Asymmetric Encryption with RSA

$ 7absec
-- Aaftab Harun
(7absec)

$ 7absec
Introduction
Encryption V/S Encoding
Prime & Coprime
Encryption Process
Decryption Process
Conclusion
11:10 AM
11:20 AM
11:30 AM
11:40 AM
12:10 PM
12:20 PM

$ 7absec
Asymmetric cryptography, also known as public-key cryptography, is a process that
uses a pair of related keys -- one public key and one private key -- to encrypt and
decrypt a message and protect it from unauthorized access or use.

$ 7absec
RSA is an asymmetric public-key encryption system that is very commonly
used in real world applications.
The RSA Encryption algorithm is based primarily around the concept
of Coprimality.

$ 7absec
https://media.geeksforgeeks.org/wp-content/uploads/20200428143327/RSA.png

$ 7absec
p = A prime number
q = A prime number
n = p * q
φ = (p - 1) * (q - 1)
e = public Key
d = Private Key
m = Message ( to encrypt/decrypt)
=== Co-prime Number

$ 7absec
• A Number that is only divisible by 1 and the number itself
• For instance 2,3,5,7,11, …
Walk Through
2: Coprime Number
3: Assigning values of p & q
4: Calculating n and phi
5: Progress upto this
6: Finding “e”
7: Finding “d”
9: Asymmetric Keys
10: Encryption & Decryption

$ 7absec
• Two numbers having 1 as greatest common divisor (gcd)
• For instance 11 & 13, 8 & 15 etc
Walk Through
1: Prime Number
6: Finding “e”
7: Finding “d”
9: Asymmetric Keys

$ 7absec
• RSA Key generation starts with two prime numbers.
• These can be randomly selected or otherwise — they
just have to be prime.
• P = 11
• Q = 13
Walk Through
1: Prime Number
2: Coprime Number
6: Finding “e”
7: Finding “d”
9: Asymmetric Keys

$ 7absec
• N is simply p and q multiplied together.
• n = p * q = 11 * 13 = 143
• Phi is the number of integers that are coprime to n
• phi = (p-1) * (q-1) = (11-1) * (13-1) = 120
Walk Through
1: Prime Number
2: Coprime Number
6: Finding “e”
7: Finding “d”
9: Asymmetric Keys

$ 7absec
RSA Encryption
• p = 11
• q = 13
• n = 143
• phi = 120
• e?
• d?
• m =“?”
Walk Through
1: Prime Number
2: Coprime Number
6: Finding “e”
7: Finding “d”
9: Asymmetric Keys

$ 7absec
• A number that is less than phi, and coprime to both n
and phi.
• The key should be greater than 2 and less than phi
(2<e<phi)
• n = 143
• phi = 120
• possible_bup_keys = []
• for i in range(2, phi):
• if gcd(n, i) == 1 and gcd (phi, i) == 1:
• possible_bup_keys.append(i)
• Print(possible_bup_keys)
Walk Through
1: Prime Number
2: Coprime Number
7: Finding “d”
9: Asymmetric Keys

$ 7absec
• A number that is grater than phi
• d*e mod phi = 1 or d*e % phi = 1
• phi = 120
• e = 7
• possible_pvt_keys = []
• for i in range(phi + 1, phi + 1000):
• if i * e % phi == 1:
• possible_pvt_keys.append(i)
• Print(possible_pvt_keys)
Walk Through
1: Prime Number
2: Coprime Number
6: Finding “e”
9: Asymmetric Keys

$ 7absec
RSA Encryption
P = 11
q = 13
n = 143
phi = 120
e = 7
d = 223
m= “ Hello”
Walk Through
1: Prime Number
2: Coprime Number
6: Finding “e”
7: Finding “d”
9: Asymmetric Keys

$ 7absec
• Public Key: (e, n)
• Private Key: (d, n)
• Public Key: (7, 143)
• Private Key (223, 143)
Walk Through
1: Prime Number
2: Coprime Number
6: Finding “e”
7: Finding “d”

$ 7absec
• Encryption
• m ** e % n
• Decryption
• enc_m ** d % n
Walk Through
1: Prime Number
2: Coprime Number
6: Finding “e”
7: Finding “d”
9: Asymmetric Keys

$ 7absec
• Asymmetric encryption is more secure than symmetric encryption.

$ 7absec
Questions/Suggestions…

Asymmetric Encryption with RSA

Recommended

Recommended

More Related Content

Similar to Asymmetric Encryption with RSA

Similar to Asymmetric Encryption with RSA (20)

Recently uploaded

Recently uploaded (20)

Asymmetric Encryption with RSA