Recent content by yavanna

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    Graduate Baby Step Giant Step: Computing m of Rational Points on Elliptic Curve

    I've tried to use this algorithm in PARI/GP with the following code, just to check if it works, it doesn't output m but the indexes [i,j] of R+iQ=jP. Ellpoint finds a random point on the curve, ellsum makes the sum between two points, ellpow(E,P,n) compute the scalar multiplication nP. But it...
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    Graduate Baby Step Giant Step: Computing m of Rational Points on Elliptic Curve

    The baby-step-giant-step method to compute the number m of rational points over an elliptic curve defined over \mathbb{F}_p http://img560.imageshack.us/img560/3852/babym.jpg Uploaded with ImageShack.us In the second part R=(p+1)P, but for every point on the curve (p+1)P is the identity...
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    Graduate Proof of a^{\frac{p-1}{2}}=-1 mod p

    Yes, i was trying some examples and I think it only works with primitive roots... But why?
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    Graduate Proof of a^{\frac{p-1}{2}}=-1 mod p

    If p is a prime and a an integer coprime with p, why is a^{\frac{p-1}{2}}\equiv -1 mod p ?
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    Graduate Endomorphism ring over an elliptic curve

    I found that the endomorphism group over an elliptic curve is isomorphic to a complex quadratic order: End(E)\simeq \mathbb{Z}[\delta]=\mathbb{Z}+\delta\mathbb{Z}, where \delta=\frac{\sqrt{\Delta}}{2} if \Delta is even \delta=\frac{1+\sqrt{\Delta}}{2} if \Delta is odd Does anyone know where...
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    Computational complexity with an epsilon

    What does that mean when there's an \epsilon in the complexity, such as O(n^{2+\epsilon}) for every \epsilon >0
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    Graduate Proving X=Y with Conditional Expectation

    How can I do this? Let X,Y r.v., \mathbb{E}(X|Y)=Y and \mathbb{E}(Y|X)=X. Proove that X=Y a.s.
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    Graduate Does (X_{n})_{n_{\geq 1}} converge almost surely to 0?

    Does (X_{n})_{n_{\geq 1}}, X_{n}=\frac{n}{ln(n)}Y_{n}, where Y_{n} \sim Exp(n) converge a.s. to 0?