Squashed 'src/secp256k1/' changes from 0559fc6e41..8746600eec

8746600eec Merge bitcoin-core/secp256k1#1093: hash: Make code agnostic of endianness
37d36927df tests: Add tests for _read_be32 and _write_be32
912b7ccc44 Merge bitcoin-core/secp256k1#1094: doc: Clarify configure flags for optional modules
55512d30b7 doc: clean up module help text in configure.ac
d9d94a9969 doc: mention optional modules in README
616b43dd3b util: Remove endianness detection
8d89b9e6e5 hash: Make code agnostic of endianness
d0ad5814a5 Merge bitcoin-core/secp256k1#995: build: stop treating schnorrsig, extrakeys modules as experimental
1ac7e31c5b Merge bitcoin-core/secp256k1#1089: Schnorrsig API improvements
587239dbe3 Merge bitcoin-core/secp256k1#731: Change SHA256 byte counter from size_t to uint64_t
f8d9174357 Add SHA256 bit counter tests
7f09d0f311 README: mention that ARM assembly is experimental
b8f8b99f0f docs: Fix return value for functions that don't have invalid inputs
f813bb0df3 schnorrsig: Adapt example to new API
99e6568fc6 schnorrsig: Rename schnorrsig_sign to schnorsig_sign32 and deprecate
fc94a2da44 Use SECP256K1_DEPRECATED for existing deprecated API functions
3db0560606 Add SECP256K1_DEPRECATED attribute for marking API parts as deprecated
80cf4eea5f build: stop treating schnorrsig, extrakeys modules as experimental
e0508ee9db Merge bitcoin-core/secp256k1#1090: configure: Remove redundant pkg-config code
21b2ebaf74 configure: Remove redundant pkg-config code
0e5cbd01b3 Merge bitcoin-core/secp256k1#1088: configure: Use modern way to set AR
0d253d52e8 configure: Use modern way to set AR
9b514ce1d2 Add test vector for very long SHA256 messages
8e3dde1137 Simplify struct initializer for SHA256 padding
eb28464a8b Change SHA256 byte counter from size_t to uint64_t
ac83be33d0 Merge bitcoin-core/secp256k1#1079: configure: Add hidden --enable-dev-mode to enable all the stuff
e0838d663d configure: Add hidden --enable-dev-mode to enable all the stuff
fabd579dfa configure: Remove redundant code that sets _enable variables
0d4226c051 configure: Use canonical variable prefix _enable consistently
64b34979ed Merge bitcoin-core/secp256k1#748: Add usage examples
7c9502cece Add a copy of the CC0 license to the examples
42e03432e6 Add usage examples to the readme
517644eab1 Optionally compile the examples in autotools, compile+run in travis
422a7cc86a Add a ecdh shared secret example
b0cfbcc143 Add a Schnorr signing and verifying example
fee7d4bf9e Add an ECDSA signing and verifying example
1253a27756 Merge bitcoin-core/secp256k1#1033: Add _fe_half and use in _gej_add_ge and _gej_double
3ef94aa5ba Merge bitcoin-core/secp256k1#1026: ecdh: Add test computing shared_secret=basepoint with random inputs
3531a43b5b ecdh: Make generator_basepoint test depend on global iteration count
c881dd49bd ecdh: Add test computing shared_secret=basepoint with random inputs
077528317d Merge bitcoin-core/secp256k1#1074: ci: Retry brew update a few times to avoid random failures
e51ad3b737 ci: Retry `brew update` a few times to avoid random failures
b1cb969e8a ci: Revert "Attempt to make macOS builds more reliable"
5dcc6f8dbd Merge bitcoin-core/secp256k1#1069: build: Replace use of deprecated autoconf macro AC_PROG_CC_C89
59547943d6 Merge bitcoin-core/secp256k1#1072: ci: Attempt to make macOS builds more reliable
85b00a1c65 Merge bitcoin-core/secp256k1#1068: sage: Fix incompatibility with sage 9.4
ebb1beea78 sage: Ensure that constraints are always fastfracs
d8d54859ed ci: Run sage prover on CI
77cfa98dbc sage: Normalize sign of polynomial factors in prover
eae75869cf sage: Exit with non-zero status in case of failures
d9396a56da ci: Attempt to make macOS builds more reliable
e0db3f8a25 build: Replace use of deprecated autoconf macro AC_PROG_CC_C89
e848c3799c Update sage files for new formulae
d64bb5d4f3 Add fe_half tests for worst-case inputs
b54d843eac sage: Fix printing of errors
4eb8b932ff Further improve doubling formula using fe_half
557b31fac3 Doubling formula using fe_half
2cbb4b1a42 Run more iterations of run_field_misc
9cc5c257ed Add test for secp256k1_fe_half
925f78d55e Add _fe_half and use in _gej_add_ge
e108d0039c sage: Fix incompatibility with sage 9.4
d8a2463246 Merge bitcoin-core/secp256k1#899: Reduce stratch space needed by ecmult_strauss_wnaf.
0a40a4861a Merge bitcoin-core/secp256k1#1049: Faster fixed-input ecmult tests
070e772211 Faster fixed-input ecmult tests
c8aa516b57 Merge bitcoin-core/secp256k1#1064: Modulo-reduce msg32 inside RFC6979 nonce fn to match spec. Fixes #1063
b797a500ec Create a SECP256K1_ECMULT_TABLE_VERIFY macro.
a731200cc3 Replace ECMULT_TABLE_GET_GE_STORAGE macro with a function.
fe34d9f341 Eliminate input_pos state field from ecmult_strauss_wnaf.
0397d00ba0 Eliminate na_1 and na_lam state fields from ecmult_strauss_wnaf.
7ba3ffcca0 Remove the unused pre_a_lam allocations.
b3b57ad6ee Eliminate the pre_a_lam array from ecmult_strauss_wnaf.
ae7ba0f922 Remove the unused prej allocations.
e5c18892db Eliminate the prej array from ecmult_strauss_wnaf.
c9da1baad1 Move secp256k1_fe_one to field.h
45f37b6506 Modulo-reduce msg32 inside RFC6979 nonce fn to match spec. Fixes #1063.
a1102b1219 Merge bitcoin-core/secp256k1#1029: Simpler and faster ecdh skew fixup
e82144edfb Fixup skew before global Z fixup
40b624c90b Add tests for _gej_cmov
8c13a9bfe1 ECDH skews by 0 or 1
1515099433 Simpler and faster ecdh skew fixup
39a36db94a Merge bitcoin-core/secp256k1#1054: tests: Fix test whose result is implementation-defined
a310e79ee5 Merge bitcoin-core/secp256k1#1052: Use xoshiro256++ instead of RFC6979 for tests
423b6d19d3 Merge bitcoin-core/secp256k1#964: Add release-process.md
9281c9f4e1 Merge bitcoin-core/secp256k1#1053: ecmult: move `_ecmult_odd_multiples_table_globalz_windowa`
77a19750b4 Use xoshiro256++ PRNG instead of RFC6979 in tests
5f2efe684e secp256k1_testrand_int(2**N) -> secp256k1_testrand_bits(N)
05e049b73c ecmult: move `_ecmult_odd_multiples_table_globalz_windowa`
3d7cbafb5f tests: Fix test whose result is implementation-defined
3ed0d02bf7 doc: add CHANGELOG template
6f42dc16c8 doc: add release_process.md
0bd3e4243c build: set library version to 0.0.0 explicitly
b4b02fd8c4 build: change libsecp version from 0.1 to 0.1.0-pre
09971a3ffd Merge bitcoin-core/secp256k1#1047: ci: Various improvements
0b83b203e1 Merge bitcoin-core/secp256k1#1030: doc: Fix upper bounds + cleanup in field_5x52_impl.h comment
1287786c7a doc: Add comment to top of field_10x26_impl.h
58da5bd589 doc: Fix upper bounds + cleanup in field_5x52_impl.h comment
b39d431aed Merge bitcoin-core/secp256k1#1044: Add another ecmult_multi test
b4ac1a1d5f ci: Run valgrind/memcheck tasks with 2 CPUs
e70acab601 ci: Use Cirrus "greedy" flag to use idle CPU time when available
d07e30176e ci: Update brew on macOS
22382f0ea0 ci: Test different ecmult window sizes
a69df3ad24 Merge bitcoin-core/secp256k1#816: Improve checks at top of _fe_negate methods
22d25c8e0a Add another ecmult_multi test
515e7953ca Improve checks at top of _fe_negate methods
26a022a3a0 ci: Remove STATICPRECOMPUTATION
10461d8bd3 precompute_ecmult: Always compute all tables up to default WINDOW_G
be6944ade9 Merge bitcoin-core/secp256k1#1042: Follow-ups to making all tables fully static
e05da9e480 Fix c++ build
c45386d994 Cleanup preprocessor indentation in precompute{,d}_ecmult{,_gen}
19d96e15f9 Split off .c file from precomputed_ecmult.h
1a6691adae Split off .c file from precomputed_ecmult_gen.h
bb36331412 Simplify precompute_ecmult_print_*
38cd84a0cb Compute ecmult tables at runtime for tests_exhaustive
e458ec26d6 Move ecmult table computation code to separate file
fc1bf9f15f Split ecmult table computation and printing
31feab053b Rename function secp256k1_ecmult_gen_{create_prec -> compute}_table
725370c3f2 Rename ecmult_gen_prec -> ecmult_gen_compute_table
075252c1b7 Rename ecmult_static_pre_g -> precomputed_ecmult
7cf47f72bc Rename ecmult_gen_static_prec_table -> precomputed_ecmult_gen
f95b8106d0 Rename gen_ecmult_static_pre_g -> precompute_ecmult
bae77685eb Rename gen_ecmult_gen_static_prec_table -> precompute_ecmult_gen

