# Elliptic Curve

- [Weierstrass Curve](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/weierstrass-curve.md)
- [Coordinate Forms](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/weierstrass-curve/coordinate-forms.md)
- [Fast Elliptic Curve Arithmetic and Improved WEIL Pairing Evaluation](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/weierstrass-curve/fast-elliptic-curve-arithmetic-and-improved-weil-pairing-evaluation.md)
- [Edwards Curve](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/edwards-curve.md)
- [Coordinate Forms](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/edwards-curve/coordinate-forms.md)
- [Twisted Edwards ↔ Short Weierstrass Transformation](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/edwards-curve/twisted-edwards-short-weierstrass-transformation.md)
- [Batch Inverse for Batch Point Additions](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/batch-inverse-for-batch-point-additions.md)
- [Scalar Multiplication](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/scalar-multiplication.md)
- [Double-and-add](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/scalar-multiplication/double-and-add.md): Reduction of scalar multiplication into double and add operations
- [GLV Decomposition](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/scalar-multiplication/glv-decomposition.md): Splitting a scalar multiplication into 2 and reducing count of double operations
- [MSM](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/msm.md)
- [Pippenger's Algorithm](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/msm/pippengers-algorithm.md): Reduction of multi-scalar multiplication (MSM) into double and add operations
- [Signed Bucket Index](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/msm/signed-bucket-index.md)
- [CycloneMSM](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/msm/cyclonemsm.md): Presentation: https://youtu.be/djA3mzn7BPg
- [EdMSM](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/msm/edmsm.md): ZPrize "Accelerating MSM on Mobile" winner
- [cuZK](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/msm/cuzk.md): Presentation: https://youtu.be/D8b4yi\_URJE
- [ICICLE MSM](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/msm/icicle-msm.md)
- [2-Chain and 2-Cycle of Elliptic Curves](https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/2-chain-and-2-cycle-of-elliptic-curves.md)


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