Cards and Finance

In a blog about Finance , I think it is good to talk about an enabler of Finance - Cryptography. Today millions of dollars are being transferred all over the world on its basis alone. It secures all data traveling through the net. But how does it work ?

Let us take Jack who wants to make a deposit with his Bank. He decides to do it over the internet . But unknown to him is the fact that his soon to be ex-wife Jane, a supreme computer hacker is monitoring all data flowing from jack's computer so she can't be cheated out of any money in her settlement.

Now Jack does not know all this. He logs on to the bank's website and clicks the necessary buttons and the money goes to the bank, but this data also goes to Jane. Now can Jane find out the information from this data. In today's day and age - No. Why ?

Well Jack has used public key cryptography to ensure the safety of his data. How does this work ? Let us for simplicity imagine that if Jane knows a special number she will be able to break Jack's code. So how does Jack ensure the code remains secret ? He knows about a certain mathmetical function of the form R = p^q ( mod (N))

Now the Bank has a public key ( or say 2 number which everyone knows ) called q,N . The bank forms N by multiplying 2 prime numbers a,b ( say 3, 5 ) and chooses q which is relatively prime to the (a-1) x ( b-1 ) , say 7. In this case q=7, N = 15 ( Usually they are very large prime numbers ). It then makes it available to the public . Now say Jack wants to send the number 2 ( p) ( which tells his bank to make a deposit to his account ) to the Bank. He hence uses the formula and calculates R ( in this case R= 2^7 ( Mod (15) )= 8 )

Now Jane knows R = 8, q = 7, N =15, So she should be able to find out p easily ! Right ? Wrong ! The mathmetical function is a one-way function , which means calculating R is easy once one knows p, but it is impossible to figure out p given the value of R . But if one knows the components of N ( i.e the 2 prime numbers chosen by the bank ) one can easily calculate p by a special method given a value of R.

Thus it is possible to transmit data for Jack without Jane getting to find out about it as she can't find out p, but the bank is able to find out p, and based on it make a deposit in Jack's Account leaving Jane hanging in the air.

[Note: This is a very simplified version of explaining public key cryptography. If any one wants to know more read the book by Simon Singh called the 'Code Book']