$.($RSA Library$)$

Implement a library called rsa.py that provides functions needed for developing the RSA cryp tosystem. The library must support the following API: rsa keygen$($lo$,$ hi$)$ generates and returns the public$/$private keys as a tuple $($n$,$e$,$d$),$ picking prime numbers p and q needed to generate the keys from the interval $[$lo$,$ hi$)$ encrypt$($x$,$ n$,$ e$)$ encrypts x $($int$)$ using the public key $($n$,$ e$)$ and returns the encrypted value decrypt$($y$,$ n$,$ d$)$ bitLength$($n$)$ dec$2$bin$($n$,$ width$)$ bin$2$dec$($n$)$ decrypts y $($int$)$ using the private key $($n$,$ d$)$ and returns the decrypted value returns the least number of bits needed to represent n returns the binary representation of n expressed in decimal, having the given width and padded with leading zeros returns the decimal representation of n expressed in binary