https://github.com/erhant/fftype
Finite-field arithmetic within the type system.
https://github.com/erhant/fftype
cryptography elliptic-curves finite-fields polynomials types typescript
Last synced: 9 months ago
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Finite-field arithmetic within the type system.
- Host: GitHub
- URL: https://github.com/erhant/fftype
- Owner: erhant
- License: mit
- Created: 2023-05-14T20:48:21.000Z (about 3 years ago)
- Default Branch: main
- Last Pushed: 2023-06-05T19:23:22.000Z (about 3 years ago)
- Last Synced: 2025-03-02T19:49:25.054Z (over 1 year ago)
- Topics: cryptography, elliptic-curves, finite-fields, polynomials, types, typescript
- Language: TypeScript
- Homepage:
- Size: 68.4 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
fftype
finite-field arithmetic within the type system
Start by installing dependencies with `yarn` or `npm i`. To run a function, assign its result to a type and simply "hover over" that type to see the results of "running" that function with some input.
### Implementations
We have the following existing implementations:
- [int4](./src/definitions/int4/): 4-Bit Non-Negative Integers
- [int5](./src/definitions/int5/): 5-Bit Non-Negative Integers
- [gf5](./src/definitions/gf5.d.ts): Galois Field of order 5
- [gf13](./src/definitions/gf13.d.ts): Galois Field of order 13
To use an implementation, simply export them at [`source.d.ts`](./src/source.d.ts).
### Writing an implementation
When writing an implementation for a new field of order $p$, one must do the following:
- Let $k$ be the minimum number of bits required to represent $p$.
- Implement $k+1$ bits bitwise arithmetic.
- Define the type of order in $k+1$ bits.
- Define the type of field elements in $k+1$ bits.
For example, consider the Galois Field of order 5. The number 5 is representable with 3 bits as 101, so:
- We must implement 4-bit arithmetic.
- We define `type Ford = [0, 1, 0, 1]` which is 5 in bitwise representation.
- We implement the field type `type Felt = [0, 1, 0, 0] | [0, 0, Bit, Bit]` which covers all bitwise representation of numbers `0, 1, 2, 3, 4`.
As another example, consider the Galois Field of order 13. The number 13 is representable with 4 bits as 1101, so:
- We must implement 5-bit arithmetic.
- We define `type Ford = [0, 1, 1, 0, 1]` which is 13 in bitwise representation.
- We implement the field type `type Felt = [0, 1, 1, 0, 0] | [0, 1, 0, Bit, Bit] | [0, 0, Bit, Bit, Bit]` which covers all bitwise representation of numbers `0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12`.
## Testing
Tests are done via [@type-challenges/utils](https://github.com/SamVerschueren/@type-challenges/utils), you can run them via `yarn test`. Note that testing is simply compiling everything and see if you get any errors.
## Status
- [x] Bitwise Operations
- [x] Addition
- [x] Subtraction
- [x] Rotations
- [x] Shifting
- [x] Fills
- [x] Logic
- [ ] Finite Field Arithmetic
- [x] Addition
- [x] Additive Inverse
- [x] Multiplication
- [ ] Multiplicative Inverse
- [x] Subtraction via Additive Inverse
- [ ] Division via Multiplicative Inverse
- [x] Quotient
- [x] Modulus
- [x] Remainder
- [x] Comparators
Any help is appreciated...
## Resources
- [Building Complex Types](https://medium.hexlabs.io/building-complex-types-in-typescript-804c973ce66f)
- [Tail Recursion in TS](https://www.typescriptlang.org/docs/handbook/release-notes/typescript-4-5.html#tail-recursion-elimination-on-conditional-types)
