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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS Template with Elliptic Curve Cryptography
# ==============================================================================
# This is a production-ready developer code asset for building micro-SaaS applications
# with FastAPI, Pydantic v2, and elliptic curve cryptography.

from fastapi import FastAPI, HTTPException
from pydantic import BaseModel
from cryptography.hazmat.primitives import serialization
from cryptography.hazmat.primitives.asymmetric import ec
from cryptography.hazmat.backends import default_backend

# Define the FastAPI application
app = FastAPI()

# Define a Pydantic model for elliptic curve cryptography
class EllipticCurve(BaseModel):
    """Elliptic Curve Cryptography model"""
    curve: str
    private_key: str
    public_key: str

# Generate a new elliptic curve key pair
def generate_key_pair(curve: str = "secp256r1") -> EllipticCurve:
    """Generate a new elliptic curve key pair"""
    private_key = ec.generate_private_key(ec.SECP256R1(), default_backend())
    public_key = private_key.public_key()
    private_key_pem = private_key.private_bytes(
        encoding=

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