1. Handbook of Applied Cryptography - CH8, Public-Key Encryption
Jinmyeong Shin

2. Agenda
8.1 Introduction
8.2 RSA public-key encryption
8.3 Rabin public-key encryption
8.4 ElGamal public-key encryption
8.5 McEliece public-key encryption
8.6 Knapsack public-key encryption
8.7 Probabilistic public-key encryption
8.8 Notes and further references

3. 8.1 Introduction

4. 8.1 Introduction

5. 8.2.1 Description of RSA public-key encryption
Computational problem
Integer factorization problem(ch.3.2)
RSA problem (ch.3.3)
Key generation

6. 8.2.1 Description of RSA public-key encryption
Encryption and Decryption
Proof

7. 8.2.2 Security of RSA
Relation to factoring

8. 8.2.2 Security of RSA

9. 8.2.3 RSA encryption in practice

10. 8.3 Rabin public-key encryption
Computational problem
Integer factorization problem(ch.3.2)
Square roots modulo composite n(ch.3.5.2)
Key generation
Encryption and Decryption

11. 8.3 Rabin public-key encryption
Square root calculation

12. 8.3 Rabin public-key encryption
Security of Rabin public-key encryption
The task faced by a passive adversary is SQROOT problem that computing square roots modulo n. This problem is computationally equivalent Hence, factoring n is computationally intractable, the encryption scheme is provably secure against a passive adversary.
Rabin encryption scheme succumbs to a chosen-chiphertext attack.
Small encryption exponents, forward search attack and be circumvented by salting .
Multiplicative property can be avoided by adding redundancy.

13. 8.4 ElGamal public-key encryption
Computational problem
Discrete logarithm problem(ch.3.6)
Diffie-Hellman problem(ch.3.7)
Key generation

14. 8.4 ElGamal public-key encryption
Encryption and Decryption
Proof of works

15. 8.4 ElGamal public-key encryption
Efficiency of ElGamal encryption
Randomized encryption
The fundamental idea behind randomized encryption techniques is to use randomization to increase the cryptographic security of an encryption process through one or more of the following methods

16. 8.4 ElGamal public-key encryption

17. 8.4.2 Generalized ElGamal encryption
In case of the cyclic group G satisfy the following condition, ElGamal encryption scheme is also applied.
Key generation

18. 8.4.2 Generalized ElGamal encryption
Encryption and Decryption

19. 8.5 McEliece public-key encryption
Computational problem
Linear code decoding problem
Key generation

20. 8.5 McEliece public-key encryption
Encryption and Decryption
Proof of works

21. 8.5 McEliece public-key encryption
Security of McEliese encryption

22. 8.6 Knapsack public-key encryption
Computational problem
Subset sum problem
Merkle-Hellman knapsack encryption
Superincreasing sequece
Superincreasing subset sum problem

23. 8.6 Knapsack public-key encryption
Key generation

24. 8.6 Knapsack public-key encryption
Encryption and Decryption
Proof of work

25. 8.6 Knapsack public-key encryption
Insecurity of Merkle-Hellman knapsack encryption

26. 8.6 Knapsack public-key encryption
Chor-Rivest public-key encryption
Key generation

27. 8.6 Knapsack public-key encryption

28. 8.6 Knapsack public-key encryption
Decryption

29. 8.6 Knapsack public-key encryption
Proof of work

30. 8.6 Knapsack public-key encryption
Security of Chor-Rivest encryption

31. 8.7 Probabilistic public-key encryption