git-subtree-dir: src/secp256k1
git-subtree-split: 8746600eec5e7fcd35dabd480839a3a4bdfee87b

.gitattributes

@@ -1,2 +1,2 @@
-src/ecmult_static_pre_g.h linguist-generated
-src/ecmult_gen_static_prec_table.h linguist-generated
+src/precomputed_ecmult.c linguist-generated
+src/precomputed_ecmult_gen.c linguist-generated

.gitignore

@@ -3,23 +3,19 @@ bench_ecmult
 bench_internal
 tests
 exhaustive_tests
-gen_ecmult_gen_static_prec_table
-gen_ecmult_static_pre_g
+precompute_ecmult_gen
+precompute_ecmult
 valgrind_ctime_test
+ecdh_example
+ecdsa_example
+schnorr_example
 *.exe
-*.pdb
-src/BGL
-src/BGLd
-src/BGL-cli
-src/BGL-gui
-src/BGL-node
-src/BGL-tx
-src/BGL-util
-src/BGL-chainstate
-src/BGL-wallet
-src/test/fuzz/fuzz
-src/test/test_BGL
-src/qt/test/test_BGL-qt
+*.so
+*.a
+*.csv
+!.gitignore
+*.log
+*.trs
 
 # autoreconf
 Makefile.in
@@ -48,6 +44,7 @@ coverage.*.html
 
 src/libsecp256k1-config.h
 src/libsecp256k1-config.h.in
+build-aux/ar-lib
 build-aux/config.guess
 build-aux/config.sub
 build-aux/depcomp

Makefile.am

@@ -26,12 +26,14 @@ noinst_HEADERS += src/eckey.h
 noinst_HEADERS += src/eckey_impl.h
 noinst_HEADERS += src/ecmult.h
 noinst_HEADERS += src/ecmult_impl.h
+noinst_HEADERS += src/ecmult_compute_table.h
+noinst_HEADERS += src/ecmult_compute_table_impl.h
 noinst_HEADERS += src/ecmult_const.h
 noinst_HEADERS += src/ecmult_const_impl.h
 noinst_HEADERS += src/ecmult_gen.h
 noinst_HEADERS += src/ecmult_gen_impl.h
-noinst_HEADERS += src/ecmult_gen_prec.h
-noinst_HEADERS += src/ecmult_gen_prec_impl.h
+noinst_HEADERS += src/ecmult_gen_compute_table.h
+noinst_HEADERS += src/ecmult_gen_compute_table_impl.h
 noinst_HEADERS += src/field_10x26.h
 noinst_HEADERS += src/field_10x26_impl.h
 noinst_HEADERS += src/field_5x52.h
@@ -42,6 +44,8 @@ noinst_HEADERS += src/modinv32.h
 noinst_HEADERS += src/modinv32_impl.h
 noinst_HEADERS += src/modinv64.h
 noinst_HEADERS += src/modinv64_impl.h
+noinst_HEADERS += src/precomputed_ecmult.h
+noinst_HEADERS += src/precomputed_ecmult_gen.h
 noinst_HEADERS += src/assumptions.h
 noinst_HEADERS += src/util.h
 noinst_HEADERS += src/scratch.h
@@ -59,15 +63,19 @@ noinst_HEADERS += contrib/lax_der_parsing.h
 noinst_HEADERS += contrib/lax_der_parsing.c
 noinst_HEADERS += contrib/lax_der_privatekey_parsing.h
 noinst_HEADERS += contrib/lax_der_privatekey_parsing.c
+noinst_HEADERS += examples/random.h
+
+PRECOMPUTED_LIB = libsecp256k1_precomputed.la
+noinst_LTLIBRARIES = $(PRECOMPUTED_LIB)
+libsecp256k1_precomputed_la_SOURCES =  src/precomputed_ecmult.c src/precomputed_ecmult_gen.c
+libsecp256k1_precomputed_la_CPPFLAGS = $(SECP_INCLUDES)
 
 if USE_EXTERNAL_ASM
 COMMON_LIB = libsecp256k1_common.la
-noinst_LTLIBRARIES = $(COMMON_LIB)
 else
 COMMON_LIB =
 endif
-.PHONY: deploy FORCE
-.INTERMEDIATE: $(OSX_TEMP_ISO) $(COVERAGE_INFO)
+noinst_LTLIBRARIES += $(COMMON_LIB)
 
 export PYTHONPATH
 
@@ -78,26 +86,43 @@ endif
 
 libsecp256k1_la_SOURCES = src/secp256k1.c
 libsecp256k1_la_CPPFLAGS = -I$(top_srcdir)/include -I$(top_srcdir)/src $(SECP_INCLUDES)
-libsecp256k1_la_LIBADD = $(SECP_LIBS) $(COMMON_LIB)
-libsecp256k1_la_LDFLAGS = -no-undefined
+libsecp256k1_la_LIBADD = $(SECP_LIBS) $(COMMON_LIB) $(PRECOMPUTED_LIB)
+libsecp256k1_la_LDFLAGS = -no-undefined -version-info $(LIB_VERSION_CURRENT):$(LIB_VERSION_REVISION):$(LIB_VERSION_AGE)
 
 empty :=
 space := $(empty) $(empty)
 
-OSX_APP=BGL-Qt.app
-OSX_VOLNAME = $(subst $(space),-,$(PACKAGE_NAME))
-OSX_DMG = $(OSX_VOLNAME).dmg
-OSX_TEMP_ISO = $(OSX_DMG:.dmg=).temp.iso
-OSX_DEPLOY_SCRIPT=$(top_srcdir)/contrib/macdeploy/macdeployqtplus
-OSX_INSTALLER_ICONS=$(top_srcdir)/src/qt/res/icons/BGL.icns
-OSX_PLIST=$(top_builddir)/share/qt/Info.plist #not installed
-
-DIST_CONTRIB = \
-	       $(top_srcdir)/test/sanitizer_suppressions/lsan \
-	       $(top_srcdir)/test/sanitizer_suppressions/tsan \
-	       $(top_srcdir)/test/sanitizer_suppressions/ubsan \
-	       $(top_srcdir)/contrib/linearize/linearize-data.py \
-	       $(top_srcdir)/contrib/linearize/linearize-hashes.py
+noinst_PROGRAMS =
+if USE_BENCHMARK
+noinst_PROGRAMS += bench bench_internal bench_ecmult
+bench_SOURCES = src/bench.c
+bench_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
+bench_internal_SOURCES = src/bench_internal.c
+bench_internal_LDADD = $(SECP_LIBS) $(COMMON_LIB) $(PRECOMPUTED_LIB)
+bench_internal_CPPFLAGS = $(SECP_INCLUDES)
+bench_ecmult_SOURCES = src/bench_ecmult.c
+bench_ecmult_LDADD = $(SECP_LIBS) $(COMMON_LIB) $(PRECOMPUTED_LIB)
+bench_ecmult_CPPFLAGS = $(SECP_INCLUDES)
+endif
+
+TESTS =
+if USE_TESTS
+noinst_PROGRAMS += tests
+tests_SOURCES = src/tests.c
+tests_CPPFLAGS = -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
+if VALGRIND_ENABLED
+tests_CPPFLAGS += -DVALGRIND
+noinst_PROGRAMS += valgrind_ctime_test
+valgrind_ctime_test_SOURCES = src/valgrind_ctime_test.c
+valgrind_ctime_test_LDADD = libsecp256k1.la $(SECP_LIBS) $(COMMON_LIB)
+endif
+if !ENABLE_COVERAGE
+tests_CPPFLAGS += -DVERIFY
+endif
+tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB) $(PRECOMPUTED_LIB)
+tests_LDFLAGS = -static
+TESTS += tests
+endif
 
