Module oberon::inner_types

The inner representation types

Re-exports

• pub use bls12_381_plus::elliptic_curve;
• pub use bls12_381_plus::group;

Modules

• elliptic_curve
  RustCrypto: Elliptic Curve Traits
• notes
  Notes about how the BLS12-381 elliptic curve is designed, specified and implemented by this library.

Structs

• Bls12
  A [pairing::Engine] for BLS12-381 pairing operations.
• G1Affine
  This is an element of $\mathbb{G}_1$ represented in the affine coordinate space. It is ideal to keep elements in this representation to reduce memory usage and improve performance through the use of mixed curve model arithmetic.
• G1Projective
  This is an element of $\mathbb{G}_1$ represented in the projective coordinate space.
• G2Affine
  This is an element of $\mathbb{G}_2$ represented in the affine coordinate space. It is ideal to keep elements in this representation to reduce memory usage and improve performance through the use of mixed curve model arithmetic.
• G2Prepared
  This structure contains cached computations pertaining to a $\mathbb{G}_2$ element as part of the pairing function (specifically, the Miller loop) and so should be computed whenever a $\mathbb{G}_2$ element is being used in multiple pairings or is otherwise known in advance. This should be used in conjunction with the multi_miller_loop function provided by this crate.
• G2Projective
  This is an element of $\mathbb{G}_2$ represented in the projective coordinate space.
• Gt
  This is an element of $\mathbb{G}_T$, the target group of the pairing function. As with $\mathbb{G}_1$ and $\mathbb{G}_2$ this group has order $q$.
• MillerLoopResult
  Represents results of a Miller loop, one of the most expensive portions of the pairing function. MillerLoopResults cannot be compared with each other until .final_exponentiation() is called, which is also expensive.
• Scalar
  Represents an element of the scalar field $\mathbb{F}_q$ of the BLS12-381 elliptic curve construction.

Traits

• Curve
  Efficient representation of an elliptic curve point guaranteed.
• Field
  This trait represents an element of a field.
• Group
  This trait represents an element of a cryptographic group.
• GroupEncoding
• PrimeCurveAffine
  Affine representation of an elliptic curve point guaranteed to be in the correct prime order subgroup.
• PrimeField
  This represents an element of a non-binary prime field.
• ScalarLe
  A helper trait for serializing Scalars as little-endian instead of big endian.

Functions

• multi_miller_loop
  Computes $$\sum_{i=1}^n \textbf{ML}(a_i, b_i)$$ given a series of terms $$(a_1, b_1), (a_2, b_2), …, (a_n, b_n).$$
• pairing
  Invoke the pairing function without the use of precomputation and other optimizations.