init attribute-based encryption

Change-Id: Iba1a3d722110abf747a0fba366f3ebc911d25b25

25 files changed, 1750 insertions, 0 deletions

diff --git a/moon-abe/pbc-0.5.14/include/pbc.h b/moon-abe/pbc-0.5.14/include/pbc.h
new file mode 100644
index 00000000..a963719b
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc.h
@@ -0,0 +1,34 @@
+#ifndef __PBC_H__
+#define __PBC_H__
+
+#include <stdarg.h>
+#include <stdio.h>
+#include <stdint.h> // for intptr_t
+#include <stdlib.h>
+#include <gmp.h>
+
+#if defined (__cplusplus)
+extern "C" {
+#endif
+
+#include "pbc_utils.h"
+#include "pbc_field.h"
+#include "pbc_param.h"
+#include "pbc_pairing.h"
+#include "pbc_curve.h"
+#include "pbc_mnt.h"
+#include "pbc_a1_param.h"
+#include "pbc_a_param.h"
+#include "pbc_d_param.h"
+#include "pbc_e_param.h"
+#include "pbc_f_param.h"
+#include "pbc_g_param.h"
+#include "pbc_i_param.h"
+#include "pbc_random.h"
+#include "pbc_memory.h"
+
+#if defined (__cplusplus)
+}  // extern "C"
+#endif
+
+#endif //__PBC_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_a1_param.h b/moon-abe/pbc-0.5.14/include/pbc_a1_param.h
new file mode 100644
index 00000000..74dd9b1d
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_a1_param.h
@@ -0,0 +1,25 @@
+// requires
+// * gmp.h
+// * param.h
+#ifndef __PBC_A1_PARAM_H__
+#define __PBC_A1_PARAM_H__
+
+struct symtab_s;
+int pbc_param_init_a1(pbc_param_ptr par, struct symtab_s *tab);
+
+/*@manual a1param
+Generate type A1 pairing parameters and store them in 'p'.  The group order
+will be 'n'. The order of the base field is a few bits longer.  To be secure,
+generic discrete log algorithms must be infeasible in groups of order 'n', and
+finite field discrete log algorithms must be infeasible in finite fields of
+order roughly 'n'^2^.  Additionally, 'n' should be hard to factorize.
+
+For example: 'n' a product of two primes, each at least 512 bits.
+
+The file `param/a1.param` contains sample parameters for a
+type A1 pairing, but it is only for benchmarking: it is useless without
+the factorization of +n+, the order of the group.
+*/
+void pbc_param_init_a1_gen(pbc_param_t param, mpz_t n);
+
+#endif //__PBC_A1_PARAM_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_a_param.h b/moon-abe/pbc-0.5.14/include/pbc_a_param.h
new file mode 100644
index 00000000..64d70468
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_a_param.h
@@ -0,0 +1,25 @@
+// Type A pairing parameters.
+
+// Requires:
+// * param.h
+#ifndef __PBC_A_PARAM_H__
+#define __PBC_A_PARAM_H__
+
+struct symtab_s;
+int pbc_param_init_a(pbc_param_ptr par, struct symtab_s *tab);
+
+/*@manual aparam
+Generate type A pairing parameters and store them in 'p',
+where the group order r is 'rbits' long, and the order of the base field q
+is 'qbits' long. Elements take 'qbits' to represent.
+
+To be secure, generic discrete log algorithms must be infeasible in groups of
+order r, and finite field discrete log algorithms must be infeasible in finite
+fields of order q^2, e.g. 'rbits' = 160, 'qbits' = 512.
+
+The file `param/a.param` contains parameters for a type A pairing suitable for
+cryptographic use.
+*/
+void pbc_param_init_a_gen(pbc_param_ptr par, int rbits, int qbits);
+
+#endif //__PBC_A_PARAM_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_curve.h b/moon-abe/pbc-0.5.14/include/pbc_curve.h
new file mode 100644
index 00000000..9a86903d
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_curve.h
@@ -0,0 +1,79 @@
+// A subgroup of the group of points on an elliptic curve.
+// Also used to represent quotient groups.
+//
+// We use the field_t structure even though E(K) is a group. Addition and
+// multiplication both refer to the group operation.
+
+// Requires:
+// * stdio.h
+// * gmp.h
+// * field.h
+#ifndef __PBC_CURVE_H__
+#define __PBC_CURVE_H__
+
+// Some initialization functions take an order parameter. This is meant to
+// be the order of the subgroup, but might actually be the order of the twist.
+// Certain routines initialize a curve, test a random point to see if it has
+// the correct order, and if not, immediately twist the curve so that it does.
+// TODO: Move such code into curve.c, so 'order' is always accurate.
+
+// If cofac != NULL, then the field_t represents the subgroup of
+// order = #E(K) / cofac.
+//
+// If not, and order = #E(K) then the field_t represents the entire E(K).
+//
+// Otherwise, if order is a factor of #E(K), then the field_t represents
+// the quotient group of that order, namely E(K)/(#E(K)/order). No attempt is
+// made to standardize the coset representative. This mode is useful for the
+// Tate pairing (see thesis), where any coset representative of G2 suffices
+// during the pairing computation.
+
+// Initialize a subgroup of points on the curve Y^2 = X^3 + b.
+void field_init_curve_b(field_ptr f, element_ptr b, mpz_t order, mpz_t cofac);
+
+// Initialize a subgroup of points on the curve with the given j-invariant.
+void field_init_curve_j(field_t f, element_ptr j, mpz_t order, mpz_t cofac);
+
+// Initialize a subgroup of points on the curve Y^2 = X^3 + a X + b.
+void field_init_curve_ab(field_ptr f, element_ptr a, element_ptr b, mpz_t order, mpz_t cofac);
+
+// Reinitialize as the subgroup of points on the twist curve.
+// Requires j-invariant of the original curve != 0, 1728.
+// Mangles f, thus existing points of f become invalid.
+// TODO: Refactor so we can remove this from the interface.
+void field_reinit_curve_twist(field_t f);
+
+// Compute trace of Frobenius at q^n given trace at q.
+void pbc_mpz_trace_n(mpz_t res, mpz_t q, mpz_t trace, int n);
+
+// Given q, t such that #E(F_q) = q - t + 1, compute #E(F_q^k).
+void pbc_mpz_curve_order_extn(mpz_t res, mpz_t q, mpz_t t, int k);
+
+void field_init_curve_with_map(field_ptr cnew, field_ptr c,
+  field_ptr dstfield, fieldmap map);
+
+void field_init_curve_ab_map(field_t cnew, field_t c,
+  fieldmap map, field_ptr mapdest,
+  mpz_t ordernew, mpz_t cofacnew);
+
+void field_curve_use_random_solvefory(field_ptr f);
+
+void field_curve_set_quotient_cmp(field_ptr c, mpz_t quotient_cmp);
+
+#pragma GCC visibility push(hidden)
+// Internal:
+
+element_ptr curve_x_coord(element_t e);
+element_ptr curve_y_coord(element_t e);
+element_ptr curve_a_coeff(element_t e);
+element_ptr curve_b_coeff(element_t e);
+element_ptr curve_field_a_coeff(field_t f);
+element_ptr curve_field_b_coeff(field_t f);
+
+void curve_from_x(element_ptr e, element_t x);
+void curve_set_si(element_t R, long int x, long int y);
+void curve_set_gen_no_cofac(element_ptr a);
+
+#pragma GCC visibility pop
+
+#endif //__PBC_CURVE_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_d_param.h b/moon-abe/pbc-0.5.14/include/pbc_d_param.h
new file mode 100644
index 00000000..41fcfc30
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_d_param.h
@@ -0,0 +1,40 @@
+// Type D pairings, aka MNT curves.
+
+// Requires:
+// * mnt.h
+// * param.h
+#ifndef __PBC_D_PARAM_H__
+#define __PBC_D_PARAM_H__
+
+struct symtab_s;
+int pbc_param_init_d(pbc_param_ptr par, struct symtab_s *tab);
+
+/*@manual dparam
+Type D curves are generated using the complex multiplication (CM) method.  This
+function sets 'p' to a type D pairing parameters from CM parameters 'cm'.
+Other library calls search for appropriate CM parameters and the results
+can be passed to this function.
+
+To be secure, generic discrete log algorithms must be infeasible in groups of
+order r, and finite field discrete log algorithms must be infeasible in finite
+fields of order q^6^.  For usual CM parameters, r is a few bits smaller than q.
+
+Using type D pairings allows elements of group G1 to be quite short, typically
+170-bits. Because of a certain trick, elements of group G2 need only be 3 times
+longer, that is, about 510 bits rather than 6 times long. They are not quite
+as short as type F pairings, but much faster.
