Add the required methods to SECP256r1 to conform to the EllipticCurve
virtual base class. Using this updated version of SECP256r1, support in
LibTLS is implemented.
These changes generalize the interface with an elliptic curve
implementation. This allows LibTLS to support elliptic curves generally
without needing the specifics of elliptic curve implementations.
This should allow for easier addition of other elliptic curves.
This implementation of the secp256r1 elliptic curve uses two techniques
to improve the performance of the operations.
1. All coordinates are stored in Jacobian form, (X/Z^2, Y/Z^3, Z), which
removes the need for division operations during point addition or
doubling. The points are converted at the start of the computation,
and converted back at the end.
2. All values are transformed to Montgomery form, to allow for faster
modular multiplication using the Montgomery modular multiplication
method. This means that all coordinates have to be converted into
this form, and back out of this form before returning them.
If a big integer were to become negative zero, set the sign to instead
be positive. This prevents odd scenarios where users of signed big ints
would falsely think the result of some big int arithmetic is negative.
We went through some trouble to make & and | work right. Reimplement ^
in terms of & and | to make ^ work right as well.
This is less fast than a direct implementation, but let's get things
working first.
Similar to the bitwise_and change, but we have to be careful to
sign-extend two's complement numbers only up to the highest set bit
in the positive number.
Bitwise and is defined in terms of two's complement, so some converting
needs to happen for SignedBigInteger's sign/magnitude representation to
work out.
UnsignedBigInteger::bitwise_not() is repurposed to convert all
high-order zero bits to ones up to a limit, for the two's complement
conversion to work.
Fixes test262/test/language/expressions/bitwise-and/bigint.js.
Bitwise operators are defined on two's complement, but SignedBitInteger
uses sign-magnitude. Correctly convert between the two.
Let LibJS delegate to SignedBitInteger for bitwise_not, like it does
for all other bitwise_ operations on bigints.
No behavior change (LibJS is now the only client of
SignedBitInteger::bitwise_not()).
Currently, we get the following results
-1 - -2 = -1
-2 - -1 = 1
Correct would be:
-1 - -2 = 1
-2 - -1 = -1
This was already attempted to be fixed in 7ed8970, but that change was
incorrect. This directly translates to LibJS BigInts having the same
incorrect behavior - it even was tested.
Using a file(GLOB) to find all the test files in a directory is an easy
hack to get things started, but has some drawbacks. Namely, if you add
a test, it won't be found again without re-running CMake. `ninja` seems
to do this automatically, but it would be nice to one day stop seeing it
rechecking our globbed directories.
