Suppose we use elgamal elliptic curves for secure communication. Bob selects a prime $p$, an elliptic curve $E$, a point $\alpha$ on $E \pmod p$, and a secret integer $f$. Suppose that Bob has selected $p =8115633240307$; $E: y^2 = x^3 + 45x + 1$; $\alpha = (1728910711, 274151521448)$, $f=7$; How would we calculate $\beta = [f]\alpha = [7](1728910711, 274151521448)$?.
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$\alpha+\alpha+\alpha+\alpha+\alpha+\alpha+\alpha$ – mikeazo May 15 '13 at 20:53
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http://crypto.stackexchange.com/questions/3907/how-does-one-calculate-the-scalar-multiplication-on-elliptic-curves might help too. – mikeazo May 15 '13 at 20:55
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@mikeazo Ya i looked at that and i couldnt relate. By α+α+α+α+α+α+α , how would addition of the points go? – Bobb Dizzles May 15 '13 at 20:57
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@BobbDizzles You need to look up the point addition and doubling formulas for your curve form. – CodesInChaos May 15 '13 at 21:37
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@CodesInChaos you mean like this?: http://www.voltage.com/blog/math-2/adding-points-on-an-elliptic-curve/ – Bobb Dizzles May 15 '13 at 21:40
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I'd use an existing ECC library which offers a scalar multiplication function. But if you implement it yourself you can look at the Explicit-Formulas Database which as addition/doubling formulas for many curve forms. – CodesInChaos May 15 '13 at 21:44
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The equations are in the answers I linked to. What exactly don't you understand. – mikeazo May 15 '13 at 23:04
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I'm going to close this for now. Please update to address exactly what you don't understand from the question I linked to above. Then we can reopen (just flag the question). – mikeazo May 21 '13 at 22:25