 if USE_EXHAUSTIVE_TESTS
 noinst_PROGRAMS += exhaustive_tests
@@ -106,37 +131,72 @@ exhaustive_tests_CPPFLAGS = $(SECP_INCLUDES)
 if !ENABLE_COVERAGE
 exhaustive_tests_CPPFLAGS += -DVERIFY
 endif
+# Note: do not include $(PRECOMPUTED_LIB) in exhaustive_tests (it uses runtime-generated tables).
 exhaustive_tests_LDADD = $(SECP_LIBS) $(COMMON_LIB)
 exhaustive_tests_LDFLAGS = -static
 TESTS += exhaustive_tests
 endif
 
+if USE_EXAMPLES
+noinst_PROGRAMS += ecdsa_example
+ecdsa_example_SOURCES = examples/ecdsa.c
+ecdsa_example_CPPFLAGS = -I$(top_srcdir)/include
+ecdsa_example_LDADD = libsecp256k1.la
+ecdsa_example_LDFLAGS = -static
+if BUILD_WINDOWS
+ecdsa_example_LDFLAGS += -lbcrypt
+endif
+TESTS += ecdsa_example
+if ENABLE_MODULE_ECDH
+noinst_PROGRAMS += ecdh_example
+ecdh_example_SOURCES = examples/ecdh.c
+ecdh_example_CPPFLAGS = -I$(top_srcdir)/include
+ecdh_example_LDADD = libsecp256k1.la
+ecdh_example_LDFLAGS = -static
+if BUILD_WINDOWS
+ecdh_example_LDFLAGS += -lbcrypt
+endif
+TESTS += ecdh_example
+endif
+if ENABLE_MODULE_SCHNORRSIG
+noinst_PROGRAMS += schnorr_example
+schnorr_example_SOURCES = examples/schnorr.c
+schnorr_example_CPPFLAGS = -I$(top_srcdir)/include
+schnorr_example_LDADD = libsecp256k1.la
+schnorr_example_LDFLAGS = -static
+if BUILD_WINDOWS
+schnorr_example_LDFLAGS += -lbcrypt
+endif
+TESTS += schnorr_example
+endif
+endif
+
 ### Precomputed tables
-EXTRA_PROGRAMS = gen_ecmult_static_pre_g gen_ecmult_gen_static_prec_table
+EXTRA_PROGRAMS = precompute_ecmult precompute_ecmult_gen
 CLEANFILES = $(EXTRA_PROGRAMS)
 
-gen_ecmult_static_pre_g_SOURCES = src/gen_ecmult_static_pre_g.c
-gen_ecmult_static_pre_g_CPPFLAGS = $(SECP_INCLUDES)
-gen_ecmult_static_pre_g_LDADD = $(SECP_LIBS) $(COMMON_LIB)
+precompute_ecmult_SOURCES = src/precompute_ecmult.c
+precompute_ecmult_CPPFLAGS = $(SECP_INCLUDES)
+precompute_ecmult_LDADD = $(SECP_LIBS) $(COMMON_LIB)
 
