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
RSA Laboratories describes why pretty well
In practical applications, it is common to choose a small public exponent for the public key.
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With the typical modular exponentiation algorithms used to implement the RSA algorithm, public key operations take O(k^2) steps, private key operations take O(k^3) steps