Handbook of Applied Cryptography - CH8, Public-Key Encryption

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Presentation transcript:

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

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

8.1 Introduction

8.1 Introduction

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

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

8.2.2 Security of RSA Relation to factoring

8.2.2 Security of RSA

8.2.3 RSA encryption in practice

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

8.3 Rabin public-key encryption Square root calculation

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.

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

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

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

8.4 ElGamal public-key encryption

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

8.4.2 Generalized ElGamal encryption Encryption and Decryption

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

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

8.5 McEliece public-key encryption Security of McEliese encryption

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

8.6 Knapsack public-key encryption Key generation

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

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

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

8.6 Knapsack public-key encryption

8.6 Knapsack public-key encryption Decryption

8.6 Knapsack public-key encryption Proof of work

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

8.7 Probabilistic public-key encryption