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Finite field subtraction

  • 15-06-2008 4:02pm
    #1
    AARRRGH
    Closed Accounts Posts: 12,382 ✭✭✭✭


    Hello

    I hope someone can help me with this.

    Let's imagine I want to perform the following subtraction operation -

    (7, 1) - (2, 3)

    Both are geometric points on an elliptic curve.

    As far as I know, finite field subtraction is simply finite field addition using the additive inverse of the bit I want to subtract, i.e. (7, 1) + [additiveInverse(2, 3)]

    Is this correct?

    Does anyone know how I can calculate the additive inverse of a point?

    Is it simply (-2, -3)?

    Any help greatly appreciated.

    Thanks!


Comments

  • #2
    AARRRGH
    Closed Accounts Posts: 12,382 ✭✭✭✭AARRRGH


    Hmmm. I'm after finding this on the internet:

    J = (Xj, Yj)
    K = (Xk, Yk)

    J - K = J + (-K)
    where -K = (Xk, Xk + Yk)

    Does this ring any bells with anyone?

    Thanks


  • #3
    LeixlipRed
    Closed Accounts Posts: 6,081 ✭✭✭LeixlipRed


    -(x,y)=(x,-y)


  • #4
    AARRRGH
    Closed Accounts Posts: 12,382 ✭✭✭✭AARRRGH


    Thanks LeixlipRed, that's what I thought.

    Cheers!


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