How to compute the hash of a JSON document?

You don’t need to serialize the document to a temporary buffer to compute its hash (e.g., CRC or MD5).
Instead, you can write a custom writer that will do that on the fly.

Here is a writer that uses the FastCRC library to compute the CRC32 of a JSON or MessagePack document:

#include <FastCRC.h>  // https://github.com/FrankBoesing/FastCRC

class CrcWriter {
public:
  CrcWriter() {
    _hash = _hasher.crc32(NULL, 0);
  }

  size_t write(uint8_t c) {
    _hash = _hasher.crc32_upd(&c, 1);
    return 1;
  }

  size_t write(const uint8_t *buffer, size_t length) {
    _hash = _hasher.crc32_upd(buffer, length);
    return length;
  }

  uint32_t hash() const {
    return _hash;
  }

private:
  FastCRC32 _hasher;
  uint32_t _hash;
};

Use this class like so:

CrcWriter writer;
serializeJson(doc, writer);
Serial.println(writer.hash());