This introduces the signed-digit multi-comb multiplication algorithm
for constant-time G multiplications (ecmult_gen). It is based on
section 3.3 of "Fast and compact elliptic-curve cryptography" by
Mike Hamburg (see https://eprint.iacr.org/2012/309).
Original implementation by Peter Dettman, with changes by Pieter Wuille
to use scalars for recoding, and additional comments.
Instead of having the starting point of the ecmult_gen computation be
offset, do it with the final point. This enables reasoning over the
set of points reachable in intermediary computations, which can be
leveraged by potential future optimization.
Because the final point is in affine coordinates, its projective
blinding is no longer possible. It will be reintroduced again in
a different way, in a later commit.
Also introduce some more comments and more descriptive names.
This is a backwards-compatible API change: Before this commit, a context
initialized for signing was required to call functions that rely on
ecmult_gen. After this commit, this is no longer necessary because the
static ecmult_gen table is always present. In practice this means that
the corresponding functions will just work instead of calling the
illegal callback when given a context which is not (officially)
initialized for signing.
This is in line with 6815761, which made the analogous change with
respect to ecmult and contexts initialized for signing. But as opposed
to 681571, which removed the ecmult context entirely, we cannot remove
the ecmult_gen context entirely because it is still used for random
blinding. Moreover, since the secp256k1_context_no_precomp context is
const and cannot meaningfully support random blinding, we refrain (for
now) from changing its API, i.e., the illegal callback will still be
called when trying to use ecmult_gen operations with the static
secp256k1_context_no_precomp context.
make ECMULT_GEN_PREC_BITS configurable
ecmult_static_context.h: add compile time config assertion (#3) - Prevents accidentally using a file which was generated with a
different configuration.
README: mention valgrind issue
With --with-ecmult-gen-precision=8, valgrind needs a max stack size
adjustment to not run into a stack switching heuristic:
http://valgrind.org/docs/manual/manual-core.html
> -max-stackframe= [default: 2000000]
> The maximum size of a stack frame. If the stack pointer moves by more than this amount then Valgrind will assume that the program is switching to a different stack.
You may need to use this option if your program has large stack-allocated arrays.
basic-config: undef ECMULT_WINDOW_SIZE before (re-)defining it
Identifiers starting with an underscore and followed immediately by a capital letter are reserved by the C++ standard.
The only header guards not fixed are those in the headers auto-generated from java.
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.
