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Now to calculate Q this will take a lot of time since it means I will need to perform point addition an insane number of times unless I'm not understanding something about it. You're missing a point; elliptic curve point addition is associative; that is, for any three points $A, B, C$, we have: $$(A + B) + C = A + (B+C)$$ Now, why is this a big deal? ...


4

What's difference between n & #E(FP)? The difference is that $n$ is the smallest positive integer where $nG = O$; while you correctly state that $\#E \cdot G = O$, that doesn't mean that $\#E$ is the smallest integer that makes this happen. There may be a smaller integer $n$; $n$ will always be a factor of $\#E$, however it can be smaller. As for ...


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You want to find a point $(X,Y)$ on an elliptic curve $y^2 = x^3 + ax + b$ knowing only $X$ and a single bit indicating whether $Y$ is even or odd. To find $Y$, you use the relation defining the curve: you know that $Y^2 = X^3 + aX + b$ since the point is on the curve. So you compute $X^3 + aX + b$ using your value of $X$ and the public parameters $a, b$, ...


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I recently came across a paper that may interest you that I think answers your question. To quote from the abstract: Unfortunately, in all existing HD wallets---including BIP32 wallets---an attacker can easily recover the master private key given the master public key and any child private key. This vulnerability precludes use cases such as a combined ...


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ElGamal works for any ring. What is badly specified is the glue between the protocols (some network packets) and the exact implementation variants in the math library. C25519 use arithmetic over Montgomery curves. Ed25519 use arithmetic over twisted Edwards curves. Huff curves implementations can be "faster", but there are not in the repository of curves ...


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1. What standard curves could I use? I know curves like p192 etc exists, am I allowed to use these? Yes, of course you may use those, for more curves - including safer ones - check the safecurves website. 2. How can I find valid points to use for messages and generator on these huge curves? So far I've done it using brute force on smaller curves with a ...



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