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Math Help - cryptosystems anyone?

  1. #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!
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  2. #2
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    Quote Originally Posted by hunkydory19 View Post
    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!
    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
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  3. #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!
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by hunkydory19 View Post
    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
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  5. #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!
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