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c11y - Cyber Security

RSA Decryption Guide

Prime factors: p = 13, q = 83

Totient φ(n) = 984

Private exponent d = 595

Verification:

✓ p × q = 13 × 83 = 1079 = n ✓
✓ φ(n) = (13 - 1) × (83 - 1) = 984 ✓
✓ d × e mod φ(n) = 595 × 43 mod 984 = 1 ≡ 1 ✓

Decryption:

Decrypted values: 83 75 89 45 75 82 89 71 45 53 53 51 48
Plaintext: SKY-KRYG-5530

Introduction

Section titled “Introduction”

Current values:

  • Modulus: 1079
  • Public exponent: 43
  • Cipher text: 996 894 379 631 894 82 379 852 631 677 677 194 893

Step 1: Prime Factorization

Section titled “Step 1: Prime Factorization”

Find prime factors and where:

n=?∗?n = ? * ?

Step 2: Totient

Section titled “Step 2: Totient”

Calculate :

ϕ(n)=(?−1)∗(?−1)=?\phi(n) = (? - 1) * (? - 1) = ?

Step 3: Private Key

Section titled “Step 3: Private Key”

Find such that:

d∗43≡1(mod?)d * 43 ≡ 1 (mod ?)
d=?d = ?

Step 4: Verify the Solution

Section titled “Step 4: Verify the Solution”

Verify that:

?×?=1079? × ? = 1079
φ(n)=(?−1)×(?−1)=?φ(n) = (? - 1) × (? - 1) = ?
?×43≡1mod  ?? × 43 ≡ 1 \mod ?

Step 5: Use an RSA Decryption Tool

Section titled “Step 5: Use an RSA Decryption Tool”

Finally, input the following values into an RSA decryption tool:

  • n = 1079
  • e = 43
  • d = ?

Click “Decrypt” to obtain the plaintext message.