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Markov Chains || Step-By-Step || ~xRay Pixy

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Learn Markov Chains step-by-step using real-life examples. Video Chapters: Markov Chains 00:00 Introduction 00:19 Topics Covered 01:49 Markov Chains Applications 02:04 Markov Property 03:18 Example 1 03:54 States, State Space, Transition Probabilities 06:17 Transition Matrix 08:17 Example 02 09:17 Example 03 10:26 Example 04 12:25 Example 05 14:16 Example 06 16:49 Example 07 18:11 Example 08 24:56 Conclusion
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introduction to Merkle-Hellman knapsacks Algorithm

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 Ralph Merkle and Martin Hellman Developed the first algorithm for Public Key for public-key Encryption, called the knapsacks Algorithm.

This algorithm is based on the Knapsack Problem.[this is actually a simple problem]

Given a pile of Items, each with different weights, is it possible to put some of them in a bag (i.e., knapsack) in such a way that the knapsack has a certain weight?

If M1, M2, M3,.., Mn are given values and S is the Sum, Find out bi so that:

           S = b1M1 + b2M2 + ... + bnMn

Each bi can be 0 or 1.  [1 indicates the item is in the knapsack and 0 indicates that it is not].

A Block of Plain text equal in length to the number of items in the pile would select the items in the knapsack. The ciphertext is the resulting sum. 

For example: if the knapsack is 1, 7, 8, 12, 14, 20 then the plain text and the resulting Ciphertext is shown as: 



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