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Week - 1

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Lecture 1:
Introduction to Cryptography​

Definition​

  • Cryptography is the science of secure communication over an insecure channel.
  • It ensures that only the intended receiver can understand the message.

Basic Communication Model​

  • Alice → Sender
  • Bob → Receiver
  • Oscar → Attacker (eavesdropper)

Goal​

  • Communicate securely even when the channel is public.

Core Concepts​

Plaintext​

  • Original message (e.g., age = 24)

Ciphertext​

  • Encrypted message (e.g., 50)

Key (k)​

  • Secret value shared between Alice and Bob

Encryption & Decryption​

Encryption​

  • Process of converting plaintext → ciphertext

Decryption​

  • Process of converting ciphertext → plaintext

Example (Step-by-Step)​

Given:​

  • Plaintext = 24
  • Key = 26

Encryption:​

Ciphertext = Plaintext + Key
           = 24 + 26
           = 50

Decryption:​

Plaintext = Ciphertext - Key
          = 50 - 26
          = 24

Key Points​

  • Oscar can see ciphertext but cannot determine plaintext without key
  • Encryption algorithm can be public
  • Security depends on secrecy of key

Key Distribution Problem​

  • Sharing the key securely is difficult

  • Cannot send key over same public channel

  • Must use:

    • Secure channel
    • Trusted method

  • Keys should be changed frequently (session keys)

Cryptography vs Cryptanalysis​

FieldDescription
CryptographyDesigning secure systems
CryptanalysisBreaking security systems
CryptologyCombination of both

Types of Cryptography​

1. Symmetric Key Cryptography​

  • Same key used for encryption and decryption

  • Also called:

    • Private key
    • Single key system

Examples:​

  • Shift Cipher
  • Caesar Cipher
  • Playfair Cipher

2. Public Key Cryptography​

  • Uses two keys:

    • Public key
    • Private key

  • Solves key distribution problem

  • Example concept: Diffie-Hellman

Cryptosystem (Formal Model)​

A cryptosystem consists of 5 components:

SymbolMeaning
PPlaintext space
CCiphertext space
KKey space
EEncryption algorithms
DDecryption algorithms

Cryptosystem Flow​

Important Condition​

For every key k:

D(k)(E(k)(m)) = m
  • Decryption must return original message

Properties of Algorithms​

  • Must be:

    • Efficient (polynomial time)
    • Not extremely complex (not NP-hard)

Attacker’s Goal​

  • Find:

    • Key (k), or
    • Original plaintext (m)

Final Takeaways​

  • Cryptography enables secure communication on public networks
  • Key is the most critical component
  • Encryption hides data, decryption reveals it
  • Two main systems: symmetric & public-key
  • Cryptosystem is formally defined using 5 components
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Lecture 2:
Classical Cryptosystem​

Shift Cipher​

  • Uses Z26Z_{26} (0–25) for letters (A=0,B=1,…,Z=25A=0, B=1, …, Z=25)
  • Encryption: ( C=(P+k)mod  26C = (P + k) \mod 26 )
  • Decryption: ( P=(C−k)mod  26P = (C - k) \mod 26 )
  • Example: plaintext → numbers → add key → convert back to letters

Caesar Cipher​

  • Special case of shift cipher with k = 3
  • Circular shifting (Z wraps to A)

Weakness of Shift Cipher​

  • Key space = 26 (very small)
  • Easily broken using brute force (try all keys)
  • Attacker stops when meaningful text appears
  • Not secure

Kerckhoffs Principle​

  • Algorithm is public
  • Only key is secret

Substitution Cipher​

Concept​

  • Replace each letter using a permutation (mapping)

Key Space​

  • 26! (factorial) → very large → stronger than shift cipher

Encryption​

  • Apply permutation ( ϕ\phi ) to each letter

Decryption​

  • Apply inverse permutation ( ϕ−1\phi^{-1} )

Example Idea​

  • Mapping: A → D, B → X, etc.
  • Encrypt: substitute letters
  • Decrypt: reverse mapping

Key Takeaways​

  • Shift cipher is simple but insecure
  • Caesar cipher = shift cipher (k=3)
  • Small key space → easy to break
  • Substitution cipher improves security with large key space
  • Still classical (not modern secure)
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Lecture 3:
Cryptanalysis on Substitution Cipher (Frequency Analysis )​

Substitution Cipher Security​

Key Space​

  • Total keys = 26! (~4 × 10²⁶) → very large
  • Brute force is computationally infeasible

Frequency Analysis Attack​

Idea​

  • English text has predictable letter frequencies:

    • e → most frequent
    • then t, a, ...