+
+I sometimes refer to a type D curve as a triplet of numbers: the discriminant,
+the number of bits in the prime q, and the number of bits in the prime r. The
+`gen/listmnt` program prints these numbers.
+
+Among the bundled type D curve parameters are the curves 9563-201-181,
+62003-159-158 and 496659-224-224 which have shortened names `param/d201.param`,
+`param/d159.param` and `param/d225.param` respectively.
+
+See `gen/listmnt.c` and `gen/gendparam.c` for how to generate type D pairing
+parameters.
+*/
+void pbc_param_init_d_gen(pbc_param_ptr p, pbc_cm_ptr cm);
+
+#endif //__PBC_D_PARAM_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_e_param.h b/moon-abe/pbc-0.5.14/include/pbc_e_param.h
new file mode 100644
index 00000000..e59ebe82
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_e_param.h
@@ -0,0 +1,29 @@
+// Type E pairings.
+
+// Requires:
+// * param.h
+#ifndef __PBC_E_PARAM_H__
+#define __PBC_E_PARAM_H__
+
+struct symtab_s;
+int pbc_param_init_e(pbc_param_ptr par, struct symtab_s *tab);
+
+/*@manual eparam
+Generate type E pairing parameters and store them in 'p',
+where the group order r is 'rbits' long, and the order of the base field q
+is 'qbits' long. To be secure, generic discrete log algorithms must
+be infeasible in groups of order r, and finite field discrete log algorithms
+must be infeasible in finite fields of order q,
+e.g. 'rbits' = 160, 'qbits' = 1024.
+
+This pairing is just a curiosity: it can be implemented entirely in a field of
+prime order, that is, only arithmetic modulo a prime is needed and there is
+never a need to extend a field.
+
+If discrete log in field extensions are found to be substantially easier to
+solve than previously thought, or discrete log can be solved in elliptic curves
+as easily as they can be in finite fields, this pairing type may become useful.
+*/
+void pbc_param_init_e_gen(pbc_param_t p, int rbits, int qbits);
+
+#endif //__PBC_E_PARAM_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_f_param.h b/moon-abe/pbc-0.5.14/include/pbc_f_param.h
new file mode 100644
index 00000000..5c484a98
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_f_param.h
@@ -0,0 +1,27 @@
+// Type F pairings.
+
+// Requires:
+// * param.h
+#ifndef __PBC_F_PARAM_H__
+#define __PBC_F_PARAM_H__
+
+struct symtab_s;
+int pbc_param_init_f(pbc_param_ptr par, struct symtab_s *tab);
+
+/*@manual fparam
+Generate type F pairing parameters and store them in 'p'.
+Both the group order r and the order of the base field q will be roughly
+'bits'-bit numbers.
+To be secure, generic discrete log algorithms must
+be infeasible in groups of order r, and finite field discrete log algorithms
+must be infeasible in finite fields of order q^12, e.g. 'bits' = 160.
+
+Type F should be used when the top priority is to minimize bandwidth (e.g.
+short signatures). The current implementation makes them slow.
+
+If finite field discrete log algorithms improve further, type D pairings will
+have to use larger fields, but type F can still remain short, up to a point.
+*/
+void pbc_param_init_f_gen(pbc_param_t p, int bits);
+
+#endif //__PBC_F_PARAM_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_field.h b/moon-abe/pbc-0.5.14/include/pbc_field.h
new file mode 100644
index 00000000..5bcb8c83
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_field.h
@@ -0,0 +1,694 @@
+/*
+ * field_t: represents fields, rings and groups.
+ * element_t: represents an element of a field_t.
+ */
+
+// Requires:
+// * stdarg.h
+// * stdio.h
+// * gmp.h
+// * utils.h
+#ifndef __PBC_FIELD_H__
+#define __PBC_FIELD_H__
+
+struct field_s;
+
+struct element_s {
+  struct field_s *field;
+  void *data;
+};
+typedef struct element_s *element_ptr;
+typedef struct element_s element_t[1];
+
+struct element_pp_s {
+  struct field_s *field;
+  void *data;
+};
+typedef struct element_pp_s element_pp_t[1];
+typedef struct element_pp_s *element_pp_ptr;
+
+void pbc_assert(int expr, char *msg, const char *func);
+void pbc_assert_match2(element_ptr a, element_ptr b, const char *func);
+void pbc_assert_match3(element_ptr a, element_ptr b, element_ptr c,
+                       const char *func);
+
+struct multiz_s;
+typedef struct multiz_s *multiz;
+
+struct pairing_s;
+struct field_s {
+  void (*field_clear)(struct field_s *f);
+  void (*init)(element_ptr);
+  void (*clear)(element_ptr);
+
+  void (*set_mpz)(element_ptr, mpz_ptr);
+  void (*set_multiz)(element_ptr, multiz);
+  void (*set)(element_ptr, element_ptr);
+  void (*set0)(element_ptr);
+  void (*set1)(element_ptr);
+  int (*set_str)(element_ptr e, const char *s, int base);
+  size_t(*out_str)(FILE *stream, int base, element_ptr);
+  void (*add)(element_ptr, element_ptr, element_ptr);
+  void (*sub)(element_ptr, element_ptr, element_ptr);
+  void (*mul)(element_ptr, element_ptr, element_ptr);
+
+  int (*is_sqr)(element_ptr);
+  void (*sqrt)(element_ptr, element_ptr);
+
+  // Defaults exist for these functions.
+  int (*item_count)(element_ptr);
+  element_ptr (*item)(element_ptr, int);
+  element_ptr (*get_x)(element_ptr);
+  element_ptr (*get_y)(element_ptr);
+  void (*set_si)(element_ptr, signed long int);
+  void (*add_ui)(element_ptr, element_ptr, unsigned long int);
+  void (*mul_mpz)(element_ptr, element_ptr, mpz_ptr);
+  void (*mul_si)(element_ptr, element_ptr, signed long int);
+  void (*div)(element_ptr, element_ptr, element_ptr);
+  void (*doub)(element_ptr, element_ptr);  // Can't call it "double"!
+  void (*multi_doub)(element_ptr*, element_ptr*, int n);
+  void (*multi_add)(element_ptr*, element_ptr*, element_ptr*, int n);
+  void (*halve)(element_ptr, element_ptr);
+  void (*square)(element_ptr, element_ptr);
+
+  void (*cubic) (element_ptr, element_ptr);
+  void (*pow_mpz)(element_ptr, element_ptr, mpz_ptr);
+  void (*invert)(element_ptr, element_ptr);
+  void (*neg)(element_ptr, element_ptr);
+  void (*random)(element_ptr);
+  void (*from_hash)(element_ptr, void *data, int len);
+  int (*is1)(element_ptr);
+  int (*is0)(element_ptr);
+  int (*sign)(element_ptr);  // satisfies sign(x) = -sign(-x)
+  int (*cmp)(element_ptr, element_ptr);
+  int (*to_bytes)(unsigned char *data, element_ptr);
+  int (*from_bytes)(element_ptr, unsigned char *data);
+  int (*length_in_bytes)(element_ptr);
+  int fixed_length_in_bytes;  // length of an element in bytes; -1 for variable
+  int (*snprint)(char *s, size_t n, element_ptr e);
+  void (*to_mpz)(mpz_ptr, element_ptr);
+  void (*out_info)(FILE *, struct field_s *);
+  void (*pp_init)(element_pp_t p, element_t in);
+  void (*pp_clear)(element_pp_t p);
+  void (*pp_pow)(element_t out, mpz_ptr power, element_pp_t p);
+
+  struct pairing_s *pairing;
+
+  mpz_t order;                // 0 for infinite order
+  element_ptr nqr;            // nonquadratic residue
+
+  char *name;
+  void *data;
+};
+typedef struct field_s *field_ptr;
+typedef struct field_s field_t[1];
+
+typedef void (*fieldmap) (element_t dst, element_t src);
+
+void field_out_info(FILE* out, field_ptr f);
+
+/*@manual internal
+Initialize 'e' to be an element of the algebraic structure 'f'
+and set it to be the zero element.
+*/
+static inline void element_init(element_t e, field_ptr f) {
+  e->field = f;
+  f->init(e);
+}
+
+element_ptr element_new(field_ptr f);
+void element_free(element_ptr e);
+
+/*@manual einit
+Initialize 'e' to be an element of the algebraic structure that 'e2'
+lies in.
+*/
+static inline void element_init_same_as(element_t e, element_t e2) {
+  element_init(e, e2->field);
+}
+
+/*@manual einit
+Free the space occupied by 'e'. Call this when
+the variable 'e' is no longer needed.
+*/
+static inline void element_clear(element_t e) {
+  e->field->clear(e);
+}
+
+/*@manual eio
+Output 'e' on 'stream' in base 'base'. The base must be between
+2 and 36.
+*/
+static inline size_t element_out_str(FILE * stream, int base, element_t e) {
+  return e->field->out_str(stream, base, e);
+}
+
+/*@manual eio
+*/
+int element_printf(const char *format, ...);
+
+/*@manual eio
+*/
+int element_fprintf(FILE * stream, const char *format, ...);
+
+/*@manual eio
+*/
+int element_snprintf(char *buf, size_t size, const char *fmt, ...);
+
+/*@manual eio
+Same as printf family
+except also has the 'B' conversion specifier for types
+of *element_t*, and 'Y', 'Z' conversion specifiers for
++mpz_t+. For example if 'e' is of type
++element_t+ then
+
+  element_printf("%B\n", e);
+
+will print the value of 'e' in a human-readable form on standard output.
+*/
+int element_vsnprintf(char *buf, size_t size, const char *fmt, va_list ap);
+
+/*@manual eio
+Convert an element to a human-friendly string.
+Behaves as *snprintf* but only on one element at a time.
+*/
+static inline int element_snprint(char *s, size_t n, element_t e) {
+  return e->field->snprint(s, n, e);
+}
+
+static inline void element_set_multiz(element_t e, multiz m) {
+  e->field->set_multiz(e, m);
+}
+
+/*@manual eio
+Set the element 'e' from 's', a null-terminated C string in base 'base'.
+Whitespace is ignored. Points have the form "['x,y']" or "'O'",
+while polynomials have the form "['a0,...,an']".
+Returns number of characters read (unlike GMP's mpz_set_str).
+A return code of zero means PBC could not find a well-formed string
+describing an element.
+*/
+static inline int element_set_str(element_t e, const char *s, int base) {
+  return e->field->set_str(e, s, base);
+}
+
+/*@manual eassign
+Set 'e' to zero.
+*/
+static inline void element_set0(element_t e) {
+  e->field->set0(e);
+}
+
+/*@manual eassign
+Set 'e' to one.
+*/
+static inline void element_set1(element_t e) {
+  e->field->set1(e);
+}
+
+/*@manual eassign
+Set 'e' to 'i'.
+*/
+static inline void element_set_si(element_t e, signed long int i) {
+  e->field->set_si(e, i);
+}
+
+/*@manual eassign
+Set 'e' to 'z'.
+*/
+static inline void element_set_mpz(element_t e, mpz_t z) {
+  e->field->set_mpz(e, z);
+}
+
+/*@manual eassign
+Set 'e' to 'a'.
+*/
+static inline void element_set(element_t e, element_t a) {
+  PBC_ASSERT_MATCH2(e, a);
+  e->field->set(e, a);
+}
+
+static inline void element_add_ui(element_t n, element_t a,
+                                  unsigned long int b) {
+  n->field->add_ui(n, a, b);
+}
+
+/*@manual econvert
+Converts 'e' to a GMP integer 'z'
+if such an operation makes sense
+*/
+static inline void element_to_mpz(mpz_t z, element_t e) {
+  e->field->to_mpz(z, e);
+}
+
+static inline long element_to_si(element_t e) {
+  mpz_t z;
+  mpz_init(z);
+  e->field->to_mpz(z, e);
+  long res = mpz_get_si(z);
+  mpz_clear(z);
+  return res;
+}
+
+/*@manual econvert
+Generate an element 'e' deterministically from
+the 'len' bytes stored in the buffer 'data'.
+*/
+static inline void element_from_hash(element_t e, void *data, int len) {
+  e->field->from_hash(e, data, len);
+}
+
+/*@manual earith
+Set 'n' to 'a' + 'b'.
+*/
+static inline void element_add(element_t n, element_t a, element_t b) {
+  PBC_ASSERT_MATCH3(n, a, b);
+  n->field->add(n, a, b);
+}
+
+/*@manual earith
+Set 'n' to 'a' - 'b'.
+*/
+static inline void element_sub(element_t n, element_t a, element_t b) {
+  PBC_ASSERT_MATCH3(n, a, b);
+  n->field->sub(n, a, b);
+}
+
+/*@manual earith
+Set 'n' = 'a' 'b'.
+*/
+static inline void element_mul(element_t n, element_t a, element_t b) {
+  PBC_ASSERT_MATCH3(n, a, b);
+  n->field->mul(n, a, b);
+}
+
+static inline void element_cubic(element_t n, element_t a) {
+  PBC_ASSERT_MATCH2(n, a);
+  n->field->cubic(n, a);
+}
+
+/*@manual earith
+*/
+static inline void element_mul_mpz(element_t n