We have a project that we have to implement AKS with input is a 128-bit-to-512-bit number (input is hexadecimal and I convert it into binary) in C++.
We can use C++ STL only. I would like to know if there are any binary operations or algorithms that I can refer to to complete this task?
I had tried to convert 512-bit number to int but then I realized it is impossible if using STL only. I have thought of checking whether the number is perfect power by making binary divisions by each number smaller than my input number but it takes too much time.
Depends on what is end purpose of using such a value, it's not necessary to treat it as integer. If it is, there are libraries which do that, but they store it internally as a static or dynamic array of bytes (and you can replicate that), and carry perations other byte by byte or in word-long blocks. A lot of vectorizing "magic" may happen there to achieve some sane performance.
If you need some universal storage, probably std::variant<uint64_t, std::string> or std::variant<uint64_t, std::vector< >> can be a basis. Just store the result of conversion in binary, byte by byte, which is really simple if input is hexadecimal - each pair of characters in input represent a byte of actual value (keeping a possibly omitted leading zero in mind). A conversion from a huge decimal representation into its binary representation would be trickier.