~~~*~~~
I met Ram in my Advanced Number Theory class. It is one of our graduate level courses. I have been teaching ANT for the past 12 years, but I don’t remember any student in all these years who had as much passion for numbers as Ram did. It was evident that he was a class apart from his peers after a few classes. He solved the standard textbooks problems with no difficulties, abstracted what he learnt, posed problems for himself and began working on them. He quickly gave up solving my assignments as well. The only reason he was still attending classes was because he said he needed – in his own words – “fresh perspectives”.
Though he was my best student, we had never met out of the classroom. He worked on his own, never collaborating with anyone. I was sure he made some discoveries worthy of publication, but he never cared to publish. I realized he was aiming for something else. With the questions he was raising in class, he seemed to be on an abstract and directionless pursuit. Though I was curious and worried about where he was headed, I never took the initiative to talk to him out of the classroom. I thought he was a mad genius and it was best to let him be.
Two months into the course, Prof NRV mentioned that a guy in his class had been skipping all other classes except ANT and that he was at the verge of losing his stipend. It was worried it could be Ram. It was. I decided that it was time I had spoken to him.
In the next class, I went to his desk and asked him to meet me in my office after class for a chat. I waited for him, but he did not turn up. He sent me an email in the evening –
“Dear Prof. Hari,
I am sorry for not turning up. I know why you wanted to meet me. I’m alright. I am working on something far more rewarding than my stipend or my classes. I have delved so deep into solving this problem that I find my classes a waste of time. I now realize that I should have enrolled for a research oriented program. Classes don’t make sense to me anymore. But back then, I didn’t know what to pick… my interests are clearer now!
The next few days are the most crucial for me. I hope to make good progress. What I might discover as the solution could be path-breaking. This makes it all the more exciting. I might be missing ANT classes as well.
I’ll meet you soon with some good news!
Ram.
P.S: One-way functions. ;-)”
~~~*~~~
Five days later, he walked into my office. He did not look like someone bringing good news. He was bearded all the time, but his shabby dressing made him look worse. He looked tired as well.
“Good afternoon, Professor.”
“Oh! Good afternoon, Ram,” I motioned him to take a seat, “It’s quite a surprise to see you these days. So, how’s your research going? When are you getting back to classes?”
“Classes? I have not even thought about them Professor, but my research is on track.”
“What are you working on?” I asked, curious about what was holding him back from attending classes.
He hesitated and then spoke, “I am working on finding a universal reversal function. Umm… For example, like a universal de-hashing function.”
I wasn’t quite clear with his terminology. I wanted to make sure if he really meant what I understood it as. “You mean a function that accepts a hash value and returns the original plain text?”
“Exactly,” he said with excitement, “But hash functions are just a sub-set of one-way functions. I intend to find a generic function that can output the original input value when we input the one-way function used and the output it generated. If we use it in the context of hash functions, it can de-hash a hash value generated by any hashing algorithm.”
“Ram,” I paused trying to figure out the best way to put it, sighed and then told him, “I cannot put this in any other way, but what you’re saying is ridiculous.”
“I knew everyone would say this,” he said clearly losing his excitement, “It’s hard to accept the fact that a hashed value can be de-hashed and a one-way function can be reversed.”
“It’s not hard, Ram. It is impossible to accept it. You are trying to deny the very nature and purpose of hash functions. That’s what they are - Once you hash a piece of text, there is no way you can get the original text back.”
“I know the definitions, Professor. I think that’s what blinds you from seeing beyond. You fail to question the definition. I believe there is no such thing as a hashing function. In fact, there is no such thing as a one-way function as well. An input put through a mathematical function resulting in an output can always be reversed. Everything is two-way. I strongly believe in that.”
“You believe?” I asked in disbelief, “one-way functions have been proved to exist!”
“Then I intend to disprove it,” he said suppressing his anger, “Let me explain, Professor. Suppose I take each computation in a one-way function, I can see it has an input and an output. The output of each computation becomes the input of the next. This becomes a chain of causality. I believe – if you have the final output and all the steps of the function – then you can trace it back to the initial input.”
It was then that I realized I was arguing with someone who always questioned the premises of argument. “And this tracing back is what one-way functions do not allow! There is loss of data!”
He remained silent and said “You are going back to the definitions again. You don’t see what I see.”
I couldn’t understand what he could see. He was incorrigible and he was losing the argument. “Okay, Let’s take an example. You say your de-hashing function can give you the original text if you input the hashed value and the hashing function?”
“Yes.”
“Then let’s take any hashing algorithm – MD5 for example. Whatever be the input, be it a 100 page Shakespearean play or just a single character – say an ‘A’ – MD5 always spits out a 16 byte output! There is no way you could de-hash the output into a 100 page text! Data is lost during hashing. You cannot conjure up the data from nowhere! And it applies to one-way functions as well.”
“Yes,” he sounded offended, “you cannot conjure up data, but you can certainly do it within the boundaries of present-day mathematics.”
“I’m sorry that I sound discouraging, but I don’t see this going anywhere, Ram. Even if you were to find such a universal de-hashing or a reversal function, there are so many problems. What about hash collisions? There could be infinitely many plain texts leading to the same hash value. If you were to de-hash it, how would you choose the correct input text from the infinite number of possible input texts?”
“It’s hard to explain to you, Professor,” he said and stood up, “I’ll show it you. It’s just a matter of days. I came here to ask you a favour. Now, I don’t need it. Thank you very much.”
He then stormed out of my office with stern determination.
~~~*~~~
I hadn’t heard of him for a week after that. Then, I received an email –
Dear Prof. Hari,
I’ve done it! I’ve managed to come up with the way to reverse a one-way function! (and to “conjure up” data! :-))
Here’s a sneak preview of my algorithm –
6dc48f564c3f21cbde15075932df63494968589b
Oh! I’m sorry I forgot it’s hashed and I’m the only one (except for Prof. Basu) who knows how to unhash it. :-)
Prof. Basu is hosting an inter-departmental seminar at the RCAMR this Friday. Researchers from the center are also invited. Prof. Basu is planning to make my discovery public that day. Please do come.
Ram.
Prof. Basu was the head of our department and the director of the Ramanujan Center for Advanced Mathematical Research. The “center” as we called it, was a privately funded research organization in our campus. I couldn’t believe Prof. Basu would invite researchers of the center for Ram’s seminar. Either it was going to be path-breaking or he would be making a fool out of himself. I thought I’d know in two days’ time.
~~~*~~~
It happened the day before the seminar. I remember that instance very vividly. I was in a class that morning. Prof. NRV walked swiftly into the class and whispered into my ears to step out. I was first confused. He said it was very important. He was sweating profusely and was acting hysterical. Just as I stepped out of the class along with him, he sputtered –
“Prof. Basu passed away in an accident today. He was on his way to the campus. And that boy – Ram – he was found burned to death in his room. It was a fire accident. No one knows how it happened.”
~~~*~~~
For the next few days, our campus was the talk of the country. There were several media reports, investigations, controversy theories and other such cacophony. After it all died away, I was left with what caused it all –
6dc48f564c3f21cbde15075932df63494968589b
It took away two lives.
It had the key to ultimate reversibility.
And it was irreversible.
~~~THE END~~~
No comments:
Post a Comment