Cryptography Activity                        Name:
Secret Sharing                               Date:                 Per:



The following represents a method that can be used to share a secret between 
n people.  The idea is this: each of n people are given an ordered pair that 
corresponds with some element of the "secret".  Alone, they can determine 
nothing about the secret from their ordered pair.  However, when n-1 of them 
get together and compare their ordered pairs, they can write an equation that 
DOES reveal something about the secret.



For our activity, the "secret" is a message.  Each letter of the message has 
been changed to a number (A = 0, B = 1, etc ... ). Each of you is given a set
of ordered pairs and the location of the message to which it corresponds.  
The secret number (which can then be changed to a letter) is the y-intercept 
of a particular line through the point you are given.  We know that it takes 
two points to determine a line, so you will need to find someone else in the 
class who also has an ordered pair for that line.  Together, you can write an 
equation for the line, determine the y-intercept, and then translate that 
number to the corresponding letter.



Other students may provide the letter for some of yours before you can get to 
them, but I want to see the work for each of you to get an equation for each 
location you received.



 Location in    Ordered pair:       Another point on the line:      Equation:
the message:



< Each student is provided one or more index numbers with one corresponding
 ordered pair.  Be sure students with the same index number receive different
 ordered pairs!  Below is the master list of ordered pairs and the correct 
equations.>



 1      (3,8) (6,10) (-3,4) (-6, 2)                              y = 2/3 x +  6
 2      (2, -23) (4, -28) (-2, -13)  (-8, 2)                     y = -512 x -18
 3      (2, 1) (8, 19) (-4, -17) (-3, -14)                       y = 3x - 5
 4      (4, 5) (8, 6) (-16. 0) (-8, 2)                           y = 1/4 x + 4
 5      (4, 1 8) (-4, 6) (8, 24) (-8, 0)                         y = 3/2 x + 12
 6      (1, -25) (-1, -19) (3, -31) (-2, -16)                    y = -3x - 22
 7      (5, 3) (-5, -3) (15, 9) (-10, -6)                        y = 3/5 x
 8      (1, -20) (-2, -23) (3, -18) (-4,     -25)                y = x - 21
 9      (5, 12) (-15, -4) (10, 16) (-5, 4)                       y = 4/5 x + 8
 10     (3, -7) (6, -6) (1 2, -4) (-9, -11)                      y = 1/3 x - 8
 11     (2, 5) (4, 3) (-3, 10) (-5, 12)                          y = -x + 7



 12     (2, -23) (4, -28) (-2, -1 3) (-8, 2)
 13     (9, 3) (-9, 19) (18, -5) (-18, 27)
 14     (5, -13) ( -5, -17) (10, -11) (-15, -21)
 15     (4, 5) (8, 6) (-I 6, 0) (-8, 2)
 16     (5, 3) (-5, -3) (1 5, 9) (-I 0, -6)
 17     (-I, -9) (2, -3) (1, -5) (-4, -1 5)
 18     (1, 10) (5@. 30) (-2, -5) (2, 1 5)
 19     (4, -7) (8, -2) (-l 2, -27) (1 6, 8)
 20     (2, 1 7) (5, 1 7) (3, 1 7) (-2, 1 7)
 21     (7, -23) (14, -20) (-21, -35) (-7, -29)
 22     (6, 7) (12, 11) (-9, -3) (-3, 1)
 23     (7, -23) (14, -20) (-21, -35) (-7, -29)
 24     (5, -1) (-10, -4) (15, 1) (-20, -6)
 25     (-l, -9) (2, -3) (1, -5) (-4, -1 5)
 26     (4, 5) (8, 6) (-I 6, 0) (-8, 2)
 27     (5, 3) (-5, -3) (1 5, 9) (-I 0, -6)
 28     (1, 6) (4, 1 8) (-2, -6) (-6, -22)
 29     (-2, -21) (4, -15) (1, -18) (-6, -25)
 30     (4, 1 8) (-4, 6) (8, 24) (-8, 0)
 31     (4, 5) (8, 6) (-16, 0) (-8, 2)
 32     (-l, -9) (2, -3) (1, -5) (-4, -1 5)
 33     (4, 1 6) (8, 1 8) (-2, 13) (-10, 9)
 34     (1, -20) (-2, -23) (3, -18) (-4, -25)
 35     (2, -23) (4, -28) (-2, -1 3) (-8, 2)


 y =  -5/2 x - 18
 y =  -8/9 x + 11
 y =  2/5 x - 15
 y =  1/4 x + 4
 y =  3/5 x
 y =  2x - 7
 y =  5x + 5
 y =  5/4 x - 12
 y =  17
 y =  3/7 x - 26
 y =  2/3 x + 3
 y =  3/7 x - 26
 y =  1/5 x - 2
 y =  2x - 7
 y =  1/4 x + 4
 y =  3/5 x
 y =  4x + 2
 y =  x - 19
 y =  3/2 x + 12
 y =  1/4 x + 4
 y =  2x - 7
 y =  1/2 x + 14
 y =  x - 21
 y =  -5/2 x - 1 8
 36     (5, 21) (10, 24) (-15, 9) (-20, 6)
 37     (2, 5) (4, 3) (-3, 10) (-5, 1 2)
 38     (5, 1 2) (-15, -4) (10, 16) (-5, 4)
 39     (9, 3) (-9, 19) (18, -5) (-18, 27)
 40     (5, -13) ( -5, -17) (10, -11) (-15, -21)
 41     (4, 5) (8, 6) (-l 6, 0) (-8, 2)
 42     (5, 3) (-5, -3) (1 5, 9) (-10, -6)
 43     (-1, -9) (2, -3) (1, -5) (-4, -15)
 44     (1, 10) (5, 30) (-2, -5) (2, 1 5)
 45     (4, -7) (8, -2) (-12, -27) (16, 8)
 46     (8, -6) (-8, -1 0) (16, -3) (-16, -15)
 47     (7, -23) (14, -20) (-21. -35) (-7, -29)
 48     (9, 3) (-9, 1 9) (18, -5) (-18, 27)
 49     (5, 12) (-15, -4) (10, 16) (-5, 4)
 50     (1, 10) (5, 30) (-2, -5) (2, 15)
 51     (1, -25) (-l, -19) (3, -31) (-2, -16)
 52     (-1, -9) (2, -3) (1, -5) (-4, -15)
 53     (5, 12) (-15, -4) (10, 16) (-5, 4)
 54     (4, 18) (-4, 6) (8, 24) (-8, 0)
 55     (1, -25) (-l, -19) (3, -31) (-2, -16)


 y = 3/5 x + 1 8
 y = -x + 7
 y = 4/5 x + 8
 y = -8/9 x + I I
 y = 2/5 x - 1 5
 y = 1/4 x + 4
 y = 3/5 x
 y = 2x - 7
 y = 5x + 5
 y = 5/4 x - 1 2
 y = 3/8 x - 9
 y = 3/7 x - 26
 y = -8/9 x + I 1
 y = 4/5 x + 8
 y = 5x + 5
 y = -3x - 22
 y = 2x - 7
 y = 4/5 x + 8
 y = 3/2 x + 12
 y = -3x - 22