Attack Steps​

  • Count frequency of letters in ciphertext
  • Map highest frequency letter → ‘e’
  • Next → ‘t’, etc.
  • Use trial & error to fill gaps

Reason it Works​

  • Substitution cipher is monoalphabetic
  • Same letter → same mapping every time

Polyalphabetic Cipher​

Concept​

  • Uses multiple substitution alphabets
  • Same letter can map to different letters

Advantage​

  • Breaks frequency patterns
  • Harder to attack using frequency analysis

Vigenère Cipher​

Idea​

  • Extension of shift cipher
  • Uses key vector (k₁, k₂, …, kₘ)

Encryption​

  • (Ci=(Pi+Ki)mod  26)( C_i = (P_i + K_i) \mod 26 )

Decryption​

  • (Pi=(Ci−Ki)mod  26)( P_i = (C_i - K_i) \mod 26 )

Process​

  1. Convert text → numbers
  2. Divide into blocks
  3. Add key (mod 26)
  4. Convert back to letters

Key Property​

  • Same letter → different outputs in different positions → prevents simple frequency attack

Transposition Cipher​

Concept​

  • Does not change letters
  • Only rearranges positions

Rail Fence Technique​

Process​

  1. Write plaintext in rows (zig-zag/grid style)
  2. Read row-wise → ciphertext

Example Idea​

  • Input: meetmeafterthepartyisover
  • Rearranged → different order → ciphertext

General Transposition Cipher​

Key​

  • Permutation of positions
  • Key space = m!

Encryption​

  • Rearrange positions using permutation π

Decryption​

  • Apply inverse permutation π⁻¹

Key Takeaways​

  • Substitution cipher:

    • Large key space but breakable via frequency analysis

  • Polyalphabetic cipher:

    • Improves security by varying mappings

  • Vigenère cipher:

    • Practical polyalphabetic method

  • Transposition cipher:

    • Rearranges data instead of replacing it

  • Classical ciphers are not secure by modern standards

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Lecture 4:
Play Fair Cipher​

Playfair Cipher (Polyalphabetic Cipher)​

Overview​

  • Classical polyalphabetic cipher
  • Proposed by Charles Wheatstone
  • Uses 5×5 key matrix (25 letters)
  • Letters I and J are combined

Key Matrix Construction​

Steps​

  1. Choose a keyword (e.g., CHARLES)
  2. Write unique letters of key
  3. Fill remaining matrix with unused alphabets
  4. Skip duplicates
  5. Combine I/J in one cell

Plaintext Preparation​

Rules​

  • Divide into pairs (digraphs)

  • If:

    • Odd length → add ‘x’
    • Same letters in pair → insert ‘x’ between them

Example​

  • meetmeatthebridge → me et me at th eb ri dg ex

  • balloon → ba lx lo on

Encryption Rules​

1. Same Row​

  • Replace each letter with right neighbor
  • Wrap around

2. Same Column​

  • Replace each letter with below neighbor
  • Wrap around

3. Rectangle Rule​

  • Replace each letter with:

    • Same row
    • Column of the other letter

Example Output​

  • me → gd
  • Final ciphertext: GD DO GD QR PR SD MH ME VB

Decryption Rules​

1. Same Row​

  • Replace with left neighbor

2. Same Column​

  • Replace with above neighbor

3. Rectangle Rule​

  • Same as encryption (swap columns)

Key Points​

  • Works on pairs of letters (digraphs)
  • More secure than monoalphabetic substitution
  • Still vulnerable to advanced analysis
  • Key must be shared secretly

Final Takeaway​

  • Playfair cipher improves security by:

    • Using letter pairs
    • Breaking simple frequency patterns

  • But still not secure by modern standards

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Lecture 5:
Block Cipher​

Block Cipher​

Definition​

  • Type of symmetric key encryption

  • Takes:

    • n-bit plaintext
    • k-bit key

  • Produces:

    • n-bit ciphertext

Basic Structure​

Round-Based Encryption​

  • Uses r rounds
  • Each round uses a round key (K₁, K₂, …, Kᵣ)
  • Final output = ciphertext

Key Scheduling​

  • Generates round keys from secret key K

  • Algorithm produces:

    • K₁, K₂, …, Kᵣ

Decryption​

  • Reverse process of encryption

  • Apply:

    • Inverse round functions
    • Round keys in reverse order

  • Requires functions to be invertible

Examples​

DES (Data Encryption Standard)​

  • Block size: 64-bit
  • Key size: 56-bit
  • Rounds: 16

AES (Advanced Encryption Standard)​

  • Block size: 128-bit

  • Key sizes:

    • 128-bit → 10 rounds
    • 192-bit → 12 rounds
    • 256-bit → 14 rounds

Substitution-Permutation Network (SPN)​

Idea​

  • Combines:

    • Substitution (S-box)
    • Permutation (bit shuffling)

SPN Encryption (1 Round)​

Steps​

  1. XOR with round key
  2. Divide into blocks
  3. Apply S-box (substitution)
  4. Apply Permutation (shuffle bits)

Multi-Round SPN​

  • Repeat above steps for multiple rounds
  • Final round may skip permutation

S-Box​

  • Maps l-bit input → l-bit output
  • Provides confusion

Permutation (P-box)​

  • Rearranges bits
  • Provides diffusion

Example Setup​

  • n = 16 bits
  • Divide into 4 blocks of 4 bits
  • Apply XOR → S-box → permutation
  • Repeat for multiple rounds

SPN Decryption​

Steps​

  1. XOR with last round key
  2. Apply inverse S-box
  3. Apply inverse permutation
  4. Repeat in reverse order

Key Points​

  • Block cipher works on fixed-size blocks

  • Uses multiple rounds for security

  • SPN structure provides:

    • Confusion (S-box)
    • Diffusion (Permutation)

  • Decryption requires invertible operations

Final Takeaway​

  • Block ciphers are foundation of modern encryption

  • SPN is core design (used in AES)

  • Security comes from:

    • Multiple rounds
    • Key scheduling
    • Substitution + permutation