Add basic modular & EC point arithmetic primitives && ECDSA signature verification #5
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Added functions for basic modular arithmetic (add, sub, mul, div) and struct `fp_element` which represents prime field element .
Added implementation of EC point addition, multiplication and inverse. Added 2 elliptic curves over prime field: secp256k1 and secp256r1
Added implementation of ECDSA signature verification. The example contract is updated to include benchmark actions for curves secp256k1 & secp256r1.
Testing in wasm suggests that VLA is faster than __builtin_alloca & alloca. __builtin_alloca is used where VLA array can't be used.
…ions Changes: - Fixed proj. point comparison when z coords differ - Fixed curve point creation and verifying it's in range [0, p-1] - Added point function `is_valid` to verify the point is valid point generated from curve base point - Added proj. point functions `normalize` & `normalized` which scales point to reflect affine point (z -> 1) - Optimized converting proj. point to affine point when z = 1 - Fixed proj. point doubling to return identity point when y = 0 - Renamed point function `invert` -> `inverted` - Added curve function `generate_point` which generates point from scalar using base point - Refactored fp curve function `make_field_element` to check that the provided integer value is in range [0, p-1] - Added additional EC tests
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EC GF(p) point interfaces are simplified to require only curve type for template parameter. All fp point type alias and helper function `make_ec_point_fp_proj` are removed. Renamed intiger type alias to `int_type` for base struct `field_element`.
Added actions ecdsak1 & ecdsar1 which verifies ECDSA-SHA256 signatures for secp256k1 and secp256r1.
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Changes
bigintfor larger number arithmeticfp_elementwhich represents field element for curves over prime fieldec_curve_fp,ec_point_fp,ec_point_fp_proj)