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Math Help - encoding and decoding help

  1. #1
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    encoding and decoding help

    I have the following....
    p=311 q=173
    m= 53803
    Euler Totient = 53320
    k=3
    message is the string of digits
    232 524 141 135 192 911 331 529 252 315
    a1= 232 a2= 524........a10=315

    In the form a^k = = b (mod 53803)

    I don't know how to find b....I have been going in circles for the past 4 hours and I can't get it... please help
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by duggaboy View Post
    I have the following....
    p=311 q=173
    m= 53803
    Euler Totient = 53320
    k=3
    message is the string of digits
    232 524 141 135 192 911 331 529 252 315
    a1= 232 a2= 524........a10=315

    In the form a^k = = b (mod 53803)

    I don't know how to find b....I have been going in circles for the past 4 hours and I can't get it... please help
    232^3 \equiv b_1 \mod 53803

    232^3=12487168=232 \cdot 53803+4872 \implies 232^3 \equiv 4872 \mod 53803


    But what exactly is k ?
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  3. #3
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    I am assuming that 3 is an okay selection for k, our assignment was to choose any k....
    is there an exact way to get a "real" k?? with out just guessing?
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  4. #4
    Moo
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    Quote Originally Posted by duggaboy View Post
    I am assuming that 3 is an okay selection for k, our assignment was to choose any k....
    is there an exact way to get a "real" k?? with out just guessing?
    Actually, you have to know if k is part of the public of the private key. That is to say if you have to find 232 powered to k, or powered to its inverse.

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  5. #5
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    Oh my my....how would go about that? The example I have is where we did this in class and we just choose a random k....
    the public key is the k and m....which is what i'm supposed to send to a secret partner : )
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