Write a proper implementation for base16 (#6909)

According to CONTRIBUTING.md:
"Algorithms in this repo should not be how-to examples for existing Python packages."

ciphers/base16.py

@@ -1,34 +1,63 @@
-import base64
-
-
-def base16_encode(inp: str) -> bytes:
+def base16_encode(data: bytes) -> str:
     """
-    Encodes a given utf-8 string into base-16.
+    Encodes the given bytes into base16.
 
-    >>> base16_encode('Hello World!')
-    b'48656C6C6F20576F726C6421'
-    >>> base16_encode('HELLO WORLD!')
-    b'48454C4C4F20574F524C4421'
-    >>> base16_encode('')
-    b''
-    """
-    # encode the input into a bytes-like object and then encode b16encode that
-    return base64.b16encode(inp.encode("utf-8"))
-
-
-def base16_decode(b16encoded: bytes) -> str:
-    """
-    Decodes from base-16 to a utf-8 string.
-
-    >>> base16_decode(b'48656C6C6F20576F726C6421')
-    'Hello World!'
-    >>> base16_decode(b'48454C4C4F20574F524C4421')
-    'HELLO WORLD!'
-    >>> base16_decode(b'')
+    >>> base16_encode(b'Hello World!')
+    '48656C6C6F20576F726C6421'
+    >>> base16_encode(b'HELLO WORLD!')
+    '48454C4C4F20574F524C4421'
+    >>> base16_encode(b'')
     ''
     """
-    # b16decode the input into bytes and decode that into a human readable string
-    return base64.b16decode(b16encoded).decode("utf-8")
+    # Turn the data into a list of integers (where each integer is a byte),
+    # Then turn each byte into its hexadecimal representation, make sure
+    # it is uppercase, and then join everything together and return it.
+    return "".join([hex(byte)[2:].zfill(2).upper() for byte in list(data)])
+
+
+def base16_decode(data: str) -> bytes:
+    """
+    Decodes the given base16 encoded data into bytes.
+
+    >>> base16_decode('48656C6C6F20576F726C6421')
+    b'Hello World!'
+    >>> base16_decode('48454C4C4F20574F524C4421')
+    b'HELLO WORLD!'
+    >>> base16_decode('')
+    b''
+    >>> base16_decode('486')
+    Traceback (most recent call last):
+      ...
+    ValueError: Base16 encoded data is invalid:
+    Data does not have an even number of hex digits.
+    >>> base16_decode('48656c6c6f20576f726c6421')
+    Traceback (most recent call last):
+      ...
+    ValueError: Base16 encoded data is invalid:
+    Data is not uppercase hex or it contains invalid characters.
+    >>> base16_decode('This is not base64 encoded data.')
+    Traceback (most recent call last):
+      ...
+    ValueError: Base16 encoded data is invalid:
+    Data is not uppercase hex or it contains invalid characters.
+    """
+    # Check data validity, following RFC3548
+    # https://www.ietf.org/rfc/rfc3548.txt
+    if (len(data) % 2) != 0:
+        raise ValueError(
+            """Base16 encoded data is invalid:
+Data does not have an even number of hex digits."""
+        )
+    # Check the character set - the standard base16 alphabet
+    # is uppercase according to RFC3548 section 6
+    if not set(data) <= set("0123456789ABCDEF"):
+        raise ValueError(
+            """Base16 encoded data is invalid:
+Data is not uppercase hex or it contains invalid characters."""
+        )
+    # For every two hexadecimal digits (= a byte), turn it into an integer.
+    # Then, string the result together into bytes, and return it.
+    return bytes(int(data[i] + data[i + 1], 16) for i in range(0, len(data), 2))
 
 
 if __name__ == "__main__":