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Math Help - Math question.

  1. #1
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    Math question.

    Hello,

    I hope someone can help me with this.

    X=M^e mod N

    from this how do we derive N if we know X, M, and e?

    I am sure it is simple to do but my head is in a fog after numerous hours in all of this math.
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  2. #2
    Super Member Gamma's Avatar
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    Whoa, I have no idea what some of these letters are coming from? Are they all integers or what? e is usually reserved for the exponential x is usually for real numbers and m and n are usually for integers, but I am hoping you have just run out of good numbers to use and all of these are just arbitrary integers.

    a \equiv b mod n iff n|(b-a)
    so if you know a,b,m all fixed integers.
    you just need to choose n to be a divisor of  b^m-a
    Then you will get the desired congruence mod n
    a\equiv b^m (mod n)
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  3. #3
    Senior Member TheAbstractionist's Avatar
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    Quote Originally Posted by DarkPrognosis View Post
    Hello,

    I hope someone can help me with this.

    X=M^e mod N

    from this how do we derive N if we know X, M, and e?

    I am sure it is simple to do but my head is in a fog after numerous hours in all of this math.
    Hi DarkPrognosis.

    Suppose X\ne M^e. If you know X, M and e, then N must be a divisor of X-M^e.

    For example, if X=26,\ M=2,\ e=3, then X-M^e=18 so N can be 1, 2, 3, 6, 9, 18. That is, 26 is congruent to 8 modulo 1, 2, 3, 6, 9 and 18.

    Unfortunately if X=M^e then N can be any integer, and there is no way to find out what it is without further information.
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  4. #4
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    oh brother.

    All are integers but if there is no way to reverse the formula I guess it doesn't matter.

    Thanks to everyone for helping with this.
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