Problem 1. (RSA Library) Implement a library called rea.py that provides functions needed for developing the RSA cryp-tosystem. The library must support the following API:rsagenerates and returns the public/private keys as a tuple (n, e, d), picking prime numbers p and q neededto generate the keys from the interval [1o, hi)encrypts x (int) using the public key (a, e) and returns the encrypted valuedecrypts y (int) using the private key (a, d) and returns the decrypted valuereturns the least number of bits needed to represent areturns the binary representation of a expressed in decimal, having the given width and padded withleading zerosreturns the decimal representation of a expressed in binarykeygen (lo, hi)евcrypt (x, a, е)decrypt (y, n, d)bitLength (n)dec2bin (n, width)bin2dec (n)> "/vorkspace/project4$ python3 rsa.py Sencrypt (S)- 1743decrypt (1743) - sbitlength (83) - 7dec2bin (83) - 1010011bin2dec (1010011) - 83Directions:4 / 7Project 4 (RSA Cryptosystem)• keygen (1o, hi)Get a list of primes from the interval [lo, hi).Sample two distinct random primes p and q from that list.Set n and m to pq and (p – 1)(g – 1), respectively.Get a list primes from the interval [2, m).Choose a random prime e from the list such that e does not divide m (you will need a loop for this).Find a de [1, m) such that ed mod m = 1 (you will need a loop for this).Return the tuple' (n, e, d).• encrypt (x, n, e)- Implement the function E(x) = x° mod n.. deerypt (y, а, d)Implement the function D(y) = yd mod n.• -prines (lo, hi)Create an empty list.- For each p E [lo, hi), if p is a prime, add p to the list.- Return the list.• sample(a, k)Create a list b that is a copy (not an alias) of a.Shuffle the first k elements of b.Return a list containing the first k elements of b.• choice (a)Get a random number r e [0, 1), where l is the number of elements in a.

Let's build our module one function at a time: 1.) keygen(lo, hi) This function will generate two…

Answered: Problem 1. (RSA Library) Implement a…

Problem 1. (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:

Computer Networking: A Top-Down Approach (7th Edition)

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Author:James Kurose, Keith Ross

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Chapter1: Computer Networks And The Internet

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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Question

Problem 1. (RSA Library) Implement a library called rea.py that provides functions needed for developing the RSA cryp-
tosystem. The library must support the following API:
rsa
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 [1o, hi)
encrypts x (int) using the public key (a, e) and returns the encrypted value
decrypts y (int) using the private key (a, d) and returns the decrypted value
returns the least number of bits needed to represent a
returns the binary representation of a expressed in decimal, having the given width and padded with
leading zeros
returns the decimal representation of a expressed in binary
keygen (lo, hi)
евcrypt (x, a, е)
decrypt (y, n, d)
bitLength (n)
dec2bin (n, width)
bin2dec (n)
> "/vorkspace/project4
$ python3 rsa.py S
encrypt (S)- 1743
decrypt (1743) - s
bitlength (83) - 7
dec2bin (83) - 1010011
bin2dec (1010011) - 83
Directions:
4 / 7
Project 4 (RSA Cryptosystem)
• keygen (1o, hi)
Get a list of primes from the interval [lo, hi).
Sample two distinct random primes p and q from that list.
Set n and m to pq and (p – 1)(g – 1), respectively.
Get a list primes from the interval [2, m).
Choose a random prime e from the list such that e does not divide m (you will need a loop for this).
Find a de [1, m) such that ed mod m = 1 (you will need a loop for this).
Return the tuple' (n, e, d).
• encrypt (x, n, e)
- Implement the function E(x) = x° mod n.
. deerypt (y, а, d)
Implement the function D(y) = yd mod n.
• -prines (lo, hi)
Create an empty list.
- For each p E [lo, hi), if p is a prime, add p to the list.
- Return the list.
• sample(a, k)
Create a list b that is a copy (not an alias) of a.
Shuffle the first k elements of b.
Return a list containing the first k elements of b.
• choice (a)
Get a random number r e [0, 1), where l is the number of elements in a.

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