![]() ![]() In light of this, it becomes clear that the permutation formula is counting one combination k! times, k = the number of chairs or spots (4 in the video). This reminded me of the principle of Inclusion/Exclusion which is basically about subtracting over counted elements. It's deceiving because the k! is actually DIVIDING the entire permutation equation. The part that confused me about the combinations formula is what the multiplication of k! in the denominator is doing to the formula. the number of permutations is equal to n!/(n-k)! so the number of combinations is equal to (n!/(n-k)!)/k! which is the same thing as n!/(k!*(n-k)!). ![]() So the formula for calculating the number of combinations is the number of permutations/k!. The group size can be calculated by permuting over the number of chairs which is equal to the factorial of the number of chairs(k!). So the number of combinations is equal to the number of permutations divided by the size of the groups(which in this case is 6). If we didn't care about these specific orders and only cared that they were on the chairs then we could group these people as one combination. So some of the permutations would be ABC, ACB, BAC, BCA, CAB and CBA. In our example, let the 5 people be A, B, C, D, and E. The number of combinations is the number of ways to arrange the people on the chairs when the order does not matter. So the formula for the number of permutations is n!/((n-k)!. For n people sitting on k chairs, the number of possibilities is equal to n*(n-1)*(n-2)*.1 divided by the number of extra ways if we had enough people per chair. We can make a general formula based on this logic. So the total number of permutations of people that can sit on the chair is 5*(5-1)*(5-2)=5*4*3=60. On the third chair (5-2) people can sit on the chair. On the second chair (5-1) people can sit on the chair. If there are 3 chairs and 5 people, how many permutations are there? Well, for the first chair, 5 people can sit on it. 2 1 1.11 Eectiveness of exhaustive search attack. ![]() 2 1 1.10 Types of attack model: adversary’s goals. 2 0 1.9 Types of assumption/adv ersaries capabilities. 2 0 1.8.1 Symme tric and Asym metri c e ncry ption. 1 9 1.6 Secur ity M ode, A ttac k(adv ersa ry) mode l. ![]() 1 7 1.4 Kerckho’s principle and s ecurity by obscurity. 1 6 1.3 Secur ity requi reme nts /cri teria. 1 6 1.2.2 Ac tiv e a nd P assiv e A ttac ks. Moreov er, welcome to conta ct me to b e an editor of the learning notes together, which will be a means for us to progress. Please contact me if there are any typos or mistakes in the proof and explanations. Those will be coming soon and the book will keep updating as I explore more on cryptography. Because the note was initially my learning note, I still do not incl ude citati ons and refere nces to some work s that the note is based on. The two modules help me construct the skeleton of this note, and thereafter I extended the contends based on Cryptography I on Coursera by Dan Boneh and some academic papers. The note is initially integrated from my notes of CS3230 (Computer Security, A+) by Reza Shokri and CS4236(C rypto graph y Theo ry and Prac tice, A) by Hugh Ander son. These new properties endow cryptography with the p otential to create great value in academics and industry. Modern cryptography evolves and develops to achieve more functionalities from initially condentiality and integrity to identity, authentication, anonymity and secure computation, etc. Cryptography is an indispensable to ol used to achiev e interesting secure purposes in computer systems. ![]()
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