Why RSA Decryption process takes longer time than the Encryption process?

Question

I have some idea that it is due to some complex calculation, but i want to know about what exactly happens which takes long time than the corresponding encryption process. Any l

Answer 1

There are two factors involved in this:

On the one hand, the public exponent can be chosen to be a small number with only two 1-bits (usually 3, 17 or 65537). This means the RSA encryption operation can be done with a few modular squarings and an addition. This cannot be reversed: If you force the private exponent to be a small number, the security of the system is obviously broken.

On the other hand, the holder of the private key can store some precalculated values derived from the original primes. With those he can use the CRT algorithm to replace the single exponentiation modulo a n-bit number with two exponentiaions modulo a n/2-bit number. This is approximately four times faster than the naive way.

So for RSA key pairs with random public exponents, private key operations can actually be faster. But the effect of choosing a small public exponent is much greater than the effect of the faster algorithm, so encryption is faster in practice.