Merge branch 'master' of https://github.com/skalenetwork/sgxwallet

8f299292 · kladkogex · 71d4b2c2 · e2043c9f · 8f299292 · 8f299292
Unverified Commit 8f299292 authored Sep 17, 2019 by kladkogex
23 changed files
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -104,6 +104,8 @@ add_custom_target(sgxd COMMAND make all
        secure_enclave/secure_enclave.c
        secure_enclave/secure_enclave_t.c
        secure_enclave/secure_enclave_t.h
+        secure_enclave/DKGUtils.h
+        secure_enclave/DKGUtils.cpp
        create_enclave.c
        create_enclave.h
        oc_alloc.c

--- a/aclocal.m4
+++ b/aclocal.m4
-# generated automatically by aclocal 1.15.1 -*- Autoconf -*-
+# generated automatically by aclocal 1.16.1 -*- Autoconf -*-

-# Copyright (C) 1996-2017 Free Software Foundation, Inc.
+# Copyright (C) 1996-2018 Free Software Foundation, Inc.

 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -20,7 +20,7 @@ You have another version of autoconf.  It may work, but is not guaranteed to.
 If you have problems, you may need to regenerate the build system entirely.
 To do so, use the procedure documented by the package, typically 'autoreconf'.])])

-# Copyright (C) 2002-2017 Free Software Foundation, Inc.
+# Copyright (C) 2002-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -32,10 +32,10 @@ To do so, use the procedure documented by the package, typically 'autoreconf'.])
 # generated from the m4 files accompanying Automake X.Y.
 # (This private macro should not be called outside this file.)
 AC_DEFUN([AM_AUTOMAKE_VERSION],
-[am__api_version='1.15'
+[am__api_version='1.16'
 dnl Some users find AM_AUTOMAKE_VERSION and mistake it for a way to
 dnl require some minimum version.  Point them to the right macro.
-m4_if([$1], [1.15.1], [],
+m4_if([$1], [1.16.1], [],
      [AC_FATAL([Do not call $0, use AM_INIT_AUTOMAKE([$1]).])])dnl
 ])

@@ -51,14 +51,14 @@ m4_define([_AM_AUTOCONF_VERSION], [])
 # Call AM_AUTOMAKE_VERSION and AM_AUTOMAKE_VERSION so they can be traced.
 # This function is AC_REQUIREd by AM_INIT_AUTOMAKE.
 AC_DEFUN([AM_SET_CURRENT_AUTOMAKE_VERSION],
-[AM_AUTOMAKE_VERSION([1.15.1])dnl
+[AM_AUTOMAKE_VERSION([1.16.1])dnl
 m4_ifndef([AC_AUTOCONF_VERSION],
  [m4_copy([m4_PACKAGE_VERSION], [AC_AUTOCONF_VERSION])])dnl
 _AM_AUTOCONF_VERSION(m4_defn([AC_AUTOCONF_VERSION]))])

 # AM_AUX_DIR_EXPAND                                         -*- Autoconf -*-

-# Copyright (C) 2001-2017 Free Software Foundation, Inc.
+# Copyright (C) 2001-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -110,7 +110,7 @@ am_aux_dir=`cd "$ac_aux_dir" && pwd`

 # AM_COND_IF                                            -*- Autoconf -*-

-# Copyright (C) 2008-2017 Free Software Foundation, Inc.
+# Copyright (C) 2008-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -147,7 +147,7 @@ fi[]dnl

 # AM_CONDITIONAL                                            -*- Autoconf -*-

-# Copyright (C) 1997-2017 Free Software Foundation, Inc.
+# Copyright (C) 1997-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -178,7 +178,7 @@ AC_CONFIG_COMMANDS_PRE(
 Usually this means the macro was only invoked conditionally.]])
 fi])])

-# Copyright (C) 1999-2017 Free Software Foundation, Inc.
+# Copyright (C) 1999-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -369,13 +369,12 @@ _AM_SUBST_NOTMAKE([am__nodep])dnl

 # Generate code to set up dependency tracking.              -*- Autoconf -*-

-# Copyright (C) 1999-2017 Free Software Foundation, Inc.
+# Copyright (C) 1999-2018 Free Software Foundation, Inc.
 #
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 # gives unlimited permission to copy and/or distribute it,
 # with or without modifications, as long as this notice is preserved.

-
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@@ -383,49 +382,41 @@ AC_DEFUN([_AM_OUTPUT_DEPENDENCY_COMMANDS],
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  # are listed without --file.  Let's play safe and only enable the eval
  # if we detect the quoting.
-  case $CONFIG_FILES in
-  *\'*) eval set x "$CONFIG_FILES" ;;
-  *)   set x $CONFIG_FILES ;;
-  esac
+  # TODO: see whether this extra hack can be removed once we start
+  # requiring Autoconf 2.70 or later.
+  AS_CASE([$CONFIG_FILES],
+          [*\'*], [eval set x "$CONFIG_FILES"],
+          [*], [set x $CONFIG_FILES])
  shift
-  for mf
+  # Used to flag and report bootstrapping failures.
+  am_rc=0
+  for am_mf
  do
    # Strip MF so we end up with the name of the file.
-    mf=`echo "$mf" | sed -e 's/:.*$//'`
-    # Check whether this is an Automake generated Makefile or not.
-    # We used to match only the files named 'Makefile.in', but
-    # some people rename them; so instead we look at the file content.
-    # Grep'ing the first line is not enough: some people post-process
-    # each Makefile.in and add a new line on top of each file to say so.
-    # Grep'ing the whole file is not good either: AIX grep has a line
+    am_mf=`AS_ECHO(["$am_mf"]) | sed -e 's/:.*$//'`
+    # Check whether this is an Automake generated Makefile which includes
+    # dependency-tracking related rules and includes.
+    # Grep'ing the whole file directly is not great: AIX grep has a line
    # limit of 2048, but all sed's we know have understand at least 4000.
-    if sed -n 's,^#.*generated by automake.*,X,p' "$mf" | grep X >/dev/null 2>&1; then
-      dirpart=`AS_DIRNAME("$mf")`
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-    for file in `sed -n "
-      s/^$am__include $am__quote\(.*(DEPDIR).*\)$am__quote"'$/\1/p' <"$mf" | \
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-      # Make sure the directory exists.
-      test -f "$dirpart/$file" && continue
-      fdir=`AS_DIRNAME(["$file"])`
-      AS_MKDIR_P([$dirpart/$fdir])
-      # echo "creating $dirpart/$file"
-      echo '# dummy' > "$dirpart/$file"
-    done
+    sed -n 's,^am--depfiles:.*,X,p' "$am_mf" | grep X >/dev/null 2>&1 \
+      || continue
+    am_dirpart=`AS_DIRNAME(["$am_mf"])`
+    am_filepart=`AS_BASENAME(["$am_mf"])`
+    AM_RUN_LOG([cd "$am_dirpart" \
+      && sed -e '/# am--include-marker/d' "$am_filepart" \
+        | $MAKE -f - am--depfiles]) || am_rc=$?
  done
+  if test $am_rc -ne 0; then
+    AC_MSG_FAILURE([Something went wrong bootstrapping makefile fragments
+    for automatic dependency tracking.  Try re-running configure with the
+    '--disable-dependency-tracking' option to at least be able to build
+    the package (albeit without support for automatic dependency tracking).])
+  fi
+  AS_UNSET([am_dirpart])
+  AS_UNSET([am_filepart])
+  AS_UNSET([am_mf])
+  AS_UNSET([am_rc])
+  rm -f conftest-deps.mk
 }
 ])# _AM_OUTPUT_DEPENDENCY_COMMANDS

@@ -434,18 +425,17 @@ AC_DEFUN([_AM_OUTPUT_DEPENDENCY_COMMANDS],
 # -----------------------------
 # This macro should only be invoked once -- use via AC_REQUIRE.
 #
-# This code is only required when automatic dependency tracking
-# is enabled.  FIXME.  This creates each '.P' file that we will
-# need in order to bootstrap the dependency handling code.
+# This code is only required when automatic dependency tracking is enabled.
+# This creates each '.Po' and '.Plo' makefile fragment that we'll need in
+# order to bootstrap the dependency handling code.
 AC_DEFUN([AM_OUTPUT_DEPENDENCY_COMMANDS],
 [AC_CONFIG_COMMANDS([depfiles],
     [test x"$AMDEP_TRUE" != x"" || _AM_OUTPUT_DEPENDENCY_COMMANDS],
-     [AMDEP_TRUE="$AMDEP_TRUE" ac_aux_dir="$ac_aux_dir"])
-])
+     [AMDEP_TRUE="$AMDEP_TRUE" MAKE="${MAKE-make}"])])

 # Do all the work for Automake.                             -*- Autoconf -*-

-# Copyright (C) 1996-2017 Free Software Foundation, Inc.
+# Copyright (C) 1996-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -532,8 +522,8 @@ AC_REQUIRE([AM_PROG_INSTALL_STRIP])dnl
 AC_REQUIRE([AC_PROG_MKDIR_P])dnl
 # For better backward compatibility.  To be removed once Automake 1.9.x
 # dies out for good.  For more background, see:
-# <http://lists.gnu.org/archive/html/automake/2012-07/msg00001.html>
-# <http://lists.gnu.org/archive/html/automake/2012-07/msg00014.html>
+# <https://lists.gnu.org/archive/html/automake/2012-07/msg00001.html>
+# <https://lists.gnu.org/archive/html/automake/2012-07/msg00014.html>
 AC_SUBST([mkdir_p], ['$(MKDIR_P)'])
 # We need awk for the "check" target (and possibly the TAP driver).  The
 # system "awk" is bad on some platforms.
@@ -600,7 +590,7 @@ END
 Aborting the configuration process, to ensure you take notice of the issue.

 You can download and install GNU coreutils to get an 'rm' implementation
-that behaves properly: <http://www.gnu.org/software/coreutils/>.
+that behaves properly: <https://www.gnu.org/software/coreutils/>.

 If you want to complete the configuration process using your problematic
 'rm' anyway, export the environment variable ACCEPT_INFERIOR_RM_PROGRAM
@@ -642,7 +632,7 @@ for _am_header in $config_headers :; do
 done
 echo "timestamp for $_am_arg" >`AS_DIRNAME(["$_am_arg"])`/stamp-h[]$_am_stamp_count])

-# Copyright (C) 2001-2017 Free Software Foundation, Inc.
+# Copyright (C) 2001-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -663,7 +653,7 @@ if test x"${install_sh+set}" != xset; then
 fi
 AC_SUBST([install_sh])])

-# Copyright (C) 2003-2017 Free Software Foundation, Inc.
+# Copyright (C) 2003-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -684,7 +674,7 @@ AC_SUBST([am__leading_dot])])

 # Check to see how 'make' treats includes.	            -*- Autoconf -*-

-# Copyright (C) 2001-2017 Free Software Foundation, Inc.
+# Copyright (C) 2001-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -692,49 +682,42 @@ AC_SUBST([am__leading_dot])])

 # AM_MAKE_INCLUDE()
 # -----------------
-# Check to see how make treats includes.
+# Check whether make has an 'include' directive that can support all
+# the idioms we need for our automatic dependency tracking code.
 AC_DEFUN([AM_MAKE_INCLUDE],
-[am_make=${MAKE-make}
-cat > confinc << 'END'
+[AC_MSG_CHECKING([whether ${MAKE-make} supports the include directive])
+cat > confinc.mk << 'END'
 am__doit:
-	@echo this is the am__doit target
+	@echo this is the am__doit target >confinc.out
 .PHONY: am__doit
 END
-# If we don't find an include directive, just comment out the code.
-AC_MSG_CHECKING([for style of include used by $am_make])
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 am__quote=
-_am_result=none
-# First try GNU make style include.
-echo "include confinc" > confmf
-# Ignore all kinds of additional output from 'make'.
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-*the\ am__doit\ target*)
-  am__include=include
-  am__quote=
-  _am_result=GNU
-  ;;
-esac
-# Now try BSD make style include.
-if test "$am__include" = "#"; then
-   echo '.include "confinc"' > confmf
-   case `$am_make -s -f confmf 2> /dev/null` in #(
-   *the\ am__doit\ target*)
-     am__include=.include
-     am__quote="\""
-     _am_result=BSD
-     ;;
-   esac
-fi
-AC_SUBST([am__include])
-AC_SUBST([am__quote])
-AC_MSG_RESULT([$_am_result])
-rm -f confinc confmf
-])
+# BSD make does it like this.
+echo '.include "confinc.mk" # ignored' > confmf.BSD
+# Other make implementations (GNU, Solaris 10, AIX) do it like this.
+echo 'include confinc.mk # ignored' > confmf.GNU
+_am_result=no
+for s in GNU BSD; do
+  AM_RUN_LOG([${MAKE-make} -f confmf.$s && cat confinc.out])
+  AS_CASE([$?:`cat confinc.out 2>/dev/null`],
+      ['0:this is the am__doit target'],
+      [AS_CASE([$s],
+          [BSD], [am__include='.include' am__quote='"'],
+          [am__include='include' am__quote=''])])
+  if test "$am__include" != "#"; then
+    _am_result="yes ($s style)"
+    break
+  fi
+done
+rm -f confinc.* confmf.*
+AC_MSG_RESULT([${_am_result}])
+AC_SUBST([am__include])])
+AC_SUBST([am__quote])])

 # Fake the existence of programs that GNU maintainers use.  -*- Autoconf -*-

-# Copyright (C) 1997-2017 Free Software Foundation, Inc.
+# Copyright (C) 1997-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -773,7 +756,7 @@ fi

 # Helper functions for option handling.                     -*- Autoconf -*-

-# Copyright (C) 2001-2017 Free Software Foundation, Inc.
+# Copyright (C) 2001-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -802,7 +785,7 @@ AC_DEFUN([_AM_SET_OPTIONS],
 AC_DEFUN([_AM_IF_OPTION],
 [m4_ifset(_AM_MANGLE_OPTION([$1]), [$2], [$3])])

-# Copyright (C) 1999-2017 Free Software Foundation, Inc.
+# Copyright (C) 1999-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -849,7 +832,7 @@ AC_LANG_POP([C])])
 # For backward compatibility.
 AC_DEFUN_ONCE([AM_PROG_CC_C_O], [AC_REQUIRE([AC_PROG_CC])])

-# Copyright (C) 2001-2017 Free Software Foundation, Inc.
+# Copyright (C) 2001-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -868,7 +851,7 @@ AC_DEFUN([AM_RUN_LOG],

 # Check to make sure that the build environment is sane.    -*- Autoconf -*-

-# Copyright (C) 1996-2017 Free Software Foundation, Inc.
+# Copyright (C) 1996-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -949,7 +932,7 @@ AC_CONFIG_COMMANDS_PRE(
 rm -f conftest.file
 ])

-# Copyright (C) 2009-2017 Free Software Foundation, Inc.
+# Copyright (C) 2009-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -1009,7 +992,7 @@ AC_SUBST([AM_BACKSLASH])dnl
 _AM_SUBST_NOTMAKE([AM_BACKSLASH])dnl
 ])

-# Copyright (C) 2001-2017 Free Software Foundation, Inc.
+# Copyright (C) 2001-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -1037,7 +1020,7 @@ fi
 INSTALL_STRIP_PROGRAM="\$(install_sh) -c -s"
 AC_SUBST([INSTALL_STRIP_PROGRAM])])

-# Copyright (C) 2006-2017 Free Software Foundation, Inc.
+# Copyright (C) 2006-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,
@@ -1056,7 +1039,7 @@ AC_DEFUN([AM_SUBST_NOTMAKE], [_AM_SUBST_NOTMAKE($@)])

 # Check how to create a tarball.                            -*- Autoconf -*-

-# Copyright (C) 2004-2017 Free Software Foundation, Inc.
+# Copyright (C) 2004-2018 Free Software Foundation, Inc.
 #
 # This file is free software; the Free Software Foundation
 # gives unlimited permission to copy and/or distribute it,

--- a/compile
+++ b/compile
-/usr/share/automake-1.15/compile
\ No newline at end of file
+/usr/share/automake-1.16/compile
\ No newline at end of file
--- a/depcomp
+++ b/depcomp
-/usr/share/automake-1.15/depcomp
\ No newline at end of file
+/usr/share/automake-1.16/depcomp
\ No newline at end of file
--- a/install-sh
+++ b/install-sh
-/usr/share/automake-1.15/install-sh
\ No newline at end of file
+/usr/share/automake-1.16/install-sh
\ No newline at end of file
--- a/missing
+++ b/missing
-/usr/share/automake-1.15/missing
\ No newline at end of file
+/usr/share/automake-1.16/missing
\ No newline at end of file
--- a/secure_enclave/DKGUtils.cpp
+++ b/secure_enclave/DKGUtils.cpp
+//
+// Created by kladko on 9/5/19.
+//
+#include "DKGUtils.h"
+
+
+#include <../trusted_libff/libff/algebra/curves/alt_bn128/alt_bn128_pp.hpp>
+#include <../trusted_libff/libff/algebra/fields/fp.hpp>
+
+#include <../trusted_libff/libff/algebra/curves/alt_bn128/alt_bn128_g2.hpp>
+
+
+#include "../sgxwallet_common.h"
+#include <cstdio>
+#include <stdio.h>
+
+
+std::string stringFromFr(libff::alt_bn128_Fr& _el) {
+
+    mpz_t t;
+    mpz_init(t);
+
+    _el.as_bigint().to_mpz(t);
+
+    char arr[mpz_sizeinbase(t, 10) + 2];
+
+    char *tmp = mpz_get_str(arr, 10, t);
+    mpz_clear(t);
+
+    return std::string(tmp);
+}
+
+template<class T>
+std::string ConvertToString(T field_elem) {
+  mpz_t t;
+  mpz_init(t);
+
+  field_elem.as_bigint().to_mpz(t);
+
+  char arr[mpz_sizeinbase (t, 10) + 2];
+
+  char * tmp = mpz_get_str(arr, 10, t);
+  mpz_clear(t);
+
+  std::string output = tmp;
+
+  return output;
+}
+
+std::vector<libff::alt_bn128_Fr> SplitStringToFr(const char* koefs, const char* symbol){
+    std::string str(koefs);
+    std::string delim(symbol);
+    std::vector<libff::alt_bn128_Fr> tokens;
+    size_t prev = 0, pos = 0;
+    do
+    {
+        pos = str.find(delim, prev);
+        if (pos == std::string::npos) pos = str.length();
+        std::string token = str.substr(prev, pos-prev);
+        if (!token.empty()) {
+            libff::alt_bn128_Fr koef(token.c_str());
+            tokens.push_back(koef);
+        }
+        prev = pos + delim.length();
+    }
+    while (pos < str.length() && prev < str.length());
+
+    return tokens;
+}
+
+void gen_dkg_poly( char* secret/*[BUF_LEN]*/, unsigned _t ){
+    libff::init_alt_bn128_params();
+    std::string result;
+    for (size_t i = 0; i < _t; ++i) {
+        libff::alt_bn128_Fr cur_coef = libff::alt_bn128_Fr::random_element();
+
+        while (i == _t - 1 && cur_coef == libff::alt_bn128_Fr::zero()) {
+            cur_coef = libff::alt_bn128_Fr::random_element();
+        }
+       result += stringFromFr(cur_coef);
+       result += ":";
+    }
+    strncpy(secret, result.c_str(), result.length());
+}
+
+libff::alt_bn128_Fr PolynomialValue(const std::vector<libff::alt_bn128_Fr>& pol, libff::alt_bn128_Fr point, unsigned _t) {
+
+  libff::alt_bn128_Fr value = libff::alt_bn128_Fr::zero();
+
+  libff::alt_bn128_Fr pow = libff::alt_bn128_Fr::one();
+  for (size_t i = 0; i < _t; ++i) {
+    if (i == _t - 1 && pol[i] == libff::alt_bn128_Fr::zero()) {
+      throw std::runtime_error("Error, incorrect degree of a polynomial");
+    }
+    value += pol[i] * pow;
+    pow *= point;
+  }
+
+  return value;
+}
+
+void calc_secret_shares(const char* decrypted_koefs, char * secret_shares,
+    unsigned _t, unsigned _n) {
+  // calculate for each node a list of secret values that will be used for verification
+  std::string result;
+  char symbol = ':';
+  std::vector<libff::alt_bn128_Fr> poly =  SplitStringToFr(decrypted_koefs, &symbol);
+  for (size_t i = 0; i < _n; ++i) {
+    libff::alt_bn128_Fr secret_share = PolynomialValue(poly, libff::alt_bn128_Fr(i + 1), _t);
+    result += stringFromFr(secret_share);
+    result += ":";
+  }
+  strncpy(secret_shares, result.c_str(), result.length());
+}
+
+void calc_public_shares(const char* decrypted_koefs, char * public_shares,
+                        unsigned _t) {
+  // calculate for each node a list of public shares
+  std::string result;
+  char symbol = ':';
+  std::vector<libff::alt_bn128_Fr> poly =  SplitStringToFr(decrypted_koefs, &symbol);
+  for (size_t i = 0; i < _t; ++i) {
+    libff::alt_bn128_G2 pub_share =  poly.at(i) * libff::alt_bn128_G2::one();
+    pub_share.to_affine_coordinates();
+    result += ConvertToString(pub_share.X.c0);
+    result += ":";
+    result += ConvertToString(pub_share.X.c1);
+    result += ":";
+    result += ConvertToString(pub_share.Y.c0);
+    result += ":";
+    result += ConvertToString(pub_share.Y.c1);
+    result += ",";
+  }
+  strncpy(public_shares, result.c_str(), result.length());
+}
+
+
--- a/secure_enclave/DKGUtils.h
+++ b/secure_enclave/DKGUtils.h
+//
+// Created by kladko on 9/5/19.
+//
+
+#ifndef SGXD_DKGUTILS_H
+#define SGXD_DKGUTILS_H
+
+#ifdef __cplusplus
+#define EXTERNC extern "C"
+#else
+#define EXTERNC
+#endif
+
+EXTERNC void gen_dkg_poly( char* secret, unsigned _t);
+
+EXTERNC void calc_secret_shares(const char* decrypted_koefs, char * secret_shares,
+                        unsigned _t, unsigned _n);
+EXTERNC void calc_public_shares(const char* decrypted_koefs, char * public_shares,
+                        unsigned _t);
+#endif //SGXD_DKGUTILS_H
+
--- a/secure_enclave/Makefile.am
+++ b/secure_enclave/Makefile.am
@@ -85,7 +85,8 @@ CLEANFILES+= secure_enclave_t.c secure_enclave_t.h

 secure_enclave_SOURCES = secure_enclave_t.c secure_enclave_t.h \
 	secure_enclave.c \
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+	@echo "Creating default enclave configuration file:"
+	@echo "$(ENCLAVE_CFG)"
+	@echo "<EnclaveConfiguration>">$(ENCLAVE).config.xml
+	@echo " <ProdID>0</ProdID>">>$(ENCLAVE).config.xml
+	@echo " <ISVSVN>0</ISVSVN>">>$(ENCLAVE).config.xml
+	@echo " <StackMaxSize>0x40000</StackMaxSize>">>$(ENCLAVE).config.xml
+	@echo " <HeapMaxSize>0x100000</HeapMaxSize>">>$(ENCLAVE).config.xml
+	@echo " <TCSNum>1</TCSNum>">>$(ENCLAVE).config.xml
+	@echo " <TCSPolicy>1</TCSPolicy>">>$(ENCLAVE).config.xml
+	@echo " <!-- Recommend changing 'DisableDebug' to 1 to make the enclave undebuggable for enclave release -->">>$(ENCLAVE).config.xml
+	@echo " <DisableDebug>0</DisableDebug>">>$(ENCLAVE).config.xml
+	@echo " <MiscSelect>0</MiscSelect>">>$(ENCLAVE).config.xml
+	@echo " <MiscMask>0xFFFFFFFF</MiscMask>">>$(ENCLAVE).config.xml
+	@echo " </EnclaveConfiguration>">>$(ENCLAVE).config.xml
+	@echo ""
+
+# Tell versions [3.59,3.63) of GNU make to not export all variables.
+# Otherwise a system limit (for SysV at least) may be exceeded.
+.NOEXPORT:
--- a/secure_enclave/secure_enclave.c
+++ b/secure_enclave/secure_enclave.c
@@ -339,3 +339,47 @@ void ecdsa_sign_message(int *err_status, char *err_string, uint8_t *encrypted_ke
    *err_status = 0;

 }
+
+void gen_dkg_secret (int *err_status, char *err_string, uint8_t *encrypted_dkg_secret, uint32_t* enc_len, size_t _t){
+
+  char* dkg_secret = (char*)malloc(DKG_BUFER_LENGTH);
+
+  gen_dkg_poly(dkg_secret, _t);
+
+  uint32_t sealedLen = sgx_calc_sealed_data_size(0, DKG_BUFER_LENGTH);//sizeof(sgx_sealed_data_t) +  sizeof(dkg_secret);
+
+  sgx_status_t status = sgx_seal_data(0, NULL, DKG_BUFER_LENGTH, (uint8_t*)dkg_secret, sealedLen,(sgx_sealed_data_t*)encrypted_dkg_secret);
+
+  if(  status !=  SGX_SUCCESS) {
+    snprintf(err_string, BUF_LEN,"SGX seal data failed");
+  }
+
+  *enc_len = sealedLen;
+}
+
+void decrypt_dkg_secret (int *err_status, char* err_string, uint8_t* encrypted_dkg_secret, uint8_t* decrypted_dkg_secret, uint32_t enc_len){
+
+  //uint32_t dec_size = DKG_BUFER_LENGTH;//sgx_get_encrypt_txt_len( ( sgx_sealed_data_t *)encrypted_dkg_secret);
+
+  sgx_status_t status = sgx_unseal_data(
+      (const sgx_sealed_data_t *)encrypted_dkg_secret, NULL, 0, decrypted_dkg_secret, &enc_len);
+
+  if (status != SGX_SUCCESS) {
+    snprintf(err_string, BUF_LEN,"sgx_unseal_data failed with status %d", status);
+    return;
+  }
+}
+
+void get_secret_shares(int *err_status, char* err_string, uint8_t* encrypted_dkg_secret, uint32_t enc_len, char* secret_shares,
+    unsigned _t, unsigned _n){
+  char* decrypted_dkg_secret = (char*)malloc(DKG_MAX_SEALED_LEN);
+  decrypt_dkg_secret(err_status, err_string, (uint8_t*)encrypted_dkg_secret, decrypted_dkg_secret, enc_len);
+  calc_secret_shares(decrypted_dkg_secret, secret_shares, _t, _n);
+}
+
+void get_public_shares(int *err_status, char* err_string, uint8_t* encrypted_dkg_secret, uint32_t enc_len, char* public_shares,
+                       unsigned _t, unsigned _n){
+    char* decrypted_dkg_secret = (char*)malloc(DKG_MAX_SEALED_LEN);
+    decrypt_dkg_secret(err_status, err_string, (uint8_t*)encrypted_dkg_secret, decrypted_dkg_secret, enc_len);
+    calc_public_shares(decrypted_dkg_secret, public_shares, _t);
+}
--- a/secure_enclave/secure_enclave.edl
+++ b/secure_enclave/secure_enclave.edl
@@ -58,6 +58,38 @@ from "sgx_tsgxssl.edl" import *;
            		    uint32_t enc_len,
            		    [in, count = 1024] uint8_t* hash,
            		    [out, count = 1024] char* signature);
+
+        public void gen_dkg_secret (
+                    	[user_check] int *err_status,
+                    	[out, count = 1024] char* err_string,
+                    	[out, count = 2000] uint8_t* encrypted_dkg_secret,
+                    	[user_check] uint32_t * enc_len,
+                    	size_t _t);
+
+        public void decrypt_dkg_secret (
+                            	[user_check] int *err_status,
+                            	[out, count = 1024] char* err_string,
+                            	[in, count = 2000] uint8_t* encrypted_dkg_secret,
+                            	[out, count = 2000] uint8_t* decrypted_dkg_secret,
+                            	uint32_t enc_len);
+
+        public void get_secret_shares (
+                                [user_check] int *err_status,
+                                [out, count = 1024] char* err_string,
+                                [in, count = 2000] uint8_t* decrypted_dkg_secret,
+                                uint32_t enc_len,
+                                [out, count = 2000] char* secret_shares,
+                                unsigned _t,
+                                unsigned _n);
+
+         public void get_public_shares (
+                                [user_check] int *err_status,
+                                [out, count = 1024] char* err_string,
+                                [in, count = 2000] uint8_t* decrypted_dkg_secret,
+                                uint32_t enc_len,
+                                [out, count = 4000] char* public_shares,
+                                unsigned _t,
+                                unsigned _n);
 	};



--- a/sgxwallet.c
+++ b/sgxwallet.c
@@ -44,7 +44,6 @@ void usage() {
 }

 sgx_launch_token_t token = {0};
-
 sgx_enclave_id_t eid;
 sgx_status_t status;
 int updated;

--- a/sgxwallet_common.h
+++ b/sgxwallet_common.h
@@ -2,8 +2,8 @@
 // Created by kladko on 9/3/19.
 //

-#ifndef SGXWALLET_SGXWALLET_COMMON_H
-#define SGXWALLET_SGXWALLET_COMMON_H
+#ifndef SGXD_SGXD_COMMON_H
+#define SGXD_SGXD_COMMON_H

 #include <stdio.h>
 #include <stdlib.h>
@@ -26,6 +26,8 @@

 #define ADD_ENTROPY_SIZE 32

+#define  DKG_BUFER_LENGTH 1250
+#define  DKG_MAX_SEALED_LEN 2000

 #define UNKNOWN_ERROR -1
 #define PLAINTEXT_KEY_TOO_LONG -2

--- a/testw.cpp
+++ b/testw.cpp
@@ -55,6 +55,22 @@ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

 #include "catch.hpp"

+std::string stringFromFr(libff::alt_bn128_Fr& el) {
+
+    mpz_t t;
+    mpz_init(t);
+
+    el.as_bigint().to_mpz(t);
+
+    char arr[mpz_sizeinbase(t, 10) + 2];
+
+    char *tmp = mpz_get_str(arr, 10, t);
+    mpz_clear(t);
+
+    return std::string(tmp);
+}
+
+
 void usage() {
    fprintf(stderr, "usage: sgxwallet\n");
    exit(1);
@@ -233,10 +249,103 @@ TEST_CASE("KeysDB test", "[keys-db]") {



