1. ## cryptosystems anyone?

In this cryptosystem we use the ordinary English alphabet A-Z with the letters numbered from 0 to 25. We number digraphs using the enumeration to base 26. We encode digraphs using the affine transformation f(x) = 213x + 111(mod 676).

How would you encode the message FINAL?

2. Originally Posted by hunkydory19
In this cryptosystem we use the ordinary English alphabet A-Z with the letters numbered from 0 to 25. We number digraphs using the enumeration to base 26. We encode digraphs using the affine transformation f(x) = 213x + 111(mod 676).

How would you encode the message FINAL?

Code:
A 0
B 1
C 2
D 3
E 4
F 5
G 6
H 7
I 8
J 9
K 10
L 11
M 12
N 13
O 14
P 15
Q 16
R 17
S 18
T 19
U 20
V 21
W 22
X 23
Y 24
Z 25
Using X to pad FINAL to an even number of charaters:

FI=5*26+8

NA=13*26+0

LX=11*26+23

Now apply the transformation

RonL

3. Thanks so much CaptainBlack, but there is a step in the applying the transformation bit I don't understand...

an example in my notes is

17 x 27 + 25 = 464
applying g(x) = 638x + 358(mod 729)
638 x 464 + 358 = 416(mod 729)

But where does the 416 come from?? I can't see it at all, and don't understand the explanation in my notes...

thanks again!

4. Originally Posted by hunkydory19
Thanks so much CaptainBlack, but there is a step in the applying the transformation bit I don't understand...

an example in my notes is

17 x 27 + 25 = 464
applying g(x) = 638x + 358(mod 729)
638 x 464 + 358 = 416(mod 729)

But where does the 416 come from?? I can't see it at all, and don't understand the explanation in my notes...

thanks again!
First check your arithmetic, why do you have: 17x27+25, we are working to base 26, then this should be 17x26+25, also the arithmetic is wrong, so check what this really ought to be.

however lets work with what you do have:

638x464+358=296390=406x729+416

Now a number modulo 729 is the remainder when it is divided by 729 so in this case is 416

RonL

5. Cheers CaptainBlack, that's much clearer now.

I'm just now trying to find the deciphering transformation for this example...I've done:

Let y = 213x + 111(mod 676)
Then 213x = y - 111(mod 676)

But then I'm struggling from here to find the inverse of 213 modulo 676, could anyone please explain how I go about doing this?