CYS406 · Chapter 4 · Annotated SlidesPublic-Key Cryptography and RSA
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Overview

Public-Key Cryptography and RSA

Why public-key cryptography, how it gives confidentiality and authentication, its requirements and applications, RSA key setup, encryption and decryption with a worked example, fast exponentiation, and the security of RSA (factoring, timing and chosen-ciphertext attacks).

How to read this page

Every original slide is shown unchanged. Yellow marks on a slide point to a numbered note: hover or tap a mark to jump to its note, and hover a note to see its marks. Questions tagged Past exam appeared on a real paper; Prediction questions are likely angles, not confirmed. Pick an answer to each question: a wrong pick tells you why it is wrong, so you can try again.

All 35 slides
  1. 1 Slide 1
  2. 2 Private-Key Cryptography
  3. 3 Challenges To Be Considered
  4. 4 Symmetric Cipher: Confidentiality
  5. 5 Symmetric Cipher: Authentication
  6. 6 Public-Key Cryptography
  7. 7 Why Public-Key Cryptography?
  8. 8 Public-Key Cryptography
  9. 9 Public-Key Cryptography
  10. 10 Symmetric vs Public-Key
  11. 11 Public-Key Cryptosystems
  12. 12 Public-Key Applications
  13. 13 Public-Key Requirements
  14. 14 Public-Key Requirements
  15. 15 Security of Public Key Schemes
  16. 16 RSA
  17. 17 RSA Example
  18. 18 RSA En/decryption
  19. 19 RSA Key Setup
  20. 20 Why RSA Works
  21. 21 RSA Example - Key Setup
  22. 22 RSA Example - En/Decryption
  23. 23 Exponentiation
  24. 24 Exponentiation
  25. 25 Exponentiation Example
  26. 26 Efficient Encryption
  27. 27 Efficient Decryption
  28. 28 RSA Key Generation
  29. 29 RSA Security
  30. 30 Factoring Problem
  31. 31 Progress in Factoring
  32. 32 Slide 32
  33. 33 Timing Attacks
  34. 34 Chosen Ciphertext Attacks
  35. 35 Summary
Slide 1 / 35

Slide 1

Slide 1: Slide 1
Slide 2 / 35

Private-Key Cryptography

Slide 2: Private-Key Cryptography
Slide 3 / 35

Challenges To Be Considered

Slide 3: Challenges To Be Considered
Slide 4 / 35

Symmetric Cipher: Confidentiality

Slide 4: Symmetric Cipher: Confidentiality
Slide 5 / 35

Symmetric Cipher: Authentication

Slide 5: Symmetric Cipher: Authentication
Slide 6 / 35

Public-Key Cryptography

Slide 6: Public-Key Cryptography

Notes

  1. Public-key: encrypt with the receiver’s PUBLIC key for confidentiality; sign with your PRIVATE key for authentication.

  2. Trap Confidentiality: encrypt with the RECEIVER’s public key. Signature: encrypt (sign) with the SENDER’s private key.

Exam angle

PredictionQ1

To send Bob a confidential message, Alice encrypts with:

PredictionQ2

A digital signature is created with:

Slide 7 / 35

Why Public-Key Cryptography?

Slide 7: Why Public-Key Cryptography?
Slide 8 / 35

Public-Key Cryptography

Slide 8: Public-Key Cryptography
Slide 9 / 35

Public-Key Cryptography

Slide 9: Public-Key Cryptography
Slide 10 / 35

Symmetric vs Public-Key

Slide 10: Symmetric vs Public-Key
Slide 11 / 35

Public-Key Cryptosystems

Slide 11: Public-Key Cryptosystems
Slide 12 / 35

Public-Key Applications

Slide 12: Public-Key Applications
Slide 13 / 35

Public-Key Requirements

Slide 13: Public-Key Requirements
Slide 14 / 35

Public-Key Requirements

Slide 14: Public-Key Requirements
Slide 15 / 35

Security of Public Key Schemes

Slide 15: Security of Public Key Schemes
Slide 16 / 35

RSA

Slide 16: RSA
Slide 17 / 35

RSA Example

Slide 17: RSA Example
Slide 18 / 35

RSA En/decryption

Slide 18: RSA En/decryption
Slide 19 / 35

RSA Key Setup

Slide 19: RSA Key Setup
Slide 20 / 35

Why RSA Works

Slide 20: Why RSA Works
Slide 21 / 35

RSA Example - Key Setup

Slide 21: RSA Example - Key Setup

Exam angle

PredictionQ1

p = 5, q = 11, e = 3. Find n, φ(n) and d.

Compare with the model answer

n = 55, φ = 4·10 = 40. d = 3⁻¹ mod 40 = 27 (3·27 = 81 = 2·40 + 1).

Slide 22 / 35

RSA Example - En/Decryption

Slide 22: RSA Example - En/Decryption

Exam angle

PredictionQ1

In RSA, decryption computes:

Slide 23 / 35

Exponentiation

Slide 23: Exponentiation
Slide 24 / 35

Exponentiation

Slide 24: Exponentiation
Slide 25 / 35

Exponentiation Example

Slide 25: Exponentiation Example
Slide 26 / 35

Efficient Encryption

Slide 26: Efficient Encryption
Slide 27 / 35

Efficient Decryption

Slide 27: Efficient Decryption
Slide 28 / 35

RSA Key Generation

Slide 28: RSA Key Generation
Slide 29 / 35

RSA Security

Slide 29: RSA Security
Slide 30 / 35

Factoring Problem

Slide 30: Factoring Problem

Notes

  1. Attacks: brute force on d, factoring n (keys ≥ 2048 bits), timing attacks (constant-time code, blinding), chosen-ciphertext attacks (OAEP padding).

Slide 31 / 35

Progress in Factoring

Slide 31: Progress in Factoring
Slide 32 / 35

Slide 32

Slide 32: Slide 32
Slide 33 / 35

Timing Attacks

Slide 33: Timing Attacks
Slide 34 / 35

Chosen Ciphertext Attacks

Slide 34: Chosen Ciphertext Attacks
Slide 35 / 35

Summary

Slide 35: Summary