February 19, 2002
Practical Aspects of Modern Cryptography
25
Lagrange Interpolation
n
For each point
(
i
,P(
i
))
, construct a
polynomial
P
i
with the correct value
at
i
and a value of zero at the other
given points.
n
P
i
(
x
) = P(
i
)
× ∏
(
j
≠
i
)
(
x
-
j
) ÷ ∏
(
j
≠
i
)
(
i
-
j
)
n
n
P(
x
) = ∑
i
P
i
(
x
)