Numberphile
Numbers are fascinating, don't you think?Each number is like an individual.Unique properties.So much to know about.Take a look at pi.The circumference/diameter itself is astounding.Ignore that for a moment.Look at how many other places this weird number pops up in.It's not even whole.If you weren't told all this in school,you'd look at it as some kind of dark magic in the world of numbers:P.The omnipresent number,eh?(Education makes us immune to wonder.We sort of get accustomed to looking at everything as a fact.Don't question it.Don't ponder over it.)Take the golden ratio.It turns up in the Fibonacci series and in geometry as well.Innumerable places.There are so many numbers like this! It makes me think numbers have a deeper meaning.That everything in the universe that's obscure right now has something to do with numbers.And if you find the right set of numbers,the mist clears and you see the answer staring at you.
.When I was around ten or eleven, prime numbers seemed magical to me.They seemed somewhat contradictory to what I'd imagined-- as numbers got larger,the odds are that they'd be divisible by some number or the other.Therefore,I though prime numbers would diminish exponentially and maybe come down to zero.Also,I was sure that there was an underlying pattern to prime numbers.I was convinced that if I looked at it long enough,I'd find it.I spent a month or so on pages scrawled with manually calculated primes.I never found the answer but in the meanwhile,observed a lot of other properties about them.Those were the days of no internet.Finally,someone told me that prime numbers were studied from times immemorial and that everything I'm trying to do has already been done countless times.That sounded true so I gave up my quest.Nevertheless,primes are still fascinating to me.Just look at the types of primes.Wikipedia lists close to a 100! There was one Mersenne Prime found a couple of months ago,if I remember right.
Somewhere around the same time,I was awed by Sherlock Holmes and read every book in the Canon.That's where I was first introduced to cryptography!The dancing men seemed a fantastic code to me.(Sherlock doesn't even have a computer to try brute-force.He uses probability and English to decode.How brilliant is that! Yeah,yeah,I know he isn't real.Stop rolling your eyes at me:P)I tried using it in daily life but it seemed annoying to learn.Instead,I used simple variants of number substitution--reverse,offset and all that! (Much later,I was crushed to learn that people as early as Ceasar had used this:P)The grid cipher is still pretty good--especially if you don't know this exists! If numbers seemed magical to me,imagine how wonderful cryptography felt.
Enigma laid the foundation for cryptanalysis.Now,encryption has become the standard.A week ago,Dan Brown's Digital Fortress caught my eye.I had to keep back two other books to buy this(since I sadly place a limit on the number of books I buy) but I have no regrets.It made for an immensely pleasurable read.The book talks about TRANSLTR,a supercomputer with 3 million processors--thereby making brute force child's play.20 minutes for a 128 bit key I believe.An interesting concept is that of an unbreakable code.(Of course,One Time Pad is definitely unbreakable,but it's seldom used coz of it's rather inconvenient method.)Here,he mentions a rotating cleartext,an encryption that's time variant as well.I rather like this question he poses:Brute force works as long as the machine encounters a recognisable word pattern and thereby stops.Apparently,this doesn't happen with time-shifting.How would a machine then conclude that it's found the answer?
Of course,most of what he talks about may not be true.I doubt there exists something as powerful as TRANSLTR even in the NSA.Also,the rotating cleartext seems fictitious too.Looking at history though,fiction is just a few centuries ahead of reality.All those sci-fis people laughed at in the 19th century are real today! Who knows? Very soon,we might have a TRANSLTR or something that renders the present day encryption standards useless.Then,it's only a matter of time before someone comes up with something unbreakable.Something that changes the field of cryptography,as we know it today.
Long rant this turned out to be--from numbers to cryptography! But this is something that I find very fascinating so it's a pleasure to write about:).I hope it sounds half as wonderful to someone reading it!
.When I was around ten or eleven, prime numbers seemed magical to me.They seemed somewhat contradictory to what I'd imagined-- as numbers got larger,the odds are that they'd be divisible by some number or the other.Therefore,I though prime numbers would diminish exponentially and maybe come down to zero.Also,I was sure that there was an underlying pattern to prime numbers.I was convinced that if I looked at it long enough,I'd find it.I spent a month or so on pages scrawled with manually calculated primes.I never found the answer but in the meanwhile,observed a lot of other properties about them.Those were the days of no internet.Finally,someone told me that prime numbers were studied from times immemorial and that everything I'm trying to do has already been done countless times.That sounded true so I gave up my quest.Nevertheless,primes are still fascinating to me.Just look at the types of primes.Wikipedia lists close to a 100! There was one Mersenne Prime found a couple of months ago,if I remember right.
Somewhere around the same time,I was awed by Sherlock Holmes and read every book in the Canon.That's where I was first introduced to cryptography!The dancing men seemed a fantastic code to me.(Sherlock doesn't even have a computer to try brute-force.He uses probability and English to decode.How brilliant is that! Yeah,yeah,I know he isn't real.Stop rolling your eyes at me:P)I tried using it in daily life but it seemed annoying to learn.Instead,I used simple variants of number substitution--reverse,offset and all that! (Much later,I was crushed to learn that people as early as Ceasar had used this:P)The grid cipher is still pretty good--especially if you don't know this exists! If numbers seemed magical to me,imagine how wonderful cryptography felt.
Enigma laid the foundation for cryptanalysis.Now,encryption has become the standard.A week ago,Dan Brown's Digital Fortress caught my eye.I had to keep back two other books to buy this(since I sadly place a limit on the number of books I buy) but I have no regrets.It made for an immensely pleasurable read.The book talks about TRANSLTR,a supercomputer with 3 million processors--thereby making brute force child's play.20 minutes for a 128 bit key I believe.An interesting concept is that of an unbreakable code.(Of course,One Time Pad is definitely unbreakable,but it's seldom used coz of it's rather inconvenient method.)Here,he mentions a rotating cleartext,an encryption that's time variant as well.I rather like this question he poses:Brute force works as long as the machine encounters a recognisable word pattern and thereby stops.Apparently,this doesn't happen with time-shifting.How would a machine then conclude that it's found the answer?
Of course,most of what he talks about may not be true.I doubt there exists something as powerful as TRANSLTR even in the NSA.Also,the rotating cleartext seems fictitious too.Looking at history though,fiction is just a few centuries ahead of reality.All those sci-fis people laughed at in the 19th century are real today! Who knows? Very soon,we might have a TRANSLTR or something that renders the present day encryption standards useless.Then,it's only a matter of time before someone comes up with something unbreakable.Something that changes the field of cryptography,as we know it today.
Long rant this turned out to be--from numbers to cryptography! But this is something that I find very fascinating so it's a pleasure to write about:).I hope it sounds half as wonderful to someone reading it!
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