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Results tagged with elliptic-curves
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user 106299
Elliptic curves are algebraic-geometric structures with applications in cryptography. Such a curve consists of the set of solutions to a cubic equation over a finite field equipped with a group operation. Questions relating to elliptic curves and derived algorithms should use this tag and might also consider more specific tags such as discrete-logarithm and ecdsa.
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The elliptic curve $y^2 = x^3 \pmod p$
Consider the solutions of the equation $y^2 = x^3 \pmod p$ for some prime $p=6k+1$. When considered as an elliptic curve, it has a cusp at $(0, 0)$, and addition involving this point doesn't work out. …
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The elliptic curve $y^2 = x^3 \pmod p$
Fix the generator $G=(1,1)$. Given a point $kG = (x,y)$ on this curve, one can calculate $k=x/y$.
So there is a very simple algorithm to perform point to point division.
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Set ECDLP complexity
Consider the following problem which is an easier version of the EC discrete log problem. Fix an elliptic curve and a generator $G$. Given an arbitrary set of points $S$, the task is to find $k$ such …
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Has the ideal "pairing" $\langle aG, bG\rangle \mapsto abG$ been ruled out conditionally?
Let $G$ be a prime order $Q$ elliptic curve over a prime field of size $P$ which admits the following mapping $f$
$f(aG, bG) = abG$
which can be computed in polynomial time in $\log(PQ)$.
Is the exist …
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