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ECDSA requires the ability to add two arbitrary curve points, either
of which may legitimately be the point at infinity.
Update the API so that curves must choose an explicit affine
representation for the point at infinity, and provide a method to test
for this representation. Multiplication and addition will now allow
this representation to be provided as an input, and will not fail if
the result is the point at infinity. Callers must explicitly check
for the point at infinity where needed (e.g. after computing the ECDHE
shared secret curve point).
Signed-off-by: Michael Brown <mcb30@ipxe.org>
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ECDSA verification requires the ability to add two arbitrary curve
points (as well as the ability to multiply a curve point by a scalar).
Add an elliptic curve method to perform arbitrary point addition.
Pass in curve points as affine coordinates: this will require some
redundant conversions between affine coorfinates and the internal
representation as projective coordinates in Montgomery form, but keeps
the API as simple as possible. Since we do not expect to perform a
high volume of ECDSA signature verifications, these redundant
calculations are an acceptable cost for keeping the code simple.
Signed-off-by: Michael Brown <mcb30@ipxe.org>
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ECDSA requires knowledge of the group order of the base point, and is
defined only for curves with a prime group order (e.g. the NIST
curves).
Add the group order as an explicit property of an elliptic curve, and
add tests to verify that the order is correct.
Signed-off-by: Michael Brown <mcb30@ipxe.org>
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Rename elliptic_ok() to elliptic_multiply_ok() etc, to create
namespace for tests of other elliptic curve operations.
Signed-off-by: Michael Brown <mcb30@ipxe.org>
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Signed-off-by: Michael Brown <mcb30@ipxe.org>
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