Add missing secp256r1 hints

[gabrielbosio]

• compute_doubling_slope hint
• try_get_point_from_x hint

[Smartdevs17]

Can I try solving this issue? I have added some missing hints to the compute_doubling_slope and try_get_point_from_x functions in the src/starkware/cairo/common/secp256r1/ec.cairo file. These hints are crucial for ensuring the correct computation of elliptic curve points. Below are the details of the changes:

compute_doubling_slope Function
%{
from starkware.cairo.common.cairo_secp.secp256r1_utils import SECP256R1_ALPHA, SECP256R1_P
from starkware.cairo.common.cairo_secp.secp_utils import pack
from starkware.python.math_utils import ec_double_slope

# Compute the slope.
x = pack(ids.point.x, PRIME)
y = pack(ids.point.y, PRIME)
value = slope = ec_double_slope(point=(x, y), alpha=SECP256R1_ALPHA, p=SECP256R1_P)

%}

try_get_point_from_x Function
%{
from starkware.cairo.common.cairo_secp.secp_utils import SECP256R1, pack
from starkware.python.math_utils import y_squared_from_x

y_square_int = y_squared_from_x(
    x=pack(ids.x, PRIME),
    alpha=SECP256R1.alpha,
    beta=SECP256R1.beta,
    field_prime=SECP256R1.prime,
)

# Note that (y_square_int ** ((SECP256R1.prime + 1) / 4)) ** 2 =
#   = y_square_int ** ((SECP256R1.prime + 1) / 2) =
#   = y_square_int ** ((SECP256R1.prime - 1) / 2 + 1) =
#   = y_square_int * y_square_int ** ((SECP256R1.prime - 1) / 2) = y_square_int * {+/-}1.
y = pow(y_square_int, (SECP256R1.prime + 1) // 4, SECP256R1.prime)

# We need to decide whether to take y or prime - y.
if ids.v % 2 == y % 2:
    value = y
else:
    value = (-y) % SECP256R1.prime

%}

These hints ensure the correct calculation of the slope and the y-coordinate for elliptic curve operations on the secp256r1 curve. This should enhance the functionality and accuracy of the cryptographic operations in the code.