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ECPoints.F2m to this without
checking if both points are on the same curve.
αu's for a=0 as an array
of ZTauElements.
αu's for a=0 as an array
of TNAFs.
αu's for a=1 as an array
of ZTauElements.
αu's for a=1 as an array
of TNAFs.
n.
ECMultiplier, unless already set.
UtilCM.byteToInt(byte[] x, int offset, int type)
a and b
are elements of the same field F2m
(having the same representation).
ECPoints can be added or subtracted.
F2m in polynomial basis (PB)
representation.ECPoints.SimpleBigDecimal representing the same numerical
value as value.
Uk-1 and
Uk or Vk-1 and
Vk.
μ of the elliptic curve.
μ of the elliptic curve.
s0 and
s1 used for partial modular reduction.
tw.
UtilCM.intToByte(int x, int type)
k where xm +
xk + 1 represents the reduction polynomial
f(z).
k where xm +
xk + 1 represents the reduction polynomial
f(z).
0k2 where xm +
xk3 + xk2 + xk1 + 1
represents the reduction polynomial f(z).
0k2 where xm +
xk3 + xk2 + xk1 + 1
represents the reduction polynomial f(z).
0k3 where xm +
xk3 + xk2 + xk1 + 1
represents the reduction polynomial f(z).
0k3 where xm +
xk3 + xk2 + xk1 + 1
represents the reduction polynomial f(z).
m of F2m.
m of F2m.
μ of the elliptic curve if this is
a Koblitz curve.
ECPoint p by k, i.e.
ECPoint by the given number.
this by an integer k using the
Window NAF method.
ECPoint.F2m
by k using the reduced τ-adic NAF (RTNAF)
method.
ECPoint.F2m
by an element λ of Z[τ]
using the τ-adic NAF (TNAF) method, given the TNAF
of λ.
ECPoint.F2m
by an element λ of Z[τ]
using the window τ-adic NAF (TNAF) method, given the
WTNAF of λ.
ECPoint.F2m
by a BigInteger using the reduced τ-adic
NAF (RTNAF) method.
ECPoint.F2m
by an element λ of Z[τ]
using the τ-adic NAF (TNAF) method.
ECPoint.F2m
by an element λ of Z[τ] using
the τ-adic NAF (TNAF) method.
λ of
Z[τ].
λ of
R[τ], where λ = u + vτ
and u and u are real numbers (elements of
R).
(τm - 1)/(τ - 1).
ECPoints used for the Window
NAF multiplication in
WNafMultiplier.multiply().
ECPoint.F2ms used for the
WTNAF multiplication in
WTauNafMultiplier.multiply().
λ of R[τ]
to an element of Z[τ], such that their difference
has minimal norm.
PreCompInfo.
s0 and
s1 used for partial modular reduction for
Koblitz curves.
SimpleBigDecimal.
z2 + z = beta(X9.62
D.1.6) The other solution is z + 1.
ECPoints.F2m from this
without checking if both points are on the same curve.
ints required to hold m bits.
τ() to an
ECPoint.F2m.
τ-adic NAF (non-adjacent form) of an
element λ of Z[τ].
[τ]-adic window NAF of an element
λ of Z[τ].
ECPoint representing twice(this).
λ.
τ-adic" part of λ.
τ-adic Non-Adjacent Form) algorithm.τ-adic Non-Adjacent Form) algorithm.WTauNafPreCompInfo
IntArray holding the bits.
F2.
F2m.
Z[τ].λ of
Z[τ].
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