-OSX_PACKAGING = $(OSX_DEPLOY_SCRIPT) $(OSX_INSTALLER_ICONS) \
-  $(top_srcdir)/contrib/macdeploy/detached-sig-create.sh
+precompute_ecmult_gen_SOURCES = src/precompute_ecmult_gen.c
+precompute_ecmult_gen_CPPFLAGS = $(SECP_INCLUDES)
+precompute_ecmult_gen_LDADD = $(SECP_LIBS) $(COMMON_LIB)
 
 # See Automake manual, Section "Errors with distclean".
 # We don't list any dependencies for the prebuilt files here because
 # otherwise make's decision whether to rebuild them (even in the first
 # build by a normal user) depends on mtimes, and thus is very fragile.
 # This means that rebuilds of the prebuilt files always need to be
 # forced by deleting them, e.g., by invoking `make clean-precomp`.
-src/ecmult_static_pre_g.h:
-	$(MAKE) $(AM_MAKEFLAGS) gen_ecmult_static_pre_g$(EXEEXT)
-	./gen_ecmult_static_pre_g$(EXEEXT)
-src/ecmult_gen_static_prec_table.h:
-	$(MAKE) $(AM_MAKEFLAGS) gen_ecmult_gen_static_prec_table$(EXEEXT)
-	./gen_ecmult_gen_static_prec_table$(EXEEXT)
-
-PRECOMP = src/ecmult_gen_static_prec_table.h src/ecmult_static_pre_g.h
-noinst_HEADERS += $(PRECOMP)
+src/precomputed_ecmult.c:
+	$(MAKE) $(AM_MAKEFLAGS) precompute_ecmult$(EXEEXT)
+	./precompute_ecmult$(EXEEXT)
+src/precomputed_ecmult_gen.c:
+	$(MAKE) $(AM_MAKEFLAGS) precompute_ecmult_gen$(EXEEXT)
+	./precompute_ecmult_gen$(EXEEXT)
+
+PRECOMP = src/precomputed_ecmult_gen.c src/precomputed_ecmult.c
 precomp: $(PRECOMP)
 
