroying the most valuable of human resources.


Whats this big fuss about secrecy?!!

Oh yes, there’s a lot of fuss about secrecy of data. Its something that’s hard to be unconcerned about because data is the most valuable asset today. When we ask for services at the push of a button, to avoid standing in long queues, a global identity in case of a mail box or a bank account, then definitely we are asking for services online. Which also means that our information, that’s a lot of personal data, is routed on a public information highway. Now is that meant for public to view and/or read or is it meant for the intended recipient only?

Ok. I get it now. emails give me the freedom to travel without having to look out for the postman, I can access my bank account from whereever I am without having to visit the specific branch. How could I forget this one; I can shop online, book my flight or railway tickets on my mobile and store my files on the cloud. But all of these actions make my personal data vulnerable to attack by malicious adversaries.

yep. Cybercrime is high with Online fraud techniques of mostly phishing and pharming.

I understand that money laundering is also reported to be pretty high since the advent of online banking and so is the case with sanctions violations.

Money laundering can be dangerous as the funds can be utilised for organised crime. Banks do hold a responsibility there as they do for sanctions violations also. Banks are the first line of defense against these activities. It’s their duty to question and report anomalies in financial transactions or for that matter anything that might seem suspicious. The question is however: How far possible is it to do so?

Has it happened to you? I mean have you at any point of time become a victim of online fraud?

Not as yet but I do know that as long as I depend on the internet I may be susceptible to it some day. There’s always the lurching feeling that we are only stalling the inevitable.

Yeah, the robber definitely has the advantage of swiping off the entire amount in the bank account and make his getaway hiding his tracks efficiently in the maze of networks, within minutes of receiving the relevant information. There is a solution to prevent all of this though?

It’s Prime indeed!


Why does it always have to be numbers? A Social Security number, a PAN number, Mobile number? Why do i need them dictating my life?

Guess it all started with counting. We couldn’t help that. Their children, their livestock and thus the count began. Oh please don’t try to relate them with happenings in your life. It can only lead to the undoing of the self!

What makes you say that?

‘Cause they are just numbers. There’s nothing lucky about one and unlucky about the other. You make it seem like they have a life of their own.

But don’t they?! The primes are a standing example. Their mystic nature. Infinite in its numbers, hidden in the beauty of its patterns, its unaltered presence in its rustic form at any newly found height, it’s indeed prime!

Then let’s just blame it on the Greeks! Remember the primes were found. It’s the human mind that’s caused this misery. The search has been intense and with the added power of computing, all the more so.

Well, We could always stop looking for more!

Great Idea! And that’s definitely going to happen When some think its going to make them wealthy. :-))

Wealthy?! Yeah to be rich and famous! Is that some motivation to search for numbers. Try convincing me on that one!! 

Its used to hide information.

Wow! That sounds like an advancement. Then as I said before it’s Prime indeed! So, where are they hiding all this information?

In the corporate world mostly, anywhere where there exists a database, need not necessarily be classified. Everyone opts for secrecy these days.

Haha! that’s funny! When social network on internet media makes peoples lives more open to public whats this big fuss about secrecy?!

What’s special about us

We don’t teach. We monitor. If there’s anything that does the trick to learning math then its observing very closely the progress of each student in the path of math education. Our notes are our strength. They are basic guidelines on solutions to problems where the students fill in the empty boxes and blanks between the text. Each line of mathematical statement or an unassumingly innocent description of a mathematical concept is read like a line off a novel.

With us, it takes a minimum of one year for a new entrant to allow the transformation within oneself towards taking to the subject as a normal activity, although with exceptionally brilliant students it’s taken less than only two months. To reach out to a book on math with ease, the fervor of impatience with which they wait to work on a new set of pages of our notes are some of the symptoms of a math fever that becomes inherent in our environment.

Over the years when our students get comfortable with the learning process and when they are given a fresh topic to work on: their ability to solve the problems is such – The student reads aloud the text, page after page, seeing an imprint of the complete solution in the mind’s vision, without actually having to fill in the boxes and blanks. When this happens when every page of text is turned, then we know that the student is on the road to becoming a genius.

For us, time to say goodbye is a moment of pride that fills our hearts with content and an assurance that “to be a responsible citizen” is the seed we’ve implanted and that too one who is empowered with the knowledge  of Math. at an Advanced level.

Since our day of start

We’ve been around unofficially since 2003 and officially since 2008. Those who registered newly with us for our online and classroom program are mostly students in the age group 12 to 14. In our experience of a eleven plus years, our effort taken to inculcate fearlessness toward the subject has been more than imparting the subject knowledge itself.

With our newcomers, it was mostly the ugly face of insecurity that showed itself in sweating palms, math exam fears, fear of being derided by the teacher for inadequate knowledge of the subject and most importantly fear of explaining themselves to their parents for poor performance in math. The reasons to why most parents opted for classroom program for their wards, is obvious. The least we’ve done in helping our students is to help them think mathematically. Although there were many questions on why math was taught beyond what’s prescribed in the school textbooks, we insist on the approach and our results are excellent.

At the end of our foundation program our students begin to think quickly since they have an overview of all topics and a grip on the subject. This also helps them make an easy transition to learning advanced topics. The inquisitiveness is nurtured- to analyse a question, to find more than one solution to a problem, allowing mistakes. In their growth, our students forget the existence of the teacher who they have to look up to for support, appreciation or credits.

Our students are made to realise that he/she is one’s own best teacher as learning by itself is an infinite loop that introduces new variables and lines of reason to the algorithmic recipe of problem solving during the process of analysis of each statement of proof.

If there’s something that we did not have a problem with, at least so far, and we say this with a wide grin, is absenteeism! Yes, we do make sure we have our share of fun although it may seem a lot juvenile. We’ve welcomed all those who have approached us and given them ten times more than what we’ve received.

Our satisfaction comes with building a neighbourhood that grows into a society of conscientious decision makers.