@@ -930,11 +930,14 @@ For further reference on elliptic curves, consult {{CFADLNV05}} or {{W08}}.
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Let F be the finite field GF(q) of prime characteristic p. In most cases F
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is a prime field, so q = p. Otherwise, F is a field extension, so q = p^m for
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- an integer m > 1. This document assumes that elements of field extensions
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- are written in a primitive element or polynomial basis, i.e., as
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- of m elements of GF(p) written in ascending order
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- by degree. For example, if q = p^2 and the primitive element basis is {1, i},
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- then the vector (a, b) corresponds to the element a + b * i.
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+ an integer m > 1. This document writes elements of field extensions
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+ in a primitive element or polynomial basis, i.e., as a vector
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+ of m elements of GF(p) written in ascending order by degree.
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+ The entries of this vector are indexed in ascending order starting from 1,
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+ i.e., x = (x_1, x_2, ..., x_m).
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+ For example, if q = p^2 and the primitive element basis is (1, i),
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+ then x = (a, b) corresponds to the element a + b * i, where
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+ x_1 = a and x_2 = b.
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An elliptic curve E is specified by an equation in two variables and a
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finite field F. An elliptic curve equation takes one of several standard forms,
@@ -1308,8 +1311,8 @@ Steps:
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# ## Little endian variant {#sgn0-le}
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The following sgn0 variant is defined such that sgn0\_le(x) = -1
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- just when the parity of the least significant nonzero entry of the
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- vector representation of x is 1.
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+ just when x != 0 and the parity of the least significant nonzero
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+ entry of the vector representation of x is 1.
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This variant is convenient when points are serialized
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in little-endian byte order.
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