 # Ensure the prebuilt files will be build first (only if they don't exist,

README.md

@@ -62,53 +62,67 @@ Features:
 * Suitable for embedded systems.
 * Optional module for public key recovery.
 * Optional module for ECDH key exchange.
-* Optional module for Schnorr signatures according to [BIP-340](https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki) (experimental).
-
-<b>Bitgesell is a fork of BGL with the following changes:</b> <br>
-* Block Reward [Burn rate is 90% of tx fees]
-  ```sh
-  nFees*0.1 + GetBlockSubsidy()  
-  ```
-* Block Weight [10 times smaller than Bitgesell]
-  ```sh
-  <= 400,000
-  ```
-* 100% Segwit 
-  ```sh
-  Eliminates problems with legacy type of transactions
-  ```
-* Halving Interval [Halving cycle of bitgetsell is 1yr while that of BGL is 4yr]
-  ```sh
-  210000 blocks/4
-  ```
-* Block Subsidy [Max coins = 21,000,000] <br>
-  `210000 blocks/4` <br> <hr>
-  `Hashing algorithm for blocks is Keccak (sha-3).` <br> <hr>
-  `The master branch is regularly built (see` [doc/build-*.md](https://github.com/BitgesellOfficial/bitgesell/tree/master/doc) `for instructions) and tested, but is not guaranteed to be completely stable.` <br> <hr>
-  [tags](https://github.com/BitgesellOfficial/bitgesell/tags) `are created regularly to indicate new official, stable release versions of BGL Core.` <br>
-
-
-### Built With
-
-* [C++](#)
-* [C](#)
-* [Python](#)
-* [SourcePawn](#)
-* [M4](#)
-* [Shell](#)
-
-
-<!-- GETTING STARTED -->
-## Getting Started
-
-Visit official website: [click here](https://bitgesell.ca/) <br>
+* Optional module for Schnorr signatures according to [BIP-340](https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki).
+
+Implementation details
+----------------------
+
+* General
+  * No runtime heap allocation.
+  * Extensive testing infrastructure.
+  * Structured to facilitate review and analysis.
+  * Intended to be portable to any system with a C89 compiler and uint64_t support.
+  * No use of floating types.
+  * Expose only higher level interfaces to minimize the API surface and improve application security. ("Be difficult to use insecurely.")
+* Field operations
+  * Optimized implementation of arithmetic modulo the curve's field size (2^256 - 0x1000003D1).
+    * Using 5 52-bit limbs (including hand-optimized assembly for x86_64, by Diederik Huys).
+    * Using 10 26-bit limbs (including hand-optimized assembly for 32-bit ARM, by Wladimir J. van der Laan).
+      * This is an experimental feature that has not received enough scrutiny to satisfy the standard of quality of this library but is made available for testing and review by the community.
+* Scalar operations
+  * Optimized implementation without data-dependent branches of arithmetic modulo the curve's order.
+    * Using 4 64-bit limbs (relying on __int128 support in the compiler).
+    * Using 8 32-bit limbs.
+* Modular inverses (both field elements and scalars) based on [safegcd](https://gcd.cr.yp.to/index.html) with some modifications, and a variable-time variant (by Peter Dettman).
+* Group operations
+  * Point addition formula specifically simplified for the curve equation (y^2 = x^3 + 7).
+  * Use addition between points in Jacobian and affine coordinates where possible.
+  * Use a unified addition/doubling formula where necessary to avoid data-dependent branches.
+  * Point/x comparison without a field inversion by comparison in the Jacobian coordinate space.
+* Point multiplication for verification (a*P + b*G).
+  * Use wNAF notation for point multiplicands.
+  * Use a much larger window for multiples of G, using precomputed multiples.
+  * Use Shamir's trick to do the multiplication with the public key and the generator simultaneously.
+  * Use secp256k1's efficiently-computable endomorphism to split the P multiplicand into 2 half-sized ones.
+* Point multiplication for signing
+  * Use a precomputed table of multiples of powers of 16 multiplied with the generator, so general multiplication becomes a series of additions.
+  * Intended to be completely free of timing sidechannels for secret-key operations (on reasonable hardware/toolchains)
+    * Access the table with branch-free conditional moves so memory access is uniform.
+    * No data-dependent branches
+  * Optional runtime blinding which attempts to frustrate differential power analysis.
+  * The precomputed tables add and eventually subtract points for which no known scalar (secret key) is known, preventing even an attacker with control over the secret key used to control the data internally.
+
+Build steps
+-----------
+
+libsecp256k1 is built using autotools:
 
     $ ./autogen.sh
     $ ./configure
     $ make
     $ make check  # run the test suite
     $ sudo make install  # optional
 
+To compile optional modules (such as Schnorr signatures), you need to run `./configure` with additional flags (such as `--enable-module-schnorrsig`). Run `./configure --help` to see the full list of available flags.
+
+Usage examples
+-----------
+  Usage examples can be found in the [examples](examples) directory. To compile them you need to configure with `--enable-examples`.
+  * [ECDSA example](examples/ecdsa.c)
+  * [Schnorr signatures example](examples/schnorr.c)
+  * [Deriving a shared secret (ECDH) example](examples/ecdh.c)
+  To compile the Schnorr signature and ECDH examples, you also need to configure with `--enable-module-schnorrsig` and `--enable-module-ecdh`.
+
 Test coverage
 -----------
 

ci/linux-debian.Dockerfile

@@ -19,7 +19,8 @@ RUN apt-get install --no-install-recommends --no-upgrade -y \
         gcc-arm-linux-gnueabihf libc6-dev-armhf-cross libc6-dbg:armhf \
         gcc-aarch64-linux-gnu libc6-dev-arm64-cross libc6-dbg:arm64 \
         gcc-powerpc64le-linux-gnu libc6-dev-ppc64el-cross libc6-dbg:ppc64el \
-        wine gcc-mingw-w64-x86-64
+        wine gcc-mingw-w64-x86-64 \
+        sagemath
 
 # Run a dummy command in wine to make it set up configuration
 RUN wine64-stable xcopy || true