Re: ECC point of inf question

From: Ben Livengood (ben.livengood_at_gmail.com)
Date: 10/20/05 

Date: 20 Oct 2005 11:11:42 -0700

> \infty = (x, y) + (x, -y)

The point at infinity is defined precisely because the slope is
undefined between (x,y) and (x,-y). For points on a curve to be a group
under addition there has to be an element that is the result of such an
addition.

> My take is that if some pair (x, y) do satisfy the above and the > curve is of prime order then the pair is valid for use in ECC
> operations? Is that right?

There are several important checks to make sure a curve and points on
the curve are valid, including the MOV test. The document "Elliptic
Curve Cryptography" from the Standards for Effecient Cryptography Group
(www.secg.org/collateral/sec1.pdf) is a very complete reference, and
section 3.1 describes the validation procedure for curves and base
points.

Relevant Pages

  • Re: ECC point of inf question
    ... > The point at infinity is defined precisely because the slope is ... If anything the point at infinity is a concept and can't be explicitly ... > the curve are valid, ... > Curve Cryptography" from the Standards for Effecient Cryptography Group ...
    (sci.crypt)
  • Re: Calculus XOR Probability
    ... I am assuming that when n is a specific infinity, ... That's the common notion of a curve, but a general definition may be adopted ... A sequence ... Except that a staircase of n steps is made up of 2*n segments. ...
    (sci.math)
  • Re: Hey, Jobst, on p39 of The Bicycle Wheel the graph appears to show the ?impossibility of...
    ... force' curve. ... not leftwards and rightwards force. ... out a magnifier and start counting pixels to see that the slope of the ... is going slack around 0mm deflection; ...
    (rec.bicycles.tech)
  • Re: what "REALLY" is derivative?
    ... then it's easy to solve for the slope of the line (because ... excuse to divide f- fby x - a. ... but have you tried finding derivatives of functions ... curve on a piece of paper and call your curve f. ...
    (sci.math)
  • Re: EC-PRNG
    ... That's why you compute the group order already taking the point at infinity ... If you don't, then you get a curve of order n-1, not n as you ... No matter how small the probability of the step 3c is; ... Donald Knuth's quote about not using random methods to generate random ...
    (sci.crypt)
Quantcast