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Status: Verified (1)

RFC6090, "Fundamental Elliptic Curve Cryptography Algorithms", February 2011

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

Errata ID: 3920

Status: Verified
Type: Technical

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.


Status: Held for Document Update (5)

RFC6090, "Fundamental Elliptic Curve Cryptography Algorithms", February 2011

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

Errata ID: 2777

Status: Held for Document Update
Type: Technical

Reported By: Annie Yousar
Date Reported: 2011-04-11
Held for Document Update by: Sean Turner

Section 7.2 says:

KT-I is mathematically and functionally equivalent to ECDSA, and can interoperate
with the IEEE [P1363] and ANSI [X9.62] standards for Elliptic Curve DSA (ECDSA)
based on fields of characteristic greater than three.  KT-I signatures can be
verified using the ECDSA verification algorithm, and ECDSA signatures can be
verified using the KT-I verification algorithm.

It should say:

For many hash functions KT-I is mathematically and functionally equivalent to
ECDSA, and can interoperate with the IEEE [P1363] and ANSI [X9.62] standards for
Elliptic Curve DSA (ECDSA) based on fields of characteristic greater than three.
KT-I signatures can be verified using the ECDSA verification algorithm, and ECDSA
signatures can be verified using the KT-I verification algorithm (refer to
Section 10.4).

Notes:

If the hash function h generates a bit string that has a bit length greater than the bit length of the elliptic curve group order, ECDSA as specified in P1363 uses a truncation of the hash value to the left-most bits. The KT-I algorithm does not use this truncation but reduces modulo q. Therefore ECDSA and KT-I with SHA-384 on the P-256 curve result in different signature values. Add a corresponding note in 10.4: The output of the hash used in KT signatures should truncated to the left-most bits if its bit-length is longer than the bit-length of the group order.


Errata ID: 2773

Status: Held for Document Update
Type: Editorial

Reported By: Annie Yousar
Date Reported: 2011-04-11
Held for Document Update by: Sean Turner

Section 2.2 says:

Sometimes an alternative called additive notation is used, in which a * b is denoted as a + b, and a^N is denoted as N * a. 

It should say:

Sometimes an alternative called additive notation is used, in which a * b is denoted as a + b, and a^N is denoted as Na. 

Notes:

The original text refers to Appendix E some sentences later:
"Appendix E elucidates the correspondence between the two notations."

In the Appendix E the notation "Na" is used, whereas the original text uses the notation "N*a".


Errata ID: 2774

Status: Held for Document Update
Type: Editorial

Reported By: Annie Yousar
Date Reported: 2011-04-11
Held for Document Update by: Sean Turner

Section 2.2 says:

By convention, a^0 is equal to the identity element for any a in G.

It should say:

By convention, a^0 is equal to the identity element and a^1 is equal to a itself for any a in G.

Notes:

Without this convention the explanation on the next page: "... for any integers X and Y: a^(X+Y) = (a^X)*(a^Y) ..." would be incomplete, as being undefined for the integers X=1 and/or Y=1.


Errata ID: 2775

Status: Held for Document Update
Type: Editorial

Reported By: Annie Yousar
Date Reported: 2011-04-11
Held for Document Update by: Sean Turner

Section 2.2 says:

Note that a^M is equal to g^(M modulo R) for any non-negative integer M.

It should say:

Note that a^M is equal to a^(M mod R) for any non-negative integer M.

Notes:

g is a typo. The result of the modulo operation is always denoted in the text by "mod". The notation "modulo" identifies the operation and not the result.


Errata ID: 2776

Status: Held for Document Update
Type: Editorial

Reported By: Annie Yousar
Date Reported: 2011-04-11
Held for Document Update by: Sean Turner

Section 6.2 says:

The integer x shall be converted to an octet string S of length k as follows.  The string S shall satisfy
                      k
                y =  SUM  2^(8(k-i)) Si .
                    i = 1

It should say:

The integer y shall be converted to an octet string S of length k as follows.  The string S shall satisfy
                      k
                y =  SUM  2^(8(k-i)) Si .
                    i = 1

Note that the conversion fails if y >= 2^(8*k).

Notes:

Typo corrected. The integer y can not be converted, if the octet string is to short.


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