Simple question about Elliptic Curve Cryptography

Delek (OP)

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Simple question about Elliptic Curve Cryptography

April 15, 2015, 02:42:24 PM

#1

Hi!

I was reading about ECC in the mastering bitcoin book and this image is very clear about how the multiplication is done:

However, what will happen if a resulting NG exactly hits the most left point in the curve (intersection between the function and X axis)? The tangent line will not find any other point and the multiplication will fail?

Thanks a lot for your time.

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LiteCoinGuy

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Re: Simple question about Elliptic Curve Cryptography

April 15, 2015, 04:12:47 PM

#2

https://www.youtube.com/watch?v=iB3HcPgm_FI

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YarkoL

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Re: Simple question about Elliptic Curve Cryptography

April 15, 2015, 04:41:18 PM

#3

Layman's Guide to Elliptic Curve Digital Signatures

“God does not play dice"

carstenh

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Re: Simple question about Elliptic Curve Cryptography

April 15, 2015, 04:59:47 PM

#4

That will never happen for the group used in Bitcoin. That specific point, is not a point on the elliptic curve used by Bitcoin. Such a point, call it Q, would have order 2, i.e. 2Q = O, the point at infinity. However, the points on the elliptic curve Y^2 = X^3 + 7 over Fp form a cyclic group of order a huge prime (almost as large as p). Hence not divisible by 2 and therefore no elements of order 2.