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Thread: Elliptic Curve Cryptography

  1. #1
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    Elliptic Curve Cryptography

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    May I know how to solve the equation as below:


    (1) y2 = x3 + x + 1 mod 17

    Finding Inverses
    Finding Points on the Curve

    (2) y2 = x3 + 3x + 1 mod 13

    Finding Inverses
    Finding Points on the Curve







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  2. #2
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    Re: Elliptic Curve Cryptography

    Quote Originally Posted by vokoyo View Post
    .

    May I know how to solve the equation as below:


    (1) y2 = x3 + x + 1 mod 17

    Finding Inverses
    Finding Points on the Curve
    (1) There are algorithms for solving such problems.

    or you can use the brute force method

    $\displaystyle x^3+x+1$ is a quadratic residue $\displaystyle \pmod {17} $

    so it is equal to one of

    $\displaystyle \{0,1,2,4,8,9,13,15,16\}$
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  3. #3
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    Re: Elliptic Curve Cryptography

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    Thank you for your suggestion

    Please show me your sample solution draft
    so that I can improve my calculus skills

    I fact I would like to draw the curve line or point by point






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  4. #4
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    Re: Elliptic Curve Cryptography

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    Please refer to my draft paper as below -


    Elliptic Curve Cryptography.pdf






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  5. #5
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    Re: Elliptic Curve Cryptography

    17 points

    $\displaystyle \{\{0,1\},\{0,16\},\{4,1\},\{4,16\},\{6,6\},\{6,11 \},\{9,5\},\{9,12\},\{10,5\},\{10,12\},\{11,0\},\{ 13,1\},\{13,16\},\{15,5\},\{15,12\},\{16,4\},\{16, 13\}\}$
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  6. #6
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    Re: Elliptic Curve Cryptography

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    Please show me your draft paper for reference purpose - Important and Urgent






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