Why Is The Number of Bits Used in RSA So Much More Than Other Public Key Methods?
Remember as a child you perhaps asked why the sky was blue, or why birds can fly? For some reason, as we get older we lose the ability to questions things, and everything is just taken for granted. Overall I find that those who innovate best, and those who have great ideas, are the people who have not lost their continual questioning of our world, and asking what seems like simple questions.
So, if you can answer why we talk about 512-bit, 1K and 2K keys, but in other public key methods, we only talk about 256-bit keys, then you have reach the end of this article. If not, read on …
Why RSA has more bits than others?
I was asked by one of our students, why is the number of bits used in the RSA modulus so much larger as compared with other public key methods? In elliptic curve methods, for example, the prime number only has to have 256 bits for good security, but, in RSA, we need at least 512 bits. It is a great question, and I’ll try and explain it here.
Every integer number is made up of the multiplication of prime numbers. For example:
