[CFRG] [Technical Errata Reported] RFC7748 (7879)

[RFC Errata System <[e-mail]>]

The following errata report has been submitted for RFC7748,
"Elliptic Curves for Security".

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You may review the report below and at:
https://www.rfc-editor.org/errata/eid7879

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Type: Technical
Reported by: Nawras Hussein Sabbry <[e-mail]>

Section: 5

Original Text
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z_2 = E * (AA + a24 * E)

Corrected Text
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z_2 = E * (BB + a24 * E)

Notes
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In the for loop on page 8, the variable AA should be replaced with BB in Z_2. This modification is necessary because the mathematical formula for point doubling on the Montgomery curve according to (https://en.wikipedia.org/wiki/Montgomery_curve#Montgomery_arithmetic) indicates that Z2n (equivalent to Z_2 in this case) is calculated as follows: Z2n = 4XnZn((Xn-Zn)^2 + ((A+2)/4)(4XnZn)). It is observed in this equation that the operation in the (Xn-Zn)^2 part involves subtraction similar to the variable B, while the operation in the variable A involves addition. Considering this discrepancy, it is suggested to substitute AA with BB for correctness.

Instructions:
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RFC7748 (draft-irtf-cfrg-curves-11)
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Title               : Elliptic Curves for Security
Publication Date    : January 2016
Author(s)           : A. Langley, M. Hamburg, S. Turner
Category            : INFORMATIONAL
Source              : Crypto Forum Research Group
Stream              : IRTF
Verifying Party     : IRSG