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constantine/constantine/arithmetic
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Mamy Ratsimbazafy 4ff0e3d90b
Internals refactor + renewed focus on perf (#17) 
* Lay out the refactoring objectives and tradeoffs

* Refactor the 32 and 64-bit primitives [skip ci]

* BigInts and Modular BigInts compile

* Make the bigints test compile

* Fix modular reduction

* Fix reduction tests vs GMP

* Implement montegomery mul, pow, inverse, WIP finite field compilation

* Make FiniteField compile

* Fix exponentiation compilation

* Fix Montgomery magic constant computation  for 2^64 words

* Fix typo in non-optimized CIOS - passing finite fields IO tests

* Add limbs comparisons [skip ci]

* Fix on precomputation of the Montgomery magic constant

* Passing all tests including 𝔽p2

* modular addition, the test for mersenne prime was wrong

* update benches

* Fix "nimble test" + typo on out-of-place field addition

* bigint division, normalization is needed: https://travis-ci.com/github/mratsim/constantine/jobs/298359743

* missing conversion in subborrow non-x86 fallback - https://travis-ci.com/github/mratsim/constantine/jobs/298359744

* Fix little-endian serialization

* Constantine32 flag to run 32-bit constantine on 64-bit machines

* IO Field test, ensure that BaseType is used instead of uint64 when the prime can field in uint32

* Implement proper addcarry and subborrow fallback for the compile-time VM

* Fix export issue when the logical wordbitwidth == physical wordbitwidth - passes all tests (32-bit and 64-bit)

* Fix uint128 on ARM

* Fix C++ conditional copy and ARM addcarry/subborrow

* Add investigation for SIGFPE in Travis

* Fix debug display for unsafeDiv2n1n

* multiplexer typo

* moveMem bug in glibc of Ubuntu 16.04?

* Was probably missing an early clobbered register annotation on conditional mov

* Note on Montgomery-friendly moduli

* Strongly suspect a GCC before GCC 7 codegen bug (https://gcc.gnu.org/bugzilla/show_bug.cgi?id=87139)

* hex conversion was (for debugging) not taking requested order into account + inlining comment

* Use 32-bit limbs on ARM64, uint128 builtin __udivti4 bug?

* Revert "Use 32-bit limbs on ARM64, uint128 builtin __udivti4 bug?"

This reverts commit 087f9aa7fb40bbd058d05cbd8eec7fc082911f49.

* Fix subborrow fallback for non-x86 (need to maks the borrow)
2020-03-16 16:33:51 +01:00
..
bigints.nim
Internals refactor + renewed focus on perf (#17)
2020-03-16 16:33:51 +01:00
finite_fields.nim
Internals refactor + renewed focus on perf (#17)
2020-03-16 16:33:51 +01:00
limbs.nim
Internals refactor + renewed focus on perf (#17)
2020-03-16 16:33:51 +01:00
montgomery.nim
Internals refactor + renewed focus on perf (#17)
2020-03-16 16:33:51 +01:00
precomputed.nim
Internals refactor + renewed focus on perf (#17)
2020-03-16 16:33:51 +01:00
README.md
Internals refactor + renewed focus on perf (#17)
2020-03-16 16:33:51 +01:00

README.md

BigInt and Finite Field Arithmetic

This folder contains the implementation of

  • big integers
  • finite field arithmetic (i.e. modular arithmetic)

As a tradeoff between speed, code size and compiler-enforced dependent type checking, the library is structured the following way:

  • Finite Field: statically parametrized by an elliptic curve
  • Big Integers: statically parametrized by the bit width of the field modulus
  • Limbs: statically parametrized by the number of words to handle the bitwidth

This allows to reuse the same implementation at the limbs-level for curves that required the same number of words to save on code size, for example secp256k1 and BN254. It also enables compiler unrolling, inlining and register optimization, where code size is not an issue for example for multi-precision addition.

References