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- Feb 19th 2008, 06:53 AM #1

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## 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?

If anyone knows about this topic could they please explain step by step the process encoding messages?

Thanks in advance!

- Feb 19th 2008, 07:15 AM #2

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- Feb 19th 2008, 07:51 AM #3

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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!

- Feb 19th 2008, 08:42 AM #4

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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

- Feb 20th 2008, 05:50 AM #5

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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?

Thanks in advance!