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RFC 6090, "Fundamental Elliptic Curve Cryptography Algorithms", February 2011

Source of RFC: IETF - NON WORKING GROUP
Area Assignment: sec

Errata ID: 3920
Status: Verified
Type: Technical
Publication Format(s) : TEXT

Reported By: Watson Ladd
Date Reported: 2014-03-15
Verifier Name: Kathleen Moriarty
Date Verified: 2014-07-01

Section Appendix F says:

Then, the product P3=(X3,Y3,Z3) = P1 * P2 is given by:

     if P1 is the point at infinity,
        P3 = P2
     else if P2 is the point at infinity,
        P3 = P1
     else if u is not equal to 0 but v is equal to 0,
        P3 = (0,1,0)
     else if both u and v are not equal to 0,
        X3 = v * (Z2 * (Z1 * u^2 - 2 * X1 * v^2) - v^3)
        Y3 = Z2 * (3 * X1 * u * v^2 - Y1 * v^3 - Z1 * u^3) + u * v^3
        Z3 = v^3 * Z1 * Z2
     else    // P2 equals P1, P3 = P1 * P1
         w = 3 * X1^2 + a * Z1^2
        X3 = 2 * Y1 * Z1 * (w^2 - 8 * X1 * Y1^2 * Z1)
        Y3 = 4 * Y1^2 * Z1 * (3 * w * X1 - 2 * Y1^2 * Z1) - w^3
        Z3 = 8 * (Y1 * Z1)^3

It should say:

Then, the product P3=(X3,Y3,Z3) = P1 * P2 is given by:

     if P1 is the point at infinity,
        P3 = P2
     else if P2 is the point at infinity,
        P3 = P1
     else if P1=-P2 as projective points
        P3 = (0,1,0)
     else if P1 does not equal P2
        X3 = v * (Z2 * (Z1 * u^2 - 2 * X1 * v^2) - v^3)
        Y3 = Z2 * (3 * X1 * u * v^2 - Y1 * v^3 - Z1 * u^3) + u * v^3
        Z3 = v^3 * Z1 * Z2
     else    // P2 equals P1, P3 = P1 * P1
         w = 3 * X1^2 + a * Z1^2
        X3 = 2 * Y1 * Z1 * (w^2 - 8 * X1 * Y1^2 * Z1)
        Y3 = 4 * Y1^2 * Z1 * (3 * w * X1 - 2 * Y1^2 * Z1) - w^3
        Z3 = 8 * (Y1 * Z1)^3

Notes:

The original algorithm was wrong and produces incorrect answers. There are several fixes that could take place.

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