-TEST_CASE("DKG gen test", "[dkg-gen]") {
+TEST_CASE( "DKG gen test", "[dkg-gen]" ) {

-    init_all();
+  init_all();

-// put your test here
+  uint8_t* encrypted_dkg_secret = (uint8_t*) calloc(DKG_MAX_SEALED_LEN, 1);
+
+  char* errMsg = (char*) calloc(1024,1);
+  int err_status = 0;
+  uint32_t enc_len = 0;
+
+  status = gen_dkg_secret (eid, &err_status, errMsg, encrypted_dkg_secret, &enc_len, 16);
+  REQUIRE(status == SGX_SUCCESS);
+  printf("gen_dkg_secret completed with status: %d %s \n", err_status, errMsg);
+  printf("\n Length: %d \n", enc_len);
+
+  char* secret = (char*)calloc(DKG_MAX_SEALED_LEN, sizeof(char));
+
+  char* errMsg1 = (char*) calloc(1024,1);
+
+  status = decrypt_dkg_secret(eid, &err_status, errMsg1, encrypted_dkg_secret, (uint8_t*)secret, enc_len);
+  REQUIRE(status == SGX_SUCCESS);
+
+  printf("\ndecrypt_dkg_secret completed with status: %d %s \n", err_status, errMsg1);
+  printf("decrypted secret %s \n\n", secret);
+
+  free(errMsg);
+  free(errMsg1);
+  free(encrypted_dkg_secret);
+  free(secret);
 }

