Current stable way to login into the Instagram is to provide
enc_password parameter into the /login/ endpoint. Properly encrypted password can be decrypted only at Instagram because they use asymmetric encryption and no one except Instagram knows the Private key. That is why even your Internet provider can't get your password by just listening the traffic.To encrypt your password you would need the Instagram public key, random bytes, current timestamp and a lot of patience to properly combine all bytes into one base64 payload.
Some hints how can this be done on screenshot: