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Comprehensive Overview of Public-Key Encryption Algorithms

This handbook chapter covers various public-key encryption algorithms including RSA, ElGamal, Rabin, McEliece, and Knapsack encryption. It discusses the computational problems, key generation, encryption, decryption, security aspects, and practical applications of each algorithm.

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Comprehensive Overview of Public-Key Encryption Algorithms

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  1. Handbook of Applied Cryptography- CH8, Public-Key Encryption Jinmyeong Shin 2017. 11. 13

  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 • 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 • 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

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