app.rb

require 'openssl'
require 'base64'
require 'json'
require 'httpclient'

http = HTTPClient.new(:agent_name => useragent)
key = "" #The Private key
login_info = {:guid => "00000000-0000-0000-0000-000000000000,
                  :password => "PASSWORD", 
                  :username => "USERNAME", 
                  :device_id => "android-0000000000000000,
                  :_csrftoken => "missing"
                  }.to_json
signed_body = "#{Digest::HMAC.hexdigest(login_info, key, Digest::SHA256)}.#{login_info}"
post_data = {:signed_body => signed_body, :ig_sig_key_version => 4}
result = http.post("https://instagram.com/api/v1/accounts/login/", post_data, "Content-Type" => "application/json")
p result.body

logging_function.smali

const-string v5, "LOGGING"
invoke-static {v5, v0}, Landroid/util/Log;->d(Ljava/lang/String;Ljava/lang/String;)I