The Base64Decoder converts base 64 encoded data into binary data. The partner encoder is a Base64Encoder. The character set differs from a Base64URLEncoder by using the plus (+) and forward slash (/) characters. The alphabet is specified in RFC 4648, The Base16, Base32, and Base64 Data Encodings.
The Base64URLDecoder converts URL and safe filename encoded data into binary data. The class is helpful for web technologies, like JSON and JSON Web Keys (JWK). The partner encoder is a Base64URLEncoder. The character set differs from a Base64Encoder by using the minus (-) and underscore (_) characters.
The Base64Decoder takes a pointer to a BufferedTransformation. Because a pointer is taken, the Base64Decoder owns the attached transformation, and therefore will destroy it.
Base64 is a group of similar binary-to-text encoding schemes that represent binary data in an ASCII string format by translating it into a radix-64 representation. The term Base64 originates from a specific MIME content transfer encoding.
Each base64 digit needs exactly 6 bits of information to be represented.
Source : WikiPedia | Crypto++ Base64Decoder | Crypto++ Base64URLDecoder