+std::vector<libff::alt_bn128_Fr> SplitStringToFr(const char* koefs, const char* symbol){
+  std::string str(koefs);
+  std::string delim(symbol);
+  std::vector<libff::alt_bn128_Fr> tokens;
+  size_t prev = 0, pos = 0;
+  do
+  {
+    pos = str.find(delim, prev);
+    if (pos == std::string::npos) pos = str.length();
+    std::string token = str.substr(prev, pos-prev);
+    if (!token.empty()) {
+      libff::alt_bn128_Fr koef(token.c_str());
+      tokens.push_back(koef);
+    }
+    prev = pos + delim.length();
+  }
+  while (pos < str.length() && prev < str.length());
+
+  return tokens;
+}
+
+TEST_CASE( "DKG auto secret shares test", "[dkg-s_shares]" ) {
+
+  init_all();
+
+  uint8_t* encrypted_dkg_secret = (uint8_t*) calloc(DKG_MAX_SEALED_LEN, 1);
+
+  char* errMsg = (char*) calloc(1024,1);
+  int err_status = 0;
+  uint32_t enc_len = 0;
+
+  unsigned t = 3, n = 4;
+
+  status = gen_dkg_secret (eid, &err_status, errMsg, encrypted_dkg_secret, &enc_len, 3);
+  REQUIRE(status == SGX_SUCCESS);
+  printf("gen_dkg_secret completed with status: %d %s \n", err_status, errMsg);
+  printf("\n Length: %d \n", enc_len);
+
+
+  char* errMsg1 = (char*) calloc(1024,1);
+
+  char colon = ':';
+  char* secret_shares = (char*)calloc(DKG_MAX_SEALED_LEN, sizeof(char));
+  status = get_secret_shares(eid, &err_status, errMsg1, encrypted_dkg_secret, enc_len, secret_shares, t, n);
+  REQUIRE(status == SGX_SUCCESS);
+  printf("\nget_secret_shares: %d %s \n", err_status, errMsg1);
+  printf("secret shares %s \n\n", secret_shares);
+
+  std::vector <libff::alt_bn128_Fr> s_shares = SplitStringToFr( secret_shares, &colon);
+
+  char* secret = (char*)calloc(DKG_MAX_SEALED_LEN, sizeof(char));
+  status = decrypt_dkg_secret(eid, &err_status, errMsg1, encrypted_dkg_secret, (uint8_t*)secret, enc_len);
+  REQUIRE(status == SGX_SUCCESS);
+  printf("\ndecrypt_dkg_secret completed with status: %d %s \n", err_status, errMsg1);
+  printf("decrypted secret %s \n\n", secret);
+
+  signatures::Dkg dkg_obj(t,n);
+
+  std::vector < libff::alt_bn128_Fr> poly = SplitStringToFr((char*)secret, &colon);
+  std::vector < libff::alt_bn128_Fr> s_shares_dkg = dkg_obj.SecretKeyContribution(SplitStringToFr((char*)secret, &colon));
+
+  REQUIRE(s_shares == s_shares_dkg);
+
+  free(errMsg);
+  free(errMsg1);
+  free(encrypted_dkg_secret);
+  free(secret_shares);
+
+}
--- a/trusted_libff/libff/algebra/curves/alt_bn128/alt_bn128_g2.cpp
+++ b/trusted_libff/libff/algebra/curves/alt_bn128/alt_bn128_g2.cpp
+/** @file
+ *****************************************************************************
+ * @author     This file is part of libff, developed by SCIPR Lab
+ *             and contributors (see AUTHORS).
+ * @copyright  MIT license (see LICENSE file)
+ *****************************************************************************/
+
+#include <libff/algebra/curves/alt_bn128/alt_bn128_g2.hpp>
+
+namespace libff {
+
+#ifdef PROFILE_OP_COUNTS
+long long alt_bn128_G2::add_cnt = 0;
+long long alt_bn128_G2::dbl_cnt = 0;
+#endif
+
+std::vector<size_t> alt_bn128_G2::wnaf_window_table;
+std::vector<size_t> alt_bn128_G2::fixed_base_exp_window_table;
+alt_bn128_G2 alt_bn128_G2::G2_zero;
+alt_bn128_G2 alt_bn128_G2::G2_one;
+
+alt_bn128_G2::alt_bn128_G2()
+{
+    this->X = G2_zero.X;
+    this->Y = G2_zero.Y;
+    this->Z = G2_zero.Z;
+}
+
+alt_bn128_Fq2 alt_bn128_G2::mul_by_b(const alt_bn128_Fq2 &elt)
+{
+    return alt_bn128_Fq2(alt_bn128_twist_mul_by_b_c0 * elt.c0, alt_bn128_twist_mul_by_b_c1 * elt.c1);
+}
+
+/*void alt_bn128_G2::print() const
+{
+    if (this->is_zero())
+    {
+        printf("O\n");
+    }
+    else
+    {
+        alt_bn128_G2 copy(*this);
+        copy.to_affine_coordinates();
+        gmp_printf("(%Nd*z + %Nd , %Nd*z + %Nd)\n",
+                   copy.X.c1.as_bigint().data, alt_bn128_Fq::num_limbs,
+                   copy.X.c0.as_bigint().data, alt_bn128_Fq::num_limbs,
+                   copy.Y.c1.as_bigint().data, alt_bn128_Fq::num_limbs,
+                   copy.Y.c0.as_bigint().data, alt_bn128_Fq::num_limbs);
+    }
+}
+
+void alt_bn128_G2::print_coordinates() const
+{
+    if (this->is_zero())
+    {
+        printf("O\n");
+    }
+    else
+    {
+        gmp_printf("(%Nd*z + %Nd : %Nd*z + %Nd : %Nd*z + %Nd)\n",
+                   this->X.c1.as_bigint().data, alt_bn128_Fq::num_limbs,
+                   this->X.c0.as_bigint().data, alt_bn128_Fq::num_limbs,
+                   this->Y.c1.as_bigint().data, alt_bn128_Fq::num_limbs,
+                   this->Y.c0.as_bigint().data, alt_bn128_Fq::num_limbs,
+                   this->Z.c1.as_bigint().data, alt_bn128_Fq::num_limbs,
+                   this->Z.c0.as_bigint().data, alt_bn128_Fq::num_limbs);
+    }
+}*/
+
+void alt_bn128_G2::to_affine_coordinates()
+{
+    if (this->is_zero())
+    {
+        this->X = alt_bn128_Fq2::zero();
+        this->Y = alt_bn128_Fq2::one();
+        this->Z = alt_bn128_Fq2::zero();
+    }
+    else
+    {
+        alt_bn128_Fq2 Z_inv = Z.inverse();
+        alt_bn128_Fq2 Z2_inv = Z_inv.squared();
+        alt_bn128_Fq2 Z3_inv = Z2_inv * Z_inv;
+        this->X = this->X * Z2_inv;
+        this->Y = this->Y * Z3_inv;
+        this->Z = alt_bn128_Fq2::one();
+    }
+}
+
+void alt_bn128_G2::to_special()
+{
+    this->to_affine_coordinates();
+}
+
+bool alt_bn128_G2::is_special() const
+{
+    return (this->is_zero() || this->Z == alt_bn128_Fq2::one());
+}
+
+bool alt_bn128_G2::is_zero() const
+{
+    return (this->Z.is_zero());
+}
+
+bool alt_bn128_G2::operator==(const alt_bn128_G2 &other) const
+{
+    if (this->is_zero())
+    {
+        return other.is_zero();
+    }
+
+    if (other.is_zero())
+    {
+        return false;
+    }
+
+    /* now neither is O */
+
+    // using Jacobian coordinates so:
+    // (X1:Y1:Z1) = (X2:Y2:Z2)
+    // iff
+    // X1/Z1^2 == X2/Z2^2 and Y1/Z1^3 == Y2/Z2^3
+    // iff
+    // X1 * Z2^2 == X2 * Z1^2 and Y1 * Z2^3 == Y2 * Z1^3
+
+    alt_bn128_Fq2 Z1_squared = (this->Z).squared();
+    alt_bn128_Fq2 Z2_squared = (other.Z).squared();
+
+    if ((this->X * Z2_squared) != (other.X * Z1_squared))
+    {
+        return false;
+    }
+
+    alt_bn128_Fq2 Z1_cubed = (this->Z) * Z1_squared;
+    alt_bn128_Fq2 Z2_cubed = (other.Z) * Z2_squared;
+
+    if ((this->Y * Z2_cubed) != (other.Y * Z1_cubed))
+    {
+        return false;
+    }
+
+    return true;
+}
+
+bool alt_bn128_G2::operator!=(const alt_bn128_G2& other) const
+{
+    return !(operator==(other));
+}
+
+alt_bn128_G2 alt_bn128_G2::operator+(const alt_bn128_G2 &other) const
+{
+    // handle special cases having to do with O
+    if (this->is_zero())
+    {
+        return other;
+    }
+
+    if (other.is_zero())
+    {
+        return *this;
+    }
+
+    // no need to handle points of order 2,4
+    // (they cannot exist in a prime-order subgroup)
+
+    // check for doubling case
+
+    // using Jacobian coordinates so:
+    // (X1:Y1:Z1) = (X2:Y2:Z2)
+    // iff
+    // X1/Z1^2 == X2/Z2^2 and Y1/Z1^3 == Y2/Z2^3
+    // iff
+    // X1 * Z2^2 == X2 * Z1^2 and Y1 * Z2^3 == Y2 * Z1^3
+
+    alt_bn128_Fq2 Z1Z1 = (this->Z).squared();
+    alt_bn128_Fq2 Z2Z2 = (other.Z).squared();
+
+    alt_bn128_Fq2 U1 = this->X * Z2Z2;
+    alt_bn128_Fq2 U2 = other.X * Z1Z1;
+
+    alt_bn128_Fq2 Z1_cubed = (this->Z) * Z1Z1;
+    alt_bn128_Fq2 Z2_cubed = (other.Z) * Z2Z2;
+
+    alt_bn128_Fq2 S1 = (this->Y) * Z2_cubed;      // S1 = Y1 * Z2 * Z2Z2
+    alt_bn128_Fq2 S2 = (other.Y) * Z1_cubed;      // S2 = Y2 * Z1 * Z1Z1
+
+    if (U1 == U2 && S1 == S2)
+    {
+        // dbl case; nothing of above can be reused
+        return this->dbl();
+    }
+
+    // rest of add case
+    alt_bn128_Fq2 H = U2 - U1;                            // H = U2-U1
+    alt_bn128_Fq2 S2_minus_S1 = S2-S1;
+    alt_bn128_Fq2 I = (H+H).squared();                    // I = (2 * H)^2
+    alt_bn128_Fq2 J = H * I;                              // J = H * I
+    alt_bn128_Fq2 r = S2_minus_S1 + S2_minus_S1;          // r = 2 * (S2-S1)
+    alt_bn128_Fq2 V = U1 * I;                             // V = U1 * I
+    alt_bn128_Fq2 X3 = r.squared() - J - (V+V);           // X3 = r^2 - J - 2 * V
+    alt_bn128_Fq2 S1_J = S1 * J;
+    alt_bn128_Fq2 Y3 = r * (V-X3) - (S1_J+S1_J);          // Y3 = r * (V-X3)-2 S1 J
+    alt_bn128_Fq2 Z3 = ((this->Z+other.Z).squared()-Z1Z1-Z2Z2) * H; // Z3 = ((Z1+Z2)^2-Z1Z1-Z2Z2) * H
+
+    return alt_bn128_G2(X3, Y3, Z3);
+}
+
+alt_bn128_G2 alt_bn128_G2::operator-() const
+{
+    return alt_bn128_G2(this->X, -(this->Y), this->Z);
+}
+
+
+alt_bn128_G2 alt_bn128_G2::operator-(const alt_bn128_G2 &other) const
+{
+    return (*this) + (-other);
+}
+
+alt_bn128_G2 alt_bn128_G2::add(const alt_bn128_G2 &other) const
+{
+    // handle special cases having to do with O
+    if (this->is_zero())
+    {
+        return other;
+    }
+
+    if (other.is_zero())
+    {
+        return *this;
+    }
+
+    // no need to handle points of order 2,4
+    // (they cannot exist in a prime-order subgroup)
+
+    // handle double case
+    if (this->operator==(other))
+    {
+        return this->dbl();
+    }
+
+#ifdef PROFILE_OP_COUNTS
+    this->add_cnt++;
+#endif
+    // NOTE: does not handle O and pts of order 2,4
+    // http://www.hyperelliptic.org/EFD/g1p/auto-shortw-projective.html#addition-add-1998-cmo-2
+
+    alt_bn128_Fq2 Z1Z1 = (this->Z).squared();             // Z1Z1 = Z1^2
+    alt_bn128_Fq2 Z2Z2 = (other.Z).squared();             // Z2Z2 = Z2^2
+    alt_bn128_Fq2 U1 = (this->X) * Z2Z2;                  // U1 = X1 * Z2Z2
+    alt_bn128_Fq2 U2 = (other.X) * Z1Z1;                  // U2 = X2 * Z1Z1
+    alt_bn128_Fq2 S1 = (this->Y) * (other.Z) * Z2Z2;      // S1 = Y1 * Z2 * Z2Z2
+    alt_bn128_Fq2 S2 = (other.Y) * (this->Z) * Z1Z1;      // S2 = Y2 * Z1 * Z1Z1
+    alt_bn128_Fq2 H = U2 - U1;                            // H = U2-U1
+    alt_bn128_Fq2 S2_minus_S1 = S2-S1;
+    alt_bn128_Fq2 I = (H+H).squared();                    // I = (2 * H)^2
+    alt_bn128_Fq2 J = H * I;                              // J = H * I
+    alt_bn128_Fq2 r = S2_minus_S1 + S2_minus_S1;          // r = 2 * (S2-S1)
+    alt_bn128_Fq2 V = U1 * I;                             // V = U1 * I
+    alt_bn128_Fq2 X3 = r.squared() - J - (V+V);           // X3 = r^2 - J - 2 * V
+    alt_bn128_Fq2 S1_J = S1 * J;
+    alt_bn128_Fq2 Y3 = r * (V-X3) - (S1_J+S1_J);          // Y3 = r * (V-X3)-2 S1 J
+    alt_bn128_Fq2 Z3 = ((this->Z+other.Z).squared()-Z1Z1-Z2Z2) * H; // Z3 = ((Z1+Z2)^2-Z1Z1-Z2Z2) * H
+
+    return alt_bn128_G2(X3, Y3, Z3);
+}
+
+alt_bn128_G2 alt_bn128_G2::mixed_add(const alt_bn128_G2 &other) const
+{
+#ifdef DEBUG
+    assert(other.is_special());
+#endif
+
+    // handle special cases having to do with O
+    if (this->is_zero())
+    {
+        return other;
+    }
+
+    if (other.is_zero())
+    {
+        return *this;
+    }
+
+    // no need to handle points of order 2,4
+    // (they cannot exist in a prime-order subgroup)
+
+    // check for doubling case
+
+    // using Jacobian coordinates so:
+    // (X1:Y1:Z1) = (X2:Y2:Z2)
+    // iff
+    // X1/Z1^2 == X2/Z2^2 and Y1/Z1^3 == Y2/Z2^3
+    // iff
+    // X1 * Z2^2 == X2 * Z1^2 and Y1 * Z2^3 == Y2 * Z1^3
+
+    // we know that Z2 = 1
+
+    const alt_bn128_Fq2 Z1Z1 = (this->Z).squared();
+
+    const alt_bn128_Fq2 &U1 = this->X;
+    const alt_bn128_Fq2 U2 = other.X * Z1Z1;
+
+    const alt_bn128_Fq2 Z1_cubed = (this->Z) * Z1Z1;
+
+    const alt_bn128_Fq2 &S1 = (this->Y);                // S1 = Y1 * Z2 * Z2Z2
+    const alt_bn128_Fq2 S2 = (other.Y) * Z1_cubed;      // S2 = Y2 * Z1 * Z1Z1
+
+    if (U1 == U2 && S1 == S2)
+    {
+        // dbl case; nothing of above can be reused
+        return this->dbl();
+    }
+
+#ifdef PROFILE_OP_COUNTS
+    this->add_cnt++;
+#endif
+
+    // NOTE: does not handle O and pts of order 2,4
+    // http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-madd-2007-bl
+    alt_bn128_Fq2 H = U2-(this->X);                         // H = U2-X1
+    alt_bn128_Fq2 HH = H.squared() ;                        // HH = H&2
+    alt_bn128_Fq2 I = HH+HH;                                // I = 4*HH
+    I = I + I;
+    alt_bn128_Fq2 J = H*I;                                  // J = H*I
+    alt_bn128_Fq2 r = S2-(this->Y);                         // r = 2*(S2-Y1)
+    r = r + r;
+    alt_bn128_Fq2 V = (this->X) * I ;                       // V = X1*I
+    alt_bn128_Fq2 X3 = r.squared()-J-V-V;                   // X3 = r^2-J-2*V
+    alt_bn128_Fq2 Y3 = (this->Y)*J;                         // Y3 = r*(V-X3)-2*Y1*J
+    Y3 = r*(V-X3) - Y3 - Y3;
+    alt_bn128_Fq2 Z3 = ((this->Z)+H).squared() - Z1Z1 - HH; // Z3 = (Z1+H)^2-Z1Z1-HH
+
+    return alt_bn128_G2(X3, Y3, Z3);
+}
+
+alt_bn128_G2 alt_bn128_G2::dbl() const
+{
+#ifdef PROFILE_OP_COUNTS
+    this->dbl_cnt++;
+#endif
+    // handle point at infinity
+    if (this->is_zero())
+    {
+        return (*this);
+    }
+
+    // NOTE: does not handle O and pts of order 2,4
+    // http://www.hyperelliptic.org/EFD/g1p/auto-shortw-projective.html#doubling-dbl-2007-bl
+
+    alt_bn128_Fq2 A = (this->X).squared();         // A = X1^2
+    alt_bn128_Fq2 B = (this->Y).squared();        // B = Y1^2
+    alt_bn128_Fq2 C = B.squared();                // C = B^2
+    alt_bn128_Fq2 D = (this->X + B).squared() - A - C;
+    D = D+D;                        // D = 2 * ((X1 + B)^2 - A - C)
+    alt_bn128_Fq2 E = A + A + A;                  // E = 3 * A
+    alt_bn128_Fq2 F = E.squared();                // F = E^2
+    alt_bn128_Fq2 X3 = F - (D+D);                 // X3 = F - 2 D
+    alt_bn128_Fq2 eightC = C+C;
+    eightC = eightC + eightC;
+    eightC = eightC + eightC;
+    alt_bn128_Fq2 Y3 = E * (D - X3) - eightC;     // Y3 = E * (D - X3) - 8 * C
+    alt_bn128_Fq2 Y1Z1 = (this->Y)*(this->Z);
+    alt_bn128_Fq2 Z3 = Y1Z1 + Y1Z1;               // Z3 = 2 * Y1 * Z1
+
+    return alt_bn128_G2(X3, Y3, Z3);
+}
+
+alt_bn128_G2 alt_bn128_G2::mul_by_q() const
+{
+    return alt_bn128_G2(alt_bn128_twist_mul_by_q_X * (this->X).Frobenius_map(1),
+                      alt_bn128_twist_mul_by_q_Y * (this->Y).Frobenius_map(1),
+                      (this->Z).Frobenius_map(1));
+}
+
+bool alt_bn128_G2::is_well_formed() const
+{
+    if (this->is_zero())
+    {
+        return true;
+    }
+    else
+    {
+        /*
+          y^2 = x^3 + b
+
+          We are using Jacobian coordinates, so equation we need to check is actually
+
+          (y/z^3)^2 = (x/z^2)^3 + b
+          y^2 / z^6 = x^3 / z^6 + b
+          y^2 = x^3 + b z^6
+        */
+        alt_bn128_Fq2 X2 = this->X.squared();
+        alt_bn128_Fq2 Y2 = this->Y.squared();
+        alt_bn128_Fq2 Z2 = this->Z.squared();
+
+        alt_bn128_Fq2 X3 = this->X * X2;
+        alt_bn128_Fq2 Z3 = this->Z * Z2;
+        alt_bn128_Fq2 Z6 = Z3.squared();
+
+        return (Y2 == X3 + alt_bn128_twist_coeff_b * Z6);
+    }
+}
+
+alt_bn128_G2 alt_bn128_G2::zero()
+{
+    return G2_zero;
+}
+
+alt_bn128_G2 alt_bn128_G2::one()
+{
+    return G2_one;
+}
+
+alt_bn128_G2 alt_bn128_G2::random_element()
+{
+    return (alt_bn128_Fr::random_element().as_bigint()) * G2_one;
+}
+
+/*std::ostream& operator<<(std::ostream &out, const alt_bn128_G2 &g)
+{
+    alt_bn128_G2 copy(g);
+    copy.to_affine_coordinates();
+    out << (copy.is_zero() ? 1 : 0) << OUTPUT_SEPARATOR;
+#ifdef NO_PT_COMPRESSION
+    out << copy.X << OUTPUT_SEPARATOR << copy.Y;
+#else
+     //storing LSB of Y
+    out << copy.X << OUTPUT_SEPARATOR << (copy.Y.c0.as_bigint().data[0] & 1);
+#endif
+
+    return out;
+}
+
+std::istream& operator>>(std::istream &in, alt_bn128_G2 &g)
+{
+    char is_zero;
+    alt_bn128_Fq2 tX, tY;
+
+#ifdef NO_PT_COMPRESSION
+    in >> is_zero >> tX >> tY;
+    is_zero -= '0';
+#else
+    in.read((char*)&is_zero, 1); // this reads is_zero;
+    is_zero -= '0';
+    consume_OUTPUT_SEPARATOR(in);
+
+    unsigned char Y_lsb;
+    in >> tX;
+    consume_OUTPUT_SEPARATOR(in);
+    in.read((char*)&Y_lsb, 1);
+    Y_lsb -= '0';
+
+    // y = +/- sqrt(x^3 + b)
+    if (!is_zero)
+    {
+        alt_bn128_Fq2 tX2 = tX.squared();
+        alt_bn128_Fq2 tY2 = tX2 * tX + alt_bn128_twist_coeff_b;
+        tY = tY2.sqrt();
+
+        if ((tY.c0.as_bigint().data[0] & 1) != Y_lsb)
+        {
+            tY = -tY;
+        }
+    }
+#endif
+    // using projective coordinates
+    if (!is_zero)
+    {
+        g.X = tX;
+        g.Y = tY;
+        g.Z = alt_bn128_Fq2::one();
+    }
+    else
+    {
+        g = alt_bn128_G2::zero();
+    }
+
+    return in;
+}*/
+
+void alt_bn128_G2::batch_to_special_all_non_zeros(std::vector<alt_bn128_G2> &vec)
+{
+    std::vector<alt_bn128_Fq2> Z_vec;
+    Z_vec.reserve(vec.size());
+
+    for (auto &el: vec)
+    {
+        Z_vec.emplace_back(el.Z);
+    }
+    batch_invert<alt_bn128_Fq2>(Z_vec);
+
+    const alt_bn128_Fq2 one = alt_bn128_Fq2::one();
+
+    for (size_t i = 0; i < vec.size(); ++i)
+    {
+        alt_bn128_Fq2 Z2 = Z_vec[i].squared();
+        alt_bn128_Fq2 Z3 = Z_vec[i] * Z2;
+
+        vec[i].X = vec[i].X * Z2;
+        vec[i].Y = vec[i].Y * Z3;
+        vec[i].Z = one;
+    }
+}
+
+} // libff
--- a/trusted_libff/libff/algebra/curves/alt_bn128/alt_bn128_g2.hpp
+++ b/trusted_libff/libff/algebra/curves/alt_bn128/alt_bn128_g2.hpp
+/** @file
+ *****************************************************************************
+ * @author     This file is part of libff, developed by SCIPR Lab
+ *             and contributors (see AUTHORS).
+ * @copyright  MIT license (see LICENSE file)
+ *****************************************************************************/
+
+#ifndef ALT_BN128_G2_HPP_
+#define ALT_BN128_G2_HPP_
+#include <vector>
+
+#include <libff/algebra/curves/alt_bn128/alt_bn128_init.hpp>
+#include <libff/algebra/curves/curve_utils.hpp>
+
+namespace libff {
+
+class alt_bn128_G2;
+//std::ostream& operator<<(std::ostream &, const alt_bn128_G2&);
+//std::istream& operator>>(std::istream &, alt_bn128_G2&);
+
+class alt_bn128_G2 {
+public:
+#ifdef PROFILE_OP_COUNTS
+    static long long add_cnt;
+    static long long dbl_cnt;
+#endif
+    static std::vector<size_t> wnaf_window_table;
+    static std::vector<size_t> fixed_base_exp_window_table;
+    static alt_bn128_G2 G2_zero;
+    static alt_bn128_G2 G2_one;
+
+    typedef alt_bn128_Fq base_field;
+    typedef alt_bn128_Fq2 twist_field;
+    typedef alt_bn128_Fr scalar_field;
+
+    alt_bn128_Fq2 X, Y, Z;
+
+    // using Jacobian coordinates
+    alt_bn128_G2();
+    alt_bn128_G2(const alt_bn128_Fq2& X, const alt_bn128_Fq2& Y, const alt_bn128_Fq2& Z) : X(X), Y(Y), Z(Z) {};
+
+    static alt_bn128_Fq2 mul_by_b(const alt_bn128_Fq2 &elt);
+
+    void print() const;
+    void print_coordinates() const;
+
+    void to_affine_coordinates();
+    void to_special();
+    bool is_special() const;
+
+    bool is_zero() const;
+
+    bool operator==(const alt_bn128_G2 &other) const;
+    bool operator!=(const alt_bn128_G2 &other) const;
+
+    alt_bn128_G2 operator+(const alt_bn128_G2 &other) const;
+    alt_bn128_G2 operator-() const;
+    alt_bn128_G2 operator-(const alt_bn128_G2 &other) const;
+
+    alt_bn128_G2 add(const alt_bn128_G2 &other) const;
+    alt_bn128_G2 mixed_add(const alt_bn128_G2 &other) const;
+    alt_bn128_G2 dbl() const;
+    alt_bn128_G2 mul_by_q() const;
+
+    bool is_well_formed() const;
+
+    static alt_bn128_G2 zero();
+    static alt_bn128_G2 one();
+    static alt_bn128_G2 random_element();
+
+    static size_t size_in_bits() { return twist_field::size_in_bits() + 1; }
+    static bigint<base_field::num_limbs> base_field_char() { return base_field::field_char(); }
+    static bigint<scalar_field::num_limbs> order() { return scalar_field::field_char(); }
+
+    //friend std::ostream& operator<<(std::ostream &out, const alt_bn128_G2 &g);
+    //friend std::istream& operator>>(std::istream &in, alt_bn128_G2 &g);
+
+    static void batch_to_special_all_non_zeros(std::vector<alt_bn128_G2> &vec);
+};
+
+template<mp_size_t m>
+alt_bn128_G2 operator*(const bigint<m> &lhs, const alt_bn128_G2 &rhs)
+{
+    return scalar_mul<alt_bn128_G2, m>(rhs, lhs);
+}
+
+template<mp_size_t m, const bigint<m>& modulus_p>
+alt_bn128_G2 operator*(const Fp_model<m,modulus_p> &lhs, const alt_bn128_G2 &rhs)
+{
+    return scalar_mul<alt_bn128_G2, m>(rhs, lhs.as_bigint());
+}
+
+
+} // libff
+#endif // ALT_BN128_G2_HPP_
--- a/trusted_libff/libff/algebra/curves/alt_bn128/alt_bn128_init.cpp
+++ b/trusted_libff/libff/algebra/curves/alt_bn128/alt_bn128_init.cpp
@@ -13,9 +13,13 @@ namespace libff {
 bigint<alt_bn128_r_limbs> alt_bn128_modulus_r;
 bigint<alt_bn128_q_limbs> alt_bn128_modulus_q;

-alt_bn128_Fq alt_bn128_coeff_b;
-alt_bn128_Fq alt_bn128_twist_mul_by_b_c0;
-alt_bn128_Fq alt_bn128_twist_mul_by_b_c1;
+    alt_bn128_Fq alt_bn128_coeff_b;
+    alt_bn128_Fq2 alt_bn128_twist;
+    alt_bn128_Fq2 alt_bn128_twist_coeff_b;
+    alt_bn128_Fq alt_bn128_twist_mul_by_b_c0;
+    alt_bn128_Fq alt_bn128_twist_mul_by_b_c1;
+    alt_bn128_Fq2 alt_bn128_twist_mul_by_q_X;
+    alt_bn128_Fq2 alt_bn128_twist_mul_by_q_Y;

 bigint<alt_bn128_q_limbs> alt_bn128_ate_loop_count;
 bool alt_bn128_ate_is_loop_count_neg;
@@ -82,10 +86,26 @@ void init_alt_bn128_params()
    alt_bn128_Fq::nqr = alt_bn128_Fq("3");
    alt_bn128_Fq::nqr_to_t = alt_bn128_Fq("21888242871839275222246405745257275088696311157297823662689037894645226208582");

+    /* parameters for twist field Fq2 */
+    alt_bn128_Fq2::euler = bigint<2*alt_bn128_q_limbs>("239547588008311421220994022608339370399626158265550411218223901127035046843189118723920525909718935985594116157406550130918127817069793474323196511433944");
+    alt_bn128_Fq2::s = 4;
+    alt_bn128_Fq2::t = bigint<2*alt_bn128_q_limbs>("29943448501038927652624252826042421299953269783193801402277987640879380855398639840490065738714866998199264519675818766364765977133724184290399563929243");
+    alt_bn128_Fq2::t_minus_1_over_2 = bigint<2*alt_bn128_q_limbs>("14971724250519463826312126413021210649976634891596900701138993820439690427699319920245032869357433499099632259837909383182382988566862092145199781964621");
+    alt_bn128_Fq2::non_residue = alt_bn128_Fq("21888242871839275222246405745257275088696311157297823662689037894645226208582");
+    alt_bn128_Fq2::nqr = alt_bn128_Fq2(alt_bn128_Fq("2"),alt_bn128_Fq("1"));
+    alt_bn128_Fq2::nqr_to_t = alt_bn128_Fq2(alt_bn128_Fq("5033503716262624267312492558379982687175200734934877598599011485707452665730"),alt_bn128_Fq("314498342015008975724433667930697407966947188435857772134235984660852259084"));
+    alt_bn128_Fq2::Frobenius_coeffs_c1[0] = alt_bn128_Fq("1");
+    alt_bn128_Fq2::Frobenius_coeffs_c1[1] = alt_bn128_Fq("21888242871839275222246405745257275088696311157297823662689037894645226208582");
+

    /* choice of short Weierstrass curve and its twist */

    alt_bn128_coeff_b = alt_bn128_Fq("3");
+    alt_bn128_coeff_b = alt_bn128_Fq("3");
+    alt_bn128_twist = alt_bn128_Fq2(alt_bn128_Fq("9"), alt_bn128_Fq("1"));
+    alt_bn128_twist_coeff_b = alt_bn128_coeff_b * alt_bn128_twist.inverse();
+    alt_bn128_twist_mul_by_b_c0 = alt_bn128_coeff_b * alt_bn128_Fq2::non_residue;
+    alt_bn128_twist_mul_by_b_c1 = alt_bn128_coeff_b * alt_bn128_Fq2::non_residue;

    /* choice of group G1 */
    alt_bn128_G1::G1_zero = alt_bn128_G1(alt_bn128_Fq::zero(),

--- a/trusted_libff/libff/algebra/curves/alt_bn128/alt_bn128_init.hpp
+++ b/trusted_libff/libff/algebra/curves/alt_bn128/alt_bn128_init.hpp
@@ -9,6 +9,7 @@
 #define ALT_BN128_INIT_HPP_
 #include <libff/algebra/curves/public_params.hpp>
 #include <libff/algebra/fields/fp.hpp>
+#include <libff/algebra/fields/fp2.hpp>

 namespace libff {

@@ -23,12 +24,17 @@ extern bigint<alt_bn128_q_limbs> alt_bn128_modulus_q;

 typedef Fp_model<alt_bn128_r_limbs, alt_bn128_modulus_r> alt_bn128_Fr;
 typedef Fp_model<alt_bn128_q_limbs, alt_bn128_modulus_q> alt_bn128_Fq;
+typedef Fp2_model<alt_bn128_q_limbs, alt_bn128_modulus_q> alt_bn128_Fq2;

 // parameters for Barreto--Naehrig curve E/Fq : y^2 = x^3 + b
 extern alt_bn128_Fq alt_bn128_coeff_b;
 // parameters for twisted Barreto--Naehrig curve E'/Fq2 : y^2 = x^3 + b/xi
-extern alt_bn128_Fq alt_bn128_twist_mul_by_b_c0;
-extern alt_bn128_Fq alt_bn128_twist_mul_by_b_c1;
+    extern alt_bn128_Fq2 alt_bn128_twist;
+    extern alt_bn128_Fq2 alt_bn128_twist_coeff_b;
+    extern alt_bn128_Fq alt_bn128_twist_mul_by_b_c0;
+    extern alt_bn128_Fq alt_bn128_twist_mul_by_b_c1;
+    extern alt_bn128_Fq2 alt_bn128_twist_mul_by_q_X;
+    extern alt_bn128_Fq2 alt_bn128_twist_mul_by_q_Y;

 // parameters for pairing
 extern bigint<alt_bn128_q_limbs> alt_bn128_ate_loop_count;

--- a/trusted_libff/libff/algebra/fields/bigint.tcc
+++ b/trusted_libff/libff/algebra/fields/bigint.tcc
@@ -13,6 +13,8 @@
 #include <cstring>
 #include <random>

+#include <sgx_trts.h>
+
 namespace libff {

 template<mp_size_t n>
@@ -163,6 +165,30 @@ bool bigint<n>::test_bit(const std::size_t bitno) const
    }
 }

+    template<mp_size_t n>
+    bigint<n>& bigint<n>::randomize()
+    {
+        const size_t size = 1;
+
+        static_assert(GMP_NUMB_BITS == sizeof(mp_limb_t) * 8, "Wrong GMP_NUMB_BITS value");
+        //std::random_device rd;
+        constexpr size_t num_random_words = sizeof(mp_limb_t) * n / size;//sizeof(std::random_device::result_type);
+        //auto random_words = reinterpret_cast<std::random_device::result_type*>(this->data);
+       auto random_words = reinterpret_cast<unsigned char*>(this->data);
+
+       sgx_read_rand(random_words, num_random_words);
+      /*  auto random_words = reinterpret_cast<unsigned int*>(this->data);
+      for (size_t i = 0; i < num_random_words; ++i)
+       {
+           unsigned char rand[size];
+           sgx_read_rand(rand, size);
+           memcpy(&random_words[i], rand, size);
+           //random_words[i] = rd();
+       }*/
+
+        return (*this);
+    }
+

 } // libff
 #endif // BIGINT_TCC_
--- a/trusted_libff/libff/algebra/fields/fp.tcc
+++ b/trusted_libff/libff/algebra/fields/fp.tcc
@@ -684,6 +684,35 @@ Fp_model<n,modulus>& Fp_model<n,modulus>::invert()
    return *this;
 }

+        template<mp_size_t n, const bigint<n>& modulus>
+        Fp_model<n, modulus> Fp_model<n,modulus>::random_element() /// returns random element of Fp_model
+        {
+            /* note that as Montgomery representation is a bijection then
+               selecting a random element of {xR} is the same as selecting a
+               random element of {x} */
+            Fp_model<n, modulus> r;
+            do
+            {
+                r.mont_repr.randomize();
+
+                /* clear all bits higher than MSB of modulus */
+                size_t bitno = GMP_NUMB_BITS * n - 1;
+                while (modulus.test_bit(bitno) == false)
+                {
+                    const std::size_t part = bitno/GMP_NUMB_BITS;
+                    const std::size_t bit = bitno - (GMP_NUMB_BITS*part);
+
+                    r.mont_repr.data[part] &= ~(1ul<<bit);
+
+                    bitno--;
+                }
+            }
+                /* if r.data is still >= modulus -- repeat (rejection sampling) */
+            while (mpn_cmp(r.mont_repr.data, modulus.data, n) >= 0);
+
+            return r;
+        }
+
 template<mp_size_t n, const bigint<n>& modulus>
 Fp_model<n,modulus> Fp_model<n,modulus>::inverse() const
 {

--- a/trusted_libff/libff/algebra/fields/fp2.hpp
+++ b/trusted_libff/libff/algebra/fields/fp2.hpp
+/** @file
+ *****************************************************************************
+ Implementation of arithmetic in the finite field F[p^2].
+ *****************************************************************************
+ * @author     This file is part of libff, developed by SCIPR Lab
+ *             and contributors (see AUTHORS).
+ * @copyright  MIT license (see LICENSE file)
+ *****************************************************************************/
+
+#ifndef FP2_HPP_
+#define FP2_HPP_
+#include <vector>
+
+#include <libff/algebra/fields/fp.hpp>
+
+namespace libff {
+
+template<mp_size_t n, const bigint<n>& modulus>
+class Fp2_model;
+
+/*template<mp_size_t n, const bigint<n>& modulus>
+std::ostream& operator<<(std::ostream &, const Fp2_model<n, modulus> &);
+
+template<mp_size_t n, const bigint<n>& modulus>
+std::istream& operator>>(std::istream &, Fp2_model<n, modulus> &);*/
+
+/**
+ * Arithmetic in the field F[p^2].
+ *
+ * Let p := modulus. This interface provides arithmetic for the extension field
+ * Fp2 = Fp[U]/(U^2-non_residue), where non_residue is in Fp.
+ *
+ * ASSUMPTION: p = 1 (mod 6)
+ */
+template<mp_size_t n, const bigint<n>& modulus>
+class Fp2_model {
+public:
+    typedef Fp_model<n, modulus> my_Fp;
+
+    static bigint<2*n> euler; // (modulus^2-1)/2
+    static size_t s;       // modulus^2 = 2^s * t + 1
+    static bigint<2*n> t;  // with t odd
+    static bigint<2*n> t_minus_1_over_2; // (t-1)/2
+    static my_Fp non_residue; // X^4-non_residue irreducible over Fp; used for constructing Fp2 = Fp[X] / (X^2 - non_residue)
+    static Fp2_model<n, modulus> nqr; // a quadratic nonresidue in Fp2
+    static Fp2_model<n, modulus> nqr_to_t; // nqr^t
+    static my_Fp Frobenius_coeffs_c1[2]; // non_residue^((modulus^i-1)/2) for i=0,1
+
+    my_Fp c0, c1;
+    Fp2_model() {};
+    Fp2_model(const my_Fp& c0, const my_Fp& c1) : c0(c0), c1(c1) {};
+
+    void clear() { c0.clear(); c1.clear(); }
+    //void print() const { printf("c0/c1:\n"); c0.print(); c1.print(); }
+
+    static Fp2_model<n, modulus> zero();
+    static Fp2_model<n, modulus> one();
+    static Fp2_model<n, modulus> random_element();
+
+    bool is_zero() const { return c0.is_zero() && c1.is_zero(); }
+    bool operator==(const Fp2_model &other) const;
+    bool operator!=(const Fp2_model &other) const;
+
+    Fp2_model operator+(const Fp2_model &other) const;
+    Fp2_model operator-(const Fp2_model &other) const;
+    Fp2_model operator*(const Fp2_model &other) const;
+    Fp2_model operator-() const;
+    Fp2_model squared() const; // default is squared_complex
+    Fp2_model inverse() const;
+    Fp2_model Frobenius_map(unsigned long power) const;
+    Fp2_model sqrt() const; // HAS TO BE A SQUARE (else does not terminate)
+    Fp2_model squared_karatsuba() const;
+    Fp2_model squared_complex() const;
+
+    template<mp_size_t m>
+    Fp2_model operator^(const bigint<m> &other) const;
+
+    static size_t size_in_bits() { return 2*my_Fp::size_in_bits(); }
+    static bigint<n> base_field_char() { return modulus; }
+
+   // friend std::ostream& operator<< <n, modulus>(std::ostream &out, const Fp2_model<n, modulus> &el);
+   // friend std::istream& operator>> <n, modulus>(std::istream &in, Fp2_model<n, modulus> &el);
+};
+
+/*template<mp_size_t n, const bigint<n>& modulus>
+std::ostream& operator<<(std::ostream& out, const std::vector<Fp2_model<n, modulus> > &v);
+
+template<mp_size_t n, const bigint<n>& modulus>
+std::istream& operator>>(std::istream& in, std::vector<Fp2_model<n, modulus> > &v); */
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n, modulus> operator*(const Fp_model<n, modulus> &lhs, const Fp2_model<n, modulus> &rhs);
+
+template<mp_size_t n, const bigint<n>& modulus>
+bigint<2*n> Fp2_model<n, modulus>::euler;
+
+template<mp_size_t n, const bigint<n>& modulus>
+size_t Fp2_model<n, modulus>::s;
+
+template<mp_size_t n, const bigint<n>& modulus>
+bigint<2*n> Fp2_model<n, modulus>::t;
+
+template<mp_size_t n, const bigint<n>& modulus>
+bigint<2*n> Fp2_model<n, modulus>::t_minus_1_over_2;
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp_model<n, modulus> Fp2_model<n, modulus>::non_residue;
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n, modulus> Fp2_model<n, modulus>::nqr;
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n, modulus> Fp2_model<n, modulus>::nqr_to_t;
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp_model<n, modulus> Fp2_model<n, modulus>::Frobenius_coeffs_c1[2];
+
+} // libff
+#include <libff/algebra/fields/fp2.tcc>
+
+#endif // FP2_HPP_
--- a/trusted_libff/libff/algebra/fields/fp2.tcc
+++ b/trusted_libff/libff/algebra/fields/fp2.tcc
+/** @file
+ *****************************************************************************
+ Implementation of arithmetic in the finite field F[p^2].
+ *****************************************************************************
+ * @author     This file is part of libff, developed by SCIPR Lab
+ *             and contributors (see AUTHORS).
+ * @copyright  MIT license (see LICENSE file)
+ *****************************************************************************/
+
+#ifndef FP2_TCC_
+#define FP2_TCC_
+
+#include <libff/algebra/fields/field_utils.hpp>
+
+namespace libff {
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::zero()
+{
+    return Fp2_model<n, modulus>(my_Fp::zero(), my_Fp::zero());
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::one()
+{
+    return Fp2_model<n, modulus>(my_Fp::one(), my_Fp::zero());
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::random_element()
+{
+    Fp2_model<n, modulus> r;
+    r.c0 = my_Fp::random_element();
+    r.c1 = my_Fp::random_element();
+
+    return r;
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+bool Fp2_model<n,modulus>::operator==(const Fp2_model<n,modulus> &other) const
+{
+    return (this->c0 == other.c0 && this->c1 == other.c1);
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+bool Fp2_model<n,modulus>::operator!=(const Fp2_model<n,modulus> &other) const
+{
+    return !(operator==(other));
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::operator+(const Fp2_model<n,modulus> &other) const
+{
+    return Fp2_model<n,modulus>(this->c0 + other.c0,
+                                this->c1 + other.c1);
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::operator-(const Fp2_model<n,modulus> &other) const
+{
+    return Fp2_model<n,modulus>(this->c0 - other.c0,
+                                this->c1 - other.c1);
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n, modulus> operator*(const Fp_model<n, modulus> &lhs, const Fp2_model<n, modulus> &rhs)
+{
+    return Fp2_model<n,modulus>(lhs*rhs.c0,
+                                lhs*rhs.c1);
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::operator*(const Fp2_model<n,modulus> &other) const
+{
+    /* Devegili OhEig Scott Dahab --- Multiplication and Squaring on Pairing-Friendly Fields.pdf; Section 3 (Karatsuba) */
+    const my_Fp
+        &A = other.c0, &B = other.c1,
+        &a = this->c0, &b = this->c1;
+    const my_Fp aA = a * A;
+    const my_Fp bB = b * B;
+
+    return Fp2_model<n,modulus>(aA + non_residue * bB,
+                                (a + b)*(A+B) - aA - bB);
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::operator-() const
+{
+    return Fp2_model<n,modulus>(-this->c0,
+                                -this->c1);
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::squared() const
+{
+    return squared_complex();
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::squared_karatsuba() const
+{
+    /* Devegili OhEig Scott Dahab --- Multiplication and Squaring on Pairing-Friendly Fields.pdf; Section 3 (Karatsuba squaring) */
+    const my_Fp &a = this->c0, &b = this->c1;
+    const my_Fp asq = a.squared();
+    const my_Fp bsq = b.squared();
+
+    return Fp2_model<n,modulus>(asq + non_residue * bsq,
+                                (a + b).squared() - asq - bsq);
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::squared_complex() const
+{
+    /* Devegili OhEig Scott Dahab --- Multiplication and Squaring on Pairing-Friendly Fields.pdf; Section 3 (Complex squaring) */
+    const my_Fp &a = this->c0, &b = this->c1;
+    const my_Fp ab = a * b;
+
+    return Fp2_model<n,modulus>((a + b) * (a + non_residue * b) - ab - non_residue * ab,
+                                ab + ab);
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::inverse() const
+{
+    const my_Fp &a = this->c0, &b = this->c1;
+
+    /* From "High-Speed Software Implementation of the Optimal Ate Pairing over Barreto-Naehrig Curves"; Algorithm 8 */
+    const my_Fp t0 = a.squared();
+    const my_Fp t1 = b.squared();
+    const my_Fp t2 = t0 - non_residue * t1;
+    const my_Fp t3 = t2.inverse();
+    const my_Fp c0 = a * t3;
+    const my_Fp c1 = - (b * t3);
+
+    return Fp2_model<n,modulus>(c0, c1);
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::Frobenius_map(unsigned long power) const
+{
+    return Fp2_model<n,modulus>(c0,
+                                Frobenius_coeffs_c1[power % 2] * c1);
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::sqrt() const
+{
+    Fp2_model<n,modulus> one = Fp2_model<n,modulus>::one();
+
+    size_t v = Fp2_model<n,modulus>::s;
+    Fp2_model<n,modulus> z = Fp2_model<n,modulus>::nqr_to_t;
+    Fp2_model<n,modulus> w = (*this)^Fp2_model<n,modulus>::t_minus_1_over_2;
+    Fp2_model<n,modulus> x = (*this) * w;
+    Fp2_model<n,modulus> b = x * w; // b = (*this)^t
+
+#if DEBUG
+    // check if square with euler's criterion
+    Fp2_model<n,modulus> check = b;
+    for (size_t i = 0; i < v-1; ++i)
+    {
+        check = check.squared();
+    }
+    if (check != one)
+    {
+        assert(0);
+    }
+#endif
+
+    // compute square root with Tonelli--Shanks
+    // (does not terminate if not a square!)
+
+    while (b != one)
+    {
+        size_t m = 0;
+        Fp2_model<n,modulus> b2m = b;
+        while (b2m != one)
+        {
+            /* invariant: b2m = b^(2^m) after entering this loop */
+            b2m = b2m.squared();
+            m += 1;
+        }
+
+        int j = v-m-1;
+        w = z;
+        while (j > 0)
+        {
+            w = w.squared();
+            --j;
+        } // w = z^2^(v-m-1)
+
+        z = w.squared();
+        b = b * z;
+        x = x * w;
+        v = m;
+    }
+
+    return x;
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+template<mp_size_t m>
+Fp2_model<n,modulus> Fp2_model<n,modulus>::operator^(const bigint<m> &pow) const
+{
+    return power<Fp2_model<n, modulus>, m>(*this, pow);
+}
+
+/*template<mp_size_t n, const bigint<n>& modulus>
+std::ostream& operator<<(std::ostream &out, const Fp2_model<n, modulus> &el)
+{
+    out << el.c0 << OUTPUT_SEPARATOR << el.c1;
+    return out;
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+std::istream& operator>>(std::istream &in, Fp2_model<n, modulus> &el)
+{
+    in >> el.c0 >> el.c1;
+    return in;
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+std::ostream& operator<<(std::ostream& out, const std::vector<Fp2_model<n, modulus> > &v)
+{
+    out << v.size() << "\n";
+    for (const Fp2_model<n, modulus>& t : v)
+    {
+        out << t << OUTPUT_NEWLINE;
+    }
+
+    return out;
+}
+
+template<mp_size_t n, const bigint<n>& modulus>
+std::istream& operator>>(std::istream& in, std::vector<Fp2_model<n, modulus> > &v)
+{
+    v.clear();
+
+    size_t s;
+    in >> s;
+
+    char b;
+    in.read(&b, 1);
+
+    v.reserve(s);
+
+    for (size_t i = 0; i < s; ++i)
+    {
+        Fp2_model<n, modulus> el;
+        in >> el;
+        v.emplace_back(el);
+    }
+
+    return in;
+}*/
+
+} // libff
+#endif // FP2_TCC_