HILL CIPHER…
HILL CIPHER
Hill Cipher என்பது ஒரு classical polygraphic substitution cipher. இதில் plaintext letters-ஐ single letter-ஆக encrypt செய்யாமல், group of letters / blocks-ஆக எடுத்துக் கொண்டு matrix multiplication + modular arithmetic பயன்படுத்தி ciphertext…
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20 min
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3 programs 15 MCQs v2
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Definition
Hill Cipher என்பது ஒரு classical polygraphic substitution cipher. இதில் plaintext letters-ஐ single letter-ஆக ……
Simple Explanation
Caesar cipher: One letter → One letter Playfair cipher: Two letters → Two……
Explanation
Example
HI இதனை:…
Explanation
என்று numbers-ஆக மாற்றுகிறோம். பிறகு ஒரு Key……
Important
Hill Cipher உருவாக்கியவர்: Lester S. H……
Explanation
Type of cipher
Hill Cipher என்பது: Classical Cipher ↓ Substitution Cipher ↓ Polygraphic Substitution……
Concept
Main concept
Hill Cipher மூன்று முக்கிய concepts-ஐ பயன்படுத்துகிறது: Ma……
Explanation
Letter to number conversion
Hill Cipher-ல் பொதுவாக: A = 0 B = 1 C = ……
Flow
Plaintext ↓ Divide into blocks ↓ Convert letters to numbers ↓ Crea……
Explanation
Key matrix
Hill Cipher-ன் secret key என்……
Program
Example
Explanation
இது: 2 × 2 matrix அதனால் plaintext இரண்ட……
Explanation
Block size
Key matrix: 2 × 2 என்றால்: 2 letters per block Key matrix: 3 × 3 ……
Formula
Encryption formula
Hill Cipher encryption formula: C = K × P mod 26 Where: C = Ciphert……
Real Life Example
Simple 2×2 example
Key Matrix: K = [3 3 2 5] Pla……
Explanation
Step 1: convert letters
Using: A = 0 ... Z = 25 Then:……
Formula
C = K × P mod 26 Substitute: ……
Explanation
Step 3: first value
First row: 3 × 7 + 3 × 8 Calculate: 21 + ……
Explanation
Step 4: second value
Second row: 2 × 7 + 5 × 8 Calculate: 14 ……
Explanation
Step 5: convert back to letters
We obtained: [19 2] Using mapping……
Dry Run
Full dry run
Explanation
Why mod 26?
English alphabet contains: 26 letters Numbers: 0 to 25 Matrix multiplication resu……
Real Life Example
Another example
Key: K = [3 3 2 5] Plaintext: GO Convert: G = 6 O = 14 Vector: P = [6 14] Multiply: C = [3 3] [……
Explanation
Decryption
Hill Cipher decryption-க்கு normal key matrix-ஐ பய……
Formula
P = K⁻¹ × C mod 26 Where: P = Plain……
Important
Very important
Hill Cipher-ல் எந்த matrix-யையும் key ஆக பயன்படுத்த முடியாது. Key matrix: Invert……
Explanation
Determinant
For a 2 × 2 matrix: K = [a b ……
Explanation
Key matrix check
Take: K = [3 3 2 5] Determinant: det(K) = (3 × 5) - (3 × 2) = 15 - 6 = 9 Now check: gcd(……
Real Life Example
Invalid key example
Suppose: K = [2 4 2 6] Determinant: det(K) = 2×6 - 4×2 = 12 - 8 = 4 Now: gcd(4,26) = 2 It is not 1. Therefore……
Explanation
2×2 matrix inverse
Normal inverse formula: For: K = [a b c d] determinant: det(K) = ……
Important
Normal decimal inverse அல்ல; ……
Real Life Example
Decryption example
Key: K = [3 3 2 5] Ciphertext: TC We alread……
Explanation
Step 1: determinant
det(K) = 3×5 - 3×2 = 15 - 6 =……
Explanation
Step 2: modular inverse of 9
We need: 9⁻¹ mod 26 Find number x such that:……
Explanation
Step 3: adjugate
Original: K = [3 3 2 5] Adjugate: adj(K) = [ 5 -3 -2 3] C……
Explanation
Step 4: multiply by determinant inverse
K⁻¹ = 3 × [5 23 24 3] mod 26 Multiply: = [15 69 72 9] Now mo……
Formula
P = K⁻¹ C mod 26 P = [15 17] [19] [20 9] [ 2] First value: 15×19 + 17×2 = 285 + 34 = 319 31……
Explanation
Complete formulas
Encryption C = KP mod 26 Decryption P = K⁻¹C mod 2……
Explanation
3×3 hill cipher
Hill cipher 2×2 மட்டும் அல்ல.……
Program
Example
Explanation
Then plaintext is divided into: 3-letter bl……
Explanation
If message length is not divisible
Suppose 2×2 Hill Cipher: Plaintext: HELLO Letters: 5 But block size: 2 Divide: HE……
Explanation
Hill cipher special feature
Monoalphabetic cipher: One plaintext letter ↓ One ciphertext letter Hill Cipher: Multiple plaintext letters ↓……
Explanation
Diffusion
Hill cipher classical cryptography-ல் diffusion concept-ஐ demonstrate செய்யும் நல்ல example. Suppose plaintex……
Comparison
Hill vs caesar
Comparison
Hill vs playfair
Important
Playfair 5×5 matrix பயன்படுத்துகிறது என்பதால் அது Hill ……
Comparison
Hill vs vigenère
Explanation
Advantages
Hill Cipher advantages: Multiple letters together encrypt செய்யப்படுகிறது. Matrix mathematics பயன்படுத்துகிறத……
Explanation
Disadvantages
Matrix calculations relatively complex. Key matrix must be invertible modulo 26. Invalid matrix selected செய்……
Explanation
Known plaintext weakness
Hill cipher ஒரு linear cipher. Encryption: C = KP mod 26 Attacker-க்கு enough plaintext vectors மற்றும் corre……
Common Mistake
Common error 1
Wrong: Hill Cipher uses Caesar shifting ……
Common Mistake
Common error 2
Wrong: Any square matrix can be used as key. Cor……
Common Mistake
Common error 3
Wrong: Hill Cipher decryption uses sam……
Common Mistake
Common error 4
Wrong: Hill Cipher uses A=1, Z=26 only. Fo……
Common Mistake
Common error 5
Wrong: C = KP Complete formul……
Common Mistake
Common error 6
Wrong: Hill Cipher is a transposition ci……
Remember
HILL H H = Handle letters in groups I I = Invers……
Explanation
Super memory
Just remember: Encrypt: C = KP mod 26 Decrypt: P = K⁻¹C mod 26 V……
TRB Point
TRB / NET / SET exam-க்கு முக்கியமான points: Hill Cipher was invented by Lester S. Hill. It was introduced in……
Interview Point
Question
Why must the determinant of a Hill Cipher key matrix be relatively prime to 26? Answer: Because decryption ……
MCQ
Hill Cipher is based on:…
MCQ
Hill Cipher was proposed by:…
MCQ
Hill Cipher is a:…
MCQ
Hill Cipher encryption formul……
MCQ
Hill Cipher decryption formul……
MCQ
Hill Cipher key is usually:…
MCQ
A 2×2 Hill Cipher key process……
MCQ
A valid Hill Cipher key must ……
MCQ
Which concept is strongly dem……
MCQ
Hill Cipher uses arithmetic m……
MCQ
If A=0, what is H?…
MCQ
For the key: [3 3 2 5] the de……
MCQ
If gcd(det K,26) ≠ 1, then:…
MCQ
Which operation is essential ……
MCQ
Hill Cipher is weak against s……
Practice
Given: K = [3 3 2 5] Encrypt: HI Step 1 H = 7 I = 8 Step 2 P = [7 8] Step 3 C = ……
TRB Point
Exam short answer
Hill Cipher என்பது Lester S. Hill உருவாக்கிய ஒரு classical polygraphic substitution cipher. இது plaintext let……
Summary
HILL CIPHER | ---------------------- | | Plaintext Key Matrix | | Convert to Square Numbers Matrix | | ------……
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