1. ## 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. ## Re: Elliptic Curve Cryptography

Originally Posted by vokoyo
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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
(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

$\displaystyle \{0,1,2,4,8,9,13,15,16\}$

3. ## Re: Elliptic Curve Cryptography

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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. ## 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. ## Re: Elliptic Curve Cryptography

17 points

$\displaystyle \{\{0,1\},\{0,16\},\{4,1\},\{4,16\},\{6,6\},\{6,11 \},\{9,5\},\{9,12\},\{10,5\},\{10,12\},\{11,0\},\{ 13,1\},\{13,16\},\{15,5\},\{15,12\},\{16,4\},\{16, 13\}\}$

6. ## Re: Elliptic Curve Cryptography

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

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