This commit adds three new cryptosystems to libsecp256k1:
Pedersen commitments are a system for making blinded commitments
to a value. Functionally they work like:
commit_b,v = H(blind_b || value_v),
except they are additively homorphic, e.g.
C(b1, v1) - C(b2, v2) = C(b1 - b2, v1 - v2) and
C(b1, v1) - C(b1, v1) = 0, etc.
The commitments themselves are EC points, serialized as 33 bytes.
In addition to the commit function this implementation includes
utility functions for verifying that a set of commitments sums
to zero, and for picking blinding factors that sum to zero.
If the blinding factors are uniformly random, pedersen commitments
have information theoretic privacy.
Borromean ring signatures are a novel efficient ring signature
construction for AND/OR admissions policies (the code here implements
an AND of ORs, each of any size). This construction requires
32 bytes of signature per pubkey used plus 32 bytes of constant
overhead. With these you can construct signatures like "Given pubkeys
A B C D E F G, the signer knows the discrete logs
satisifying (A || B) & (C || D || E) & (F || G)".
ZK range proofs allow someone to prove a pedersen commitment is in
a particular range (e.g. [0..2^64)) without revealing the specific
value. The construction here is based on the above borromean
ring signature and uses a radix-4 encoding and other optimizations
to maximize efficiency. It also supports encoding proofs with a
non-private base-10 exponent and minimum-value to allow trading
off secrecy for size and speed (or just avoiding wasting space
keeping data private that was already public due to external
constraints).
A proof for a 32-bit mantissa takes 2564 bytes, but 2048 bytes of
this can be used to communicate a private message to a receiver
who shares a secret random seed with the prover.
If you compile without ./configure --enable-exhaustive-tests=no,
this will create a binary ./exhaustive_tests which will execute
every function possible on a group of small order obtained by
moving to a twist of our curve and locating a generator of small
order.
Currently defaults to order 13, though by changing some #ifdefs
you can get a couple other ones. (Currently 199, which will take
forever to run, and 14, which won't work because it's composite.)
TODO exhaustive tests for the various modules
We observe that when changing the b-value in the elliptic curve formula
`y^2 = x^3 + ax + b`, the group law is unchanged. Therefore our functions
for secp256k1 will be correct if and only if they are correct when applied
to the curve defined by `y^2 = x^3 + 4` defined over the same field. This
curve has a point P of order 199.
This commit adds a test which computes the subgroup generated by P and
exhaustively checks that addition of every pair of points gives the correct
result.
Unfortunately we cannot test const-time scalar multiplication by the same
mechanism. The reason is that these ecmult functions both compute a wNAF
representation of the scalar, and this representation is tied to the order
of the group.
Testing with the incomplete version of gej_add_ge (found in 5de4c5dff^)
shows that this detects the incompleteness when adding P - 106P, which
is exactly what we expected since 106 is a cube root of 1 mod 199.
gcc 6 will warn about our non-null checks when SECP256K1_BUILD
our NONNULL marker is nontrivial. This occurs unless SECP256K1_BUILD
is set, which we had forgotten to do for the internal benchmarks,
which compile directly against the library instead of linking.
Squashed and rebased. Thanks to @theuni and @faizkhan00 for doing
the majority of work here! Also thanks to @btchip for help with debugging
and review.
These functions are intended for compatibility with legacy software,
and are not normally needed in new secp256k1 applications.
They also do not obeying any particular standard (and likely cannot
without without undermining their compatibility), and so are a
better fit for contrib.
Libtool will do the right thing and use whatever is available
based on --enable-shared/--enable-static.
This also means that some of the things we build actually
test the dynamic library.
Designed with clear separation of the wNAF conversion, precomputation
and exponentiation (since the precomp at least we will probably want
to separate in the API for users who reuse points a lot.
Future work:
- actually separate precomp in the API
- do multiexp rather than single exponentiation
BUILT_SOURCES simply forces the header to be built first.
Use real dependencies instead. This fixes builds with dependency tracking
disabled where a real target is specified.
As a bonus, this also fixes the issue of gen_context and the header not being
rebuilt when gen_context.c is touched.
Gen_context was unable to find the required headers without some
autotools fixups. Make dist was also broken without the extra
sources for the host side table builder utility.
This vastly shrinks the size of the context required for signing on devices with
memory-mapped Flash.
Tables are generated by the new gen_context tool into a header.
- caused by 8881212ebc
- OSX's ar tool doesn't work for empty archives ("ar: no archive members specified")
- introduce COMMON_LIB variable; leave empty when not using asm
