Showstopper upstream bug - static object

[mratsim]

There are 2 kinds of implementation possible

1. Like in any language, the prime number is a global stored in the binary. Main trade-offs are:

• We don't use the typesystem at all to check that A + B are compatible (because using same modulo)
• {.noSideEffect.} tracking will be cumbersome.
• No constant folding
• We need a way to deal with "different modulus" error. Can we use exceptions given that we want to run even on embedded, using result + error code or just error code makes library usage clunky as well.

2. Embed the prime number in the type system.

Upstream: nim-lang/Nim#11142

[mratsim]

Workaround via static curve configuration.

This doesn't allow us to configure an arbitrary finite field but is enough for cryptography.
This also allow the library to ensure constants are only defined once and so stored only once in ROM to optimize binary sizes.

constantine/constantine/config/curves.nim

Lines 41 to 75 in 05009f9

	when not defined(testingCurves):
	declareCurves:
	# Barreto-Naehrig curve, pairing-friendly, Prime 254 bit, ~100-bit security
	# https://eprint.iacr.org/2013/879.pdf
	# Usage: Zero-Knowledge Proofs / zkSNARKs in ZCash and Ethereum 1
	# https://eips.ethereum.org/EIPS/eip-196
	curve BN254:
	bitsize: 254
	modulus: "0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47"
	# Equation: Y^2 = X^3 + 3
	curve BLS12_381:
	bitsize: 381
	modulus: "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"
	# Equation: y^2 = x^3 + 4
	curve P256: # secp256r1 / NIST P-256
	bitsize: 256
	modulus: "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff"
	else:
	# Fake curve for testing field arithmetic
	declareCurves:
	curve Fake101:
	bitsize: 7
	modulus: "0x65" # 101 in hex
	curve Mersenne61:
	bitsize: 61
	modulus: "0x1fffffffffffffff" # 2^61 - 1
	curve Mersenne127:
	bitsize: 127
	modulus: "0x7fffffffffffffffffffffffffffffff" # 2^127 - 1
	curve P256: # secp256r1 / NIST P-256
	bitsize: 256
	modulus: "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff"
	curve BLS12_381:
	bitsize: 381
	modulus: "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"