Unit 3 - Cryptography

Topic

Dimensions of Cryptography,

Classical Cryptographic Techniques Block Ciphers (DES, AES) : Feistal Cipher Structure, Simplifies DES, DES, Double and Triple DES, Block Cipher design Principles, AES

Modes of Operations Public-Key Cryptography : Principles Of Public-Key Cryptography, RSA Algorithm, Key Management, Diffie-Hellman Key Exchange, Elgamal Algorithm, Elliptic Curve Cryptography

DES

• Block Cipher Method
• Symmetric Cipher
• Encrypts 64 bit block

Fiestal Cipher - DES takes 16 Rounds

• Data Encryption Standard.
• Converts the plain text to cipher text.
• Block Cipher Algorithm (also Stream Cipher)
• Total of 16 Rounds.
• Text Size = 64 bits
• Key Size = 48 bits ( 8 bits for parity and 8 bits for rearrangement)

**Round Key Generator **

• Permuted Choice 1(PC1) - 8 Parity bits removed, every 8th bit removed. 56 bit
• C0 & D0 - Two equal parts. 28 bit, 28 bit.
• Left Circular Shift (LS) - Move the bits based on round number. For 1 round 1 bit shift, 2 = 2 bit shift.
• C1 & D1 - Added to make key
• LS-LS | C2-C2 are repeated.
• PC2 only

AES

RSA

• Ron R ivest - Adi S hamir - Leonard A dleman, created in 1977.
• The most common & widely used Asymmetric Encryption👁️ algorithm.
• It creates a pair of commutative keys, i.e., “encrypt with one” “decrypt with the other”.

Generating Keys

• Select two Prime Numbers (P, Q) P=7 Q=19
• Calculate Product, (P×Q) N = 133
• Calculate Totient, (P-1) x (Q-1) T = 108
• 1 < e < Φ(n)
• Select Public Key (E) E = 29 🚀30-1

1. Must be a Prime less than Totient.
2. Must NOT be a factor of the Totient.

• Select a Private Key (D) 41 🚀40+1

3. Product of D and E, divided by T must result in a remainder of 1 (D*E) MOD T = 1

Encryption and Decryption

• Encryption
  $$(Message)^E mod \ N = Cipher \ Text$$
• Decryption
  $$(Cipher\ Text)^D mod \ N = Message$$

Example Message = 60, Cipher Text = 86 8672
Example(keys switched) Message = 60 Cipher Text = 72

Working

How secure ?

• Security of RSA lies in factoring semi-prime numbers.
• Since the 1991, RSA lab’s 54 prime numbers challenge.
• Biggest Number factored : 829 bits (2020)
• 1024 haven’t been factored for 29 years.
• 1024 bit is standard since 2002
• 2048 bit is standard since 2015

Diffie-Hellman Key Exchange

• Allows two parties to share a shared secret over an unsecured medium.
• Shared Secret is never transmitted, instead values are used to derive secret.

It is same because of discrete log problem.

Elliptic Curve Discrete Log Problem
nA = E, where nA = A dot A dot A
Works similar to exponent & modulo, if you know the point you started at and ended at. It’s hard to guess how many cycle needs to be done to get B

Change it with ECDH

If we have A, B and goes out the field it will wrap around like modulo.

Same security but with smaller key.

Elliptic Curve

ElGamal Algorithm

• An asymmetric key encryption algorithm based on the Diffie-Hellman Key Exchange (DHKE).

• Created by Taher ElGamal, The “father of SSL” - Secure Sockets layers and A major contributor to Digital Signature Standard (DSS).

• page aa, page ee

• Something selected randomly is always 1 < [ ] < p-1

• Always g mod p rasie random

• Use the rest, and remember the last.

Elliptic Curve Cryptography