If two points (x1, y1) and (x2, y2) are given to gej_add_ge with
x1 != x2 but y1 = -y2, the function gives a wrong answer since
this causes it to compute "lambda = 0/0" during an intermediate
step. (Here lambda refers to an auxiallary variable in the point
addition formula, not the cube-root of 1 used by the endomorphism
optimization.)
This commit catches the 0/0 and replaces it with an alternate
expression for lambda, cmov'ing it in place if necessary.
There is zero functionality or opcount changes here; I need to do
this to make sure both R and M are computed before they are used,
since a future patch will replace either none or both of them.
Also compute r->y directly in terms of r->x, which again will be
used in a future patch.
* Make secp256k1_gej_add_var and secp256k1_gej_double return the
Z ratio to go from a.z to r.z.
* Use these Z ratios to speed up batch point conversion to affine
coordinates, and to speed up batch conversion of points to a
common Z coordinate.
* Add a point addition function that takes a point with a known
Z inverse.
* Due to secp256k1's endomorphism, all additions in the EC
multiplication code can work on affine coordinate (with an
implicit common Z coordinate), correcting the Z coordinate of
the result afterwards.
Refactoring by Pieter Wuille:
* Move more global-z logic into the group code.
* Separate code for computing the odd multiples from the code to bring it
to either storage or globalz format.
* Rename functions.
* Make all addition operations return Z ratios, and test them.
* Make the zr table format compatible with future batch chaining
(the first entry in zr becomes the ratio between the input and the
first output).
Original idea and code by Peter Dettman.
This computes (n-b)G + bG with random value b, in place of nG in
ecmult_gen() for signing.
This is intended to reduce exposure to potential power/EMI sidechannels
during signing and pubkey generation by blinding the secret value with
another value which is hopefully unknown to the attacker.
It may not be very helpful if the attacker is able to observe the setup
or if even the scalar addition has an unacceptable leak, but it has low
overhead in any case and the security should be purely additive on top
of the existing defenses against sidechannels.
Use a conditional move of the same kind we use for the affine points
in the storage type instead of multiplying with the infinity flag
and adding. This results in fewer constructions to worry about for
sidechannel behavior.
It also might be faster: It doesn't appear to benchmark as slower for
me at least; but I think the CMOV is faster than the mul_int + add,
but slower than the set+add; making it a wash.
Unbraced statements spanning multiple lines has been shown in many
projects to contribute to the introduction of bugs and a failure
to catch them in review, especially for maintenance on infrequently
modified code.
Most, but not all, of the existing practice in the codebase were not
cases that I would have expected to eventually result in bugs but
applying it as a rule makes it easier for other people to safely
contribute.
I'm not aware of any such evidence for the case with the statement
on a single line, but some people strongly prefer to never do that
and the opposite rule of "_always_ use a single line for single
statement blocks" isn't a reasonable rule for formatting reasons.
Might as well brace all these too, since that's more universally
acceptable.
[In any case, I seem to have introduced the vast majority of the
single-line form (as they're my preference where they fit).]
This also removes a broken test which is no longer needed.
