Certainly! Here's a simplified example of how you could implement authorization and authentication using FastAPI in Python:

```python
from fastapi import FastAPI, Depends, HTTPException
from fastapi.security import OAuth2PasswordBearer
from passlib.context import CryptContext
from pydantic import BaseModel
import jwt
import datetime

app = FastAPI()

# Configuration
SECRET_KEY = "mysecretkey"  # Replace with your own secret key
ALGORITHM = "HS256"  # JWT algorithm
ACCESS_TOKEN_EXPIRE_MINUTES = 30  # Access token expiration time in minutes

# Password hashing
pwd_context = CryptContext(schemes=["bcrypt"], deprecated="auto")

# OAuth2PasswordBearer for token retrieval from request headers
oauth2_scheme = OAuth2PasswordBearer(tokenUrl="token")

# User model
class User(BaseModel):
    username: str
    password: str

# Simulated database of users
users_db = {
    "user1": {
        "username": "user1",
        "password": pwd_context.hash("password1"),
    },
    "user2": {
        "username": "user2",
        "password": pwd_context.hash("password2"),
    },
}

# Function to verify password
def verify_password(plain_password, hashed_password):
    return pwd_context.verify(plain_password, hashed_password)

# Function to generate JWT token
def create_access_token(data: dict, expires_delta: datetime.timedelta):
    to_encode = data.copy()
    expire = datetime.datetime.utcnow() + expires_delta
    to_encode.update({"exp": expire})
    encoded_jwt = jwt.encode(to_encode, SECRET_KEY, algorithm=ALGORITHM)
    return encoded_jwt

# Function to decode JWT token
def decode_access_token(token: str):
    try:
        payload = jwt.decode(token, SECRET_KEY, algorithms=[ALGORITHM])
        return payload
    except jwt.ExpiredSignatureError:
        raise HTTPException(status_code=401, detail="Token has expired")
    except jwt.InvalidTokenError:
        raise HTTPException(status_code=401, detail="Invalid token")

# Route for user login
@app.post("/token")
async def login(user: User):
    if user.username not in users_db:
        raise HTTPException(status_code=401, detail="Invalid credentials")
    stored_user = users_db[user.username]
    if not verify_password(user.password, stored_user["password"]):
        raise HTTPException(status_code=401, detail="Invalid credentials")
    access_token = create_access_token(
        data={"sub": user.username},
        expires_delta=datetime.timedelta(minutes=ACCESS_TOKEN_EXPIRE_MINUTES)
    )
    return {"access_token": access_token, "token_type": "bearer"}

# Protected route
@app.get("/protected")
async def protected_route(token: str = Depends(oauth2_scheme)):
    payload = decode_access_token(token)
    username = payload["sub"]
    if username not in users_db:
        raise HTTPException(status_code=401, detail="Invalid credentials")
    return {"message": f"Welcome, {username}!"}
```

In this example, we're using FastAPI, Pydantic, passlib, and PyJWT to implement authorization and authentication. We define a User model, simulate a user database, and create routes for user login (/token) and a protected route (/protected). The verify_password function verifies the password hash, the create_access_token function generates a JWT token, and the decode_access_token function decodes and verifies the JWT token. The oauth2_scheme is used to retrieve the token from the request headers. Please note that this is a simplified example and may require further customization and security measures depending on your specific use case.
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