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@feltroidprime
feltroidprime authored Sep 30, 2024
2 parents dac43d7 + fa27403 commit 0bdea5e
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Showing 36 changed files with 6,611 additions and 139 deletions.
17 changes: 15 additions & 2 deletions hydra/garaga/algebra.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -147,10 +147,14 @@ def __rtruediv__(self, left: PyFelt | int) -> PyFelt:
def is_quad_residue(self) -> bool:
return legendre_symbol(self.value, self.p) == 1

def sqrt(self) -> PyFelt:
def sqrt(self, min_root: bool = True) -> PyFelt:
if not self.is_quad_residue():
raise ValueError("Cannot square root a non-quadratic residue")
return PyFelt(min(sqrt_mod(self.value, self.p, all_roots=True)), self.p)
roots = sqrt_mod(self.value, self.p, all_roots=True)
if min_root:
return PyFelt(min(roots), self.p)
else:
return PyFelt(max(roots), self.p)


@dataclass(slots=True)
Expand Down Expand Up @@ -313,8 +317,17 @@ def sqrt(self) -> Fp2:
b = (Fp2.one(self.p) + alpha) ** ((self.p - 1) // 2)
x = b * x0

# Return the root as is, without forcing a specific sign
return x

def lexicographically_largest(self) -> bool:
"""Check if this Fp2 element is lexicographically largest."""
if self.a1.value > (self.p - 1) // 2:
return True
if self.a1.value < (self.p - 1) // 2:
return False
return self.a0.value > (self.p - 1) // 2


@dataclass(slots=True)
class BaseField:
Expand Down
74 changes: 60 additions & 14 deletions hydra/garaga/definitions.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -87,6 +87,13 @@ def get_proving_system_curve(
return CurveID(curve_id)


@dataclass
class SWUParams:
A: int
B: int
Z: int


@dataclass(slots=True, frozen=True)
class WeierstrassCurve:
cairo_zero_namespace_name: str
Expand All @@ -99,6 +106,7 @@ class WeierstrassCurve:
fp_generator: int # A generator of the field of the curve. To verify it, use is_generator function.
Gx: int # x-coordinate of the generator point
Gy: int # y-coordinate of the generator point
swu_params: SWUParams

def to_cairo_zero(self) -> str:
code = f"namespace {self.cairo_zero_namespace_name} {{\n"
Expand Down Expand Up @@ -160,12 +168,14 @@ def __init__(
fp_generator: int,
Gx: int,
Gy: int,
swu_params: SWUParams,
):
assert a_twisted != 0 and d_twisted != 0 and a_twisted != d_twisted
# Set attributes
object.__setattr__(self, "d_twisted", d_twisted)
object.__setattr__(self, "a_twisted", a_twisted)
object.__setattr__(self, "p", p)
object.__setattr__(self, "swu_params", swu_params)
# Calculate Weierstrass parameters
a = (
-1
Expand All @@ -191,6 +201,7 @@ def __init__(
b,
fp_generator,
*(self.to_weierstrass(Gx, Gy)),
swu_params,
)

def to_weierstrass(self, x_twisted, y_twisted):
Expand Down Expand Up @@ -326,6 +337,7 @@ def bit(value, index):
0x12C85EA5DB8C6DEB4AAB71808DCB408FE3D1E7690C43D37B4CE6CC0166FA7DAA,
0x90689D0585FF075EC9E99AD690C3395BC4B313370B38EF355ACDADCD122975B,
),
swu_params=None,
),
BLS12_381_ID: PairingCurve(
cairo_zero_namespace_name="bls",
Expand Down Expand Up @@ -371,6 +383,11 @@ def bit(value, index):
0xCE5D527727D6E118CC9CDC6DA2E351AADFD9BAA8CBDD3A76D429A695160D12C923AC9CC3BACA289E193548608B82801,
0x606C4A02EA734CC32ACD2B02BC28B99CB3E287E85A763AF267492AB572E99AB3F370D275CEC1DA1AAA9075FF05F79BE,
),
swu_params=SWUParams(
A=0x144698A3B8E9433D693A02C96D4982B0EA985383EE66A8D8E8981AEFD881AC98936F8DA0E0F97F5CF428082D584C1D,
B=0x12E2908D11688030018B12E8753EEE3B2016C1F0F24F4070A0B9C14FCEF35EF55A23215A316CEAA5D1CC48E98E172BE0,
Z=11,
),
),
SECP256K1_ID: WeierstrassCurve(
cairo_zero_namespace_name="secp256k1",
Expand All @@ -383,6 +400,7 @@ def bit(value, index):
fp_generator=3,
Gx=0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,
Gy=0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8,
swu_params=None,
),
SECP256R1_ID: WeierstrassCurve(
cairo_zero_namespace_name="secp256r1",
Expand All @@ -395,6 +413,7 @@ def bit(value, index):
fp_generator=6,
Gx=0x6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296,
Gy=0x4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5,
swu_params=None,
),
ED25519_ID: TwistedEdwardsCurve(
cairo_zero_namespace_name="ED25519", # See https://neuromancer.sk/std/other/Ed25519
Expand All @@ -407,6 +426,7 @@ def bit(value, index):
fp_generator=6,
Gx=0x216936D3CD6E53FEC0A4E231FDD6DC5C692CC7609525A7B2C9562D608F25D51A,
Gy=0x6666666666666666666666666666666666666666666666666666666666666658,
swu_params=None,
),
}

Expand Down Expand Up @@ -528,12 +548,13 @@ class G1Point:
x: int
y: int
curve_id: CurveID
iso_point: bool = False

def __str__(self) -> str:
return f"G1Point({hex(self.x)}, {hex(self.y)}) on curve {self.curve_id}"
return f"G1Point({self.x}, {self.y}) on curve {self.curve_id}"

def __hash__(self):
return hash((self.x, self.y, self.curve_id))
return hash((self.x, self.y, self.curve_id, self.iso_point))

def __eq__(self, other: object) -> bool:
"""
Expand All @@ -551,6 +572,7 @@ def __eq__(self, other: object) -> bool:
self.x == other.x
and self.y == other.y
and self.curve_id.value == other.curve_id.value
and self.iso_point == other.iso_point
)

def __post_init__(self):
Expand Down Expand Up @@ -646,8 +668,13 @@ def is_on_curve(self) -> bool:
Returns:
bool: True if the point is on the curve, False otherwise.
"""
a = CURVES[self.curve_id.value].a
b = CURVES[self.curve_id.value].b
if self.iso_point:
a = CURVES[self.curve_id.value].swu_params.A
b = CURVES[self.curve_id.value].swu_params.B
else:
a = CURVES[self.curve_id.value].a
b = CURVES[self.curve_id.value].b

p = CURVES[self.curve_id.value].p
lhs = self.y**2 % p
rhs = (self.x**3 + a * self.x + b) % p
Expand Down Expand Up @@ -722,25 +749,30 @@ def scalar_mul(self, scalar: int) -> "G1Point":
if self.is_infinity():
return self
if scalar == 0:
return G1Point(0, 0, self.curve_id)

return G1Point(0, 0, self.curve_id, self.iso_point)
if self.iso_point:
a = CURVES[self.curve_id.value].swu_params.A
b = CURVES[self.curve_id.value].swu_params.B
else:
a = CURVES[self.curve_id.value].a
b = CURVES[self.curve_id.value].b
# Fastecdsa C binding.
x, y = curvemath.mul(
str(self.x),
str(self.y),
str(abs(scalar)),
str(CURVES[self.curve_id.value].p),
str(CURVES[self.curve_id.value].a),
str(CURVES[self.curve_id.value].b),
str(a),
str(b),
str(CURVES[self.curve_id.value].n),
str(CURVES[self.curve_id.value].Gx),
str(CURVES[self.curve_id.value].Gy),
)
# Fastecdsa already returns (0, 0) for the identity element.
if scalar < 0:
return -G1Point(int(x), int(y), self.curve_id)
return -G1Point(int(x), int(y), self.curve_id, self.iso_point)
else:
return G1Point(int(x), int(y), self.curve_id)
return G1Point(int(x), int(y), self.curve_id, self.iso_point)

def add(self, other: "G1Point") -> "G1Point":
"""
Expand All @@ -761,20 +793,29 @@ def add(self, other: "G1Point") -> "G1Point":
return self
if self.curve_id != other.curve_id:
raise ValueError("Points are not on the same curve")
if self.iso_point != other.iso_point:
raise ValueError("Points are not on the same curve")
if self.iso_point:
a = CURVES[self.curve_id.value].swu_params.A
b = CURVES[self.curve_id.value].swu_params.B
else:
a = CURVES[self.curve_id.value].a
b = CURVES[self.curve_id.value].b

x, y = curvemath.add(
str(self.x),
str(self.y),
str(other.x),
str(other.y),
str(CURVES[self.curve_id.value].p),
str(CURVES[self.curve_id.value].a),
str(CURVES[self.curve_id.value].b),
str(a),
str(b),
str(CURVES[self.curve_id.value].n),
str(CURVES[self.curve_id.value].Gx),
str(CURVES[self.curve_id.value].Gy),
)

return G1Point(int(x), int(y), self.curve_id)
return G1Point(int(x), int(y), self.curve_id, self.iso_point)

def __neg__(self) -> "G1Point":
"""
Expand All @@ -783,7 +824,12 @@ def __neg__(self) -> "G1Point":
Returns:
G1Point: The negated point.
"""
return G1Point(self.x, -self.y % CURVES[self.curve_id.value].p, self.curve_id)
return G1Point(
self.x,
-self.y % CURVES[self.curve_id.value].p,
self.curve_id,
self.iso_point,
)


@dataclass(frozen=True)
Expand Down
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