Elliptic Curve Cryptography: A Basic Introduction
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Elliptic Curve Cryptography: A Basic Introduction
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Re: Elliptic Curve Cryptography: A Basic Introduction
#2Anyone know of an accessible intermediate resource on ECC? There are many blogs talking about the basics of point addition , but hardly anything approachable that talks about different curve properties, what makes a curve safe, how to break vulnerable curves, and how to prove properties, etc.
Re: Elliptic Curve Cryptography: A Basic Introduction
#3This is indeed basic. Half the article explains public key cryptography, the other gives a basic overview that omits key details, such as the purpose of reflection, and how the curve can get combined with finite fields in practical applications (although point 2 does partly address this aspect). Not a bad way to get a general intuition of the algorithm, but not overly useful, either.
Re: Elliptic Curve Cryptography: A Basic Introduction
#4This is indeed basic. Half the article explains public key cryptography, the other gives a basic overview that omits key details, such as the purpose of reflection, and how the curve can get combined with finite fields in practical applications (although point 2 does partly address this aspect). Not a bad way to get a general intuition of the algorithm, but not overly useful, either.
Agree, the book "Programming Bitcoin" by Song provides a detailed explanation of the algorithm.
Re: Elliptic Curve Cryptography: A Basic Introduction
#5I learned about EC from Craig Costello's book on pairings. Amazing read with concrete examples.
Re: Elliptic Curve Cryptography: A Basic Introduction
#6I don't get the trap problem here. So I start with A, compute -B as A dot A, then continue my way until I decide to stop at E. So I had to compute the whole path, right?
Now you give me A and E, why can't I just compute the path from A until I hit E? That looks like the same effort, so what did I miss?
Re: Elliptic Curve Cryptography: A Basic Introduction
#7I don't get the trap problem here. So I start with A, compute -B as A dot A, then continue my way until I decide to stop at E. So I had to compute the whole path, right? Now you give me A and E, why can't I just compute the path from A until I hit E? That looks like the same effort, so what did I miss?
Oh that's actually the point of the exponentiation trick: I choose the private key first and then compute the path from it.
Got it, sorry xD
Re: Elliptic Curve Cryptography: A Basic Introduction
#8Anyone know of an accessible intermediate resource on ECC? There are many blogs talking about the basics of point addition , but hardly anything approachable that talks about different curve properties, what makes a curve safe, how to break vulnerable curves, and how to prove properties, etc.
The properties of curves make certain protocols safe/unsafe in my opinion. For example some curve might be a good choice for BLS while being very bad for ECDSA. Therefore the choice of the curve is really tied to the encryption/signature scheme I think. I am not an expert though. Contact the cryptographers they are really friendly (not a sarcasm)!
Re: Elliptic Curve Cryptography: A Basic Introduction
#9As some others have pointed out, this is very basic stuff, but a good introduction. I have found this series of blog posts [0] as a super useful explanation of ECC that starts with the basics but covers the math and underlying group theory well, building up to an intermediate-level understanding of the matter.
[0] https://andrea.corbellini.name/2015/05/17/elliptic-curve-cry...
Re: Elliptic Curve Cryptography: A Basic Introduction
#10I don't get the trap problem here. So I start with A, compute -B as A dot A, then continue my way until I decide to stop at E. So I had to compute the whole path, right? Now you give me A and E, why can't I just compute the path from A until I hit E? That looks like the same effort, so what did I miss?
Instead of computing nA = A + A + … + A you can use the “exponentiation” by squaring trick: nA = (n/2)A + (n/2)A + (n%2)A. It takes logarithmically many steps.