Why: this protects against potential side-channels attacks. This
counter-measure is for example effective against Template SPA. Also, the
bignum arithmetic as implemented in TinyCrypt isn't entirely regular, which
could in principle be exploited by an attacker; randomizing the coordinates
makes this less likely to happen.
Randomizing projective coordinates is also a well-known countermeasure to DPA.
In the context of the scalar multiplication in ECDSA, DPA isn't a concern
since it requires multiple measurements with various base points and the same
scalar, and the scalar mult in ECDSA is the opposite: the base point's always
the same and the scalar is always unique. But we want protection against the
other attacks as well.
How: we use the same code fragment as in uECC_shared_secret in ecc_dh.c,
adapted as follows: (1) replace p2 with k2 as that's how it's called in this
function; (2) adjust how errors are handled.
The code might not be immediately clear so here are a few more details:
regularize_k() takes two arrays as outputs, and the return value says which one
should be passed to ECCPoint_mult(). The other one is free for us to re-use to
generate a random number to be used as the initial Z value for randomizing
coordinates (otherwise the initial Z value is 1), thus avoiding the use of an
extra stack buffer.
We called in tinycrypt in the file names, but uecc in config.h, all.sh and
other places, which could be confusing. Just use tinycrypt everywhere because
that's the name of the project and repo where we took the files.
The changes were made using the following commands (with GNU sed and zsh):
sed -i 's/uecc/tinycrypt/g' **/*.[ch] tests/scripts/all.sh
sed -i 's/MBEDTLS_USE_UECC/MBEDTLS_USE_TINYCRYPT/g' **/*.[ch] tests/scripts/all.sh scripts/config.pl
