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constantine/constantine/arithmetic
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Mamy Ratsimbazafy 2613356281
Endomorphism acceleration for Scalar Multiplication (#44) 
* Add MultiScalar recoding from "Efficient and Secure Algorithms for GLV-Based Scalar Multiplication" by Faz et al

* precompute cube root of unity - Add VM precomputation of Fp - workaround upstream bug https://github.com/nim-lang/Nim/issues/14585

* Add the φ-accelerated lookup table builder

* Add a dedicated bithacks file

* cosmetic import consistency

* Build the φ precompute table with n-1 EC additions instead of 2^(n-1) additions

* remove binary

* Add the GLV precomputations to the sage scripts

* You can't avoid it, bigint multiplication is needed at one point

* Add bigint multiplication discarding some low words

* Implement the lattice decomposition in sage

* Proper decomposition for BN254

* Prepare the code for a new scalar mul

* We compile, and now debugging hunt

* More helpers to debug GLV scalar Mul

* Fix conditional negation

* Endomorphism accelerated scalar mul working for BN254 curve

* Implement endomorphism acceleration for BLS12-381 (needed cofactor clearing of the point)

* fix nimble test script after bench rename
2020-06-14 15:39:06 +02:00
..
bigints.nim
Endomorphism acceleration for Scalar Multiplication (#44)
2020-06-14 15:39:06 +02:00
finite_fields_inversion.nim
Endomorphism acceleration for Scalar Multiplication (#44)
2020-06-14 15:39:06 +02:00
finite_fields.nim
Endomorphism acceleration for Scalar Multiplication (#44)
2020-06-14 15:39:06 +02:00
limbs_modular.nim
Implement constant-time div2 on finite and extension fields
2020-04-15 02:12:45 +02:00
limbs_montgomery.nim
Endomorphism acceleration for Scalar Multiplication (#44)
2020-06-14 15:39:06 +02:00
limbs.nim
Endomorphism acceleration for Scalar Multiplication (#44)
2020-06-14 15:39:06 +02:00
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