Here is an
example of using the RSA encoding scheme.
Where I have
put blank space, you should fill in a reason.
I choose
p=17 and q=23. These are a good start
because:_____________________________________
Then I
multiply 16 x 22 and get 352. I next choose
e=21 which is a good encoding number
because:___________________________________ .
Next I use http://www.math.uwaterloo.ca/~snburris/htdocs/linear.html
to get two numbers d and y such that 21·d - 352·y=1 The number I got for d
was:________________________________
To show that
e and d are encoding and decoding numbers we take a possible message, say 78.
The sender
computes 7821 mod 391 = m = ____________
(Type 78^21
mod 391 at web site: http://www.math.uga.edu/~bjones/calc/)
Finally
check how the receiver decodes the message:
md
mod 391 =78 by using the same calculator with your numbers m and d.
HW: Repeat
the above using your own p and q. Be
sure to fill in the reasons. Don’t use
78 as your message, send the month and day of your birth.
Hint: The
number you send must be less than the product in line 3 (the 352 above). So if,
for example, your birthday is December 25, you’d want to choose p and q so that
the product obtained in line 3 is greater than 1225
This will
help:
I choose p
and q. p,q are:
_____________________________________
Then I
multiply ___x ___ and get ___. I next
choose e=____ which is a good encoding number
because:___________________________________ .
Next I use http://www.math.uwaterloo.ca/~snburris/htdocs/linear.html
to get two numbers d and y such that __·d - ___·y=1 The number I got for d
was:________________________________
To show that
e and d are encoding and decoding numbers we take a possible message, my
birthday (month and day) is:___________.
The sender
computes ___mod pq = m = ____________
Use http://www.math.uga.edu/~bjones/calc/
to compute the above quantity.
Finally
check how the receiver decodes the message:
md
mod pq =___ by using the same calculator with your numbers m and d and the modulus
obtained by multiplying p and q.