Demonetization and You – A Backgrounder on India’s Moves Against Cash

Euclidean Algorithm for Greatest Common Denominator

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A 24-by-60 rectangle is covered with ten 12-by-12 square tiles, where 12 is the GCD of 24 and 60. More generally, an a-by-b rectangle can be covered with square tiles of side-length c only if c is a common divisor of a and b. So the task is to find the largest square that tiles the rectangle completely.  See below:

Subtraction-based animation of the Euclidean algorithm. The initial rectangle has dimensions a = 1071 and b = 462. Squares of size 462×462 are placed within it leaving a 462×147 rectangle. This rectangle is tiled with 147×147 squares until a 21×147 rectangle is left, which in turn is tiled with 21×21 squares, leaving no uncovered area. The smallest square size, 21, is the GCD of 1071 and 462.

So the example compiled down to arithmetic steps would be as follows:

1071 = 2*462 + 147

462 = 3*147 + 21 

147 = 7*21 + 0   Thus 21 is the GCD of 1071 & 462

Langley’s Adventitious Angles

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RSA Code Made Easy

A code is implemented with the following statement.  Decrypt the code.

 x^197 mod 3131  

The totient of 3131 is needed and is found below:

 3131 = 31 * 101    

 {psi} (3131) = psi(31) * psi(101) = (31-1)(101-1)=3000     because 31 and 101 are prime

Eulers Theorem a^{psi(n)} mod n =1     so:

 x^{3000m} mod (3131) = 1    Where m is an integer to give us more flexibility in generating an inverse in step XXX below.   Multiply both sides by x

 x^{3000m+1} mod (3131) = (x) mod (3131)

So if you can find a power d where:

 197d = 3000m + 1  or equivalently:

 (197d) mod(3000) = (1) mod(3000) then you can take the encrypted numbers to the power of d and out will pop the plain text original series

Now you use the Euclidean algorithm to find 1 in terms of 197 and 3000. This yields:

1 = 533(197) - 35(3000)     Taking the mod(3000) of both sides

(1)mod(3000) = (533)(197)  which shows d=533   is the decryption power we are looking for

This example used smaller numbers so as to make the example transparent.  However if the input character were to be X=31 or 101 I think the system breaks down.

Introduction for Cracking using OLLYDBG

How to hack a Remote computer using Darkcomet(RAT) – Remote Access Tool

Kali Linux Notes

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Farmer buys livestock puzzle

A farmer has 100 dollars to buy 100 animals.  A cow costs 10, a pig costs 5 and a chicken costs 50 cents.  How many of each does he buy?  He must use all his money and he must buy at least 1 of each type.

10x+5y+0.5z=100 

x+y+z=100 

note Z must be even because otherwise you will get  ddd.5<> 100 in the first equation. Eliminate z by multiplying first equation by 2 and subtracting the second equation

20x+10y+z=200 

x+y+z=100 

yields

19x+9y=100   Here a solution is only found because the solution is specified to be integers

 

Brute force Integer solution

Find a solution for the above and plugging into:  x+y+z=100   now plug in number until you get an even z. Try x=1:

19+9y=100 

9y=81 

y=9 

1+9+z=100 

z=90 

and is even and thus the problem is done

 

Modulus Solution

19x+9y=100 

(19x+9y)mod 9 = 100 mod 9

(19x) mod 9 + (9y) mod 9 = 1 

(19x) mod 9  = 1 

(19 mod 9)  *( x mod 9)  = 1 

 ( x )mod 9 = 1 

Two obvious solutions are 

 x=1    and  x=10    

The first solution is viable.  The second is not because there is no money left over to buy any other type of animal.

Ulterior States – IamSatoshi Documentary

Polynomial Root Solver with Root Map in Complex Plane and Graph of Function

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