Xu Bowen

Principle and Practice of Computer AlgorithmsSummer 2015

Simple Implementation of Algorithmin Data Encryption

Characteristics of Key：

Symmetric , Public

Processing of Plaintext :

Block (DES , Knapsack , RSA)Stream (RC4 , SEAL)

Categorization

∆ Symmetric Key Cryptosystem

∆ Public Key Cryptosystem

∆ Authentication

Symmetric Key Cryptosystem

DES Algorithm --- Feistel Structure

Stream Cipher --- Exclusive OR

Symmetric Key Cryptosystem

Disadvantages :

× Key Distribution : Negotiation

× Key Management : N*(N-1)/2

Public Key Cryptosystem

Knapsack Algorithm

Knapsack Algorithm

In 1978 , Knapsack System, a public key cryptosystem, was raised by Merkle and Hellman based on its intractability

Given N+1 Positive integers :and

Decide the solution of where

() called the vectors of knapsack

Knapsack Problem (01)

Known , calculating is easy

Oppositely , known calculating is difficult

• f[i-1][j-a[i]] = true -> f[i][j] = true, recording : g[i][j] = true;

• F[i-1][j] = true -> f[i][j] = true, recording : g[i][j] = false;

Knapsack Problem (01)

Knapsack Algorithm

Special vectors of knapsack :

When given a positive integer , calculating is easy

Generally, when , calculating is also easy

This kind of knapsack is called Super Increasing Knapsack

Knapsack Algorithm

Generating the vectors of super increasing knapsack

Choose two integers ,, W < M and gcd(W, M) = 1

Calculating

Calculating

Knapsack Algorithm

Public Key : k = (

Private Key : k’ = ()*(, because it can be easily calculated)

Knapsack Algorithm

Encryption :

Plaintext : m = () where Public Key : k = ()

Knapsack Algorithm

Decryption :

mod M () mod M () mod M () mod M

Super Increasing Knapsack

Public Key Cryptosystem

RSA Algorithm

RSA Algorithm

In 1978 , RSA System, a public key cryptosystem, was raised by Rivest , Shamire and Adleman based on Decomposition of BigNumber and Detection of Primes

RSA Algorithm

Generating two big primes P, Q (PQ)

Let n = P*Q, (n) = (P-1)*(Q-1)

Choose an integer e, where 1<e<(n) and gcd((n), e) = 1

Calculating (existence : ax+by=1)

Public Key : k =

Private Key : k’ = (P, Q, )

RSA Algorithm

Encryption :

Plaintext : m , where m < nPublic Key : k =

RSA Algorithm

Decryption :

*()

RSA Algorithm

Why must we need authentication ?

Authentication

Attack to Information Security :

Passive Attack : Cut-Out & Analysis

Active Attack : Forge , Resend , Distort , Reject

Denial : deny the info sender sends

Authentication

Defense :

Passive Attack : Encryption

Active Attack , Denial : Digital Signature

Authentication

Reliability

Unforgeability

Nonduplication

Unchangeability

Nonrepudiation

Digital Signature

Digital Signature

Info Info

Summary Summary

Hash Hash

Digital signature

Encryption (RSA) Decryption (RSA)

AUTHENTICATION

Private Key Public Key

Q & A

Thx for listening

Xu Bowen