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- from finite_fields import finitefield
- def add(x_1, y_1, x_2, y_2):
- if (x_1, y_1) == (x_2, y_2):
- if y_1 == 0:
- return None
- # slope of the tangent line
- m = (3 * x_1 * x_1 + a) / (2 * y_1)
- return None
- else:
- if x_1 == x_2:
- return None
- # slope of the secant line
- m = (y_2 - y_1) / (x_2 - x_1)
- x_3 = m*m - x_1 - x_2
- y_3 = m*(x_1 - x_3) - y_1
- return (x_3, y_3)
- if __name__ == "__main__":
- # Vesta
- q = 0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001
- fq = finitefield.IntegersModP(q)
- a, b = fq(0x00), fq(0x05)
- p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
- C = (fq(0x1ca18c7c3fcb110f9e92c694ce552238f95e9f9b911599cedaff6018cfc5ed52), fq(0x3ad6133a791e41f3e062d370b40e97e77d20effc00b7ee88c4bb097d245cb438))
- D = (fq(0x3e544e611bb895166afe1a46c6e551c47968daf962d824f79f795cb53585b098), fq(0x2fd03c4da47baf2dfd251e85d18864d4885ddd0e8df648550565b850b79349e3))
- C_plus_D = (fq(0x06f822cbde350215558c46aac9e60eee31afd942ca6da568845ca4f8fe911e17), fq(0x3e294e73970abc197dfff1a14e74cb20c11b81422d9f920c7b0b0c63affdf67b))
- result = add(C[0], C[1], D[0], D[1])
- print(result)
- print(list("%x" % x.n for x in result))
- assert result[0] == C_plus_D[0]
- assert result[1] == C_plus_D[1]
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