+0  
 
+5
270
3
avatar+266 

Paypay  Jan 5, 2016

Best Answer 

 #2
avatar+78620 
+15

I didn't know how to do this before watching that video, but here goes my attempt .....

 

ONE   QUESTION   TO  GO =

 

15 - 14 - 5 - 0 - 17 - 21 - 5 - 19 - 20 - 9 - 15- 14- 0 - 20 - 15 - 0 - 7 - 15

 

Since the encoding matrix is a 2 x 2........and our "encoded" matrix will have 18 entries...... and we must have a  9 x 2   "encoded" matrix because  the columns of the encoded matrix MUST  equal  the rows of our encoding matrix ... [ this isn't specifically pointed out in the video !!!]......so, setting the character string up into the "encoded" matrix, we have...

 

[ 15    14

    5      0

   17   21

     5   19                [  1    - 2

   20     9                   -3     7 ]

   15    14

    0     20

   15     0

     7    15 ]

 

Now, multiply the above "encoded" matrix and "encoding" matrix together......It will probably be easiest to employ some modern technology here...I used this website for all of the calculations :  http://matrix.reshish.com/multiplication.php

 

.....and we get

 

[ - 27      68

       5    -10

   -46    113

   -52    123 

     -7      23

   -27      68

   -60    140

    15     -30

   -38      91]

 

This is the matrix that the "receiver" would see from the "sender"....!!!

 

However......without knowing what the encoding matrix is, it would be useless.....so, now....

 

We need to find the invese of the encoding matrix.....this is  given by

 

 

[7  2

 3  1]

 

Now, Multiply the matrix found in the first multiplication of matrices by the inverse of the encoding matrix  [ again, using the website for the calculations ]

 

 

[ - 27      68

       5    -10

   -46    113

   -52    123 

     -7      23                   [ 7    2

   -27      68                     3    1]

   -60    140

    15     -30

   -38      91]

 

And we have

 

[ 15    14

    5      0

  17     21

    5     19

  20      9

  15     14

   0      20

  15      0

   7       15 ]

 

So.....the string of resulting digits is  :

 

15-14-5-0-17-21-5-19-20-915-14-0-20-15-0-7-15

 

Matching this to the original character key, the "receiver" would be able to read the original  message :

 

ONE QUESTION TO GO   .......which is correct  !!!!

 

Note.......without the possession of the character key and encoding matrix, this message would be "unbreakable" to outside eyes.....!!!!

 

 

 

 

cool cool cool

CPhill  Jan 5, 2016
edited by CPhill  Jan 5, 2016
edited by CPhill  Jan 5, 2016
edited by CPhill  Jan 5, 2016
edited by CPhill  Jan 5, 2016
Sort: 

3+0 Answers

 #1
avatar
0

1. replace all letters with the alphabet table. You will get a number sequence.

 

2. Write down the numbers in a matrix. Since your got a 2 dimensional matrix choose your encoding matrix to be a square matrix.

 

3. multiply the matrices

 

see also

https://www.youtube.com/watch?v=h7dwHg3EZjE

Guest Jan 5, 2016
 #2
avatar+78620 
+15
Best Answer

I didn't know how to do this before watching that video, but here goes my attempt .....

 

ONE   QUESTION   TO  GO =

 

15 - 14 - 5 - 0 - 17 - 21 - 5 - 19 - 20 - 9 - 15- 14- 0 - 20 - 15 - 0 - 7 - 15

 

Since the encoding matrix is a 2 x 2........and our "encoded" matrix will have 18 entries...... and we must have a  9 x 2   "encoded" matrix because  the columns of the encoded matrix MUST  equal  the rows of our encoding matrix ... [ this isn't specifically pointed out in the video !!!]......so, setting the character string up into the "encoded" matrix, we have...

 

[ 15    14

    5      0

   17   21

     5   19                [  1    - 2

   20     9                   -3     7 ]

   15    14

    0     20

   15     0

     7    15 ]

 

Now, multiply the above "encoded" matrix and "encoding" matrix together......It will probably be easiest to employ some modern technology here...I used this website for all of the calculations :  http://matrix.reshish.com/multiplication.php

 

.....and we get

 

[ - 27      68

       5    -10

   -46    113

   -52    123 

     -7      23

   -27      68

   -60    140

    15     -30

   -38      91]

 

This is the matrix that the "receiver" would see from the "sender"....!!!

 

However......without knowing what the encoding matrix is, it would be useless.....so, now....

 

We need to find the invese of the encoding matrix.....this is  given by

 

 

[7  2

 3  1]

 

Now, Multiply the matrix found in the first multiplication of matrices by the inverse of the encoding matrix  [ again, using the website for the calculations ]

 

 

[ - 27      68

       5    -10

   -46    113

   -52    123 

     -7      23                   [ 7    2

   -27      68                     3    1]

   -60    140

    15     -30

   -38      91]

 

And we have

 

[ 15    14

    5      0

  17     21

    5     19

  20      9

  15     14

   0      20

  15      0

   7       15 ]

 

So.....the string of resulting digits is  :

 

15-14-5-0-17-21-5-19-20-915-14-0-20-15-0-7-15

 

Matching this to the original character key, the "receiver" would be able to read the original  message :

 

ONE QUESTION TO GO   .......which is correct  !!!!

 

Note.......without the possession of the character key and encoding matrix, this message would be "unbreakable" to outside eyes.....!!!!

 

 

 

 

cool cool cool

CPhill  Jan 5, 2016
edited by CPhill  Jan 5, 2016
edited by CPhill  Jan 5, 2016
edited by CPhill  Jan 5, 2016
edited by CPhill  Jan 5, 2016
 #3
avatar+91024 
0

Great work Chris,

 

This looks interesting and involved.  I will have to see if i can find time to try it for myself.

 

 

Arrrr too many toys to play with - never enough time - many are not done justice - what are great sadness.  cheeky

Melody  Jan 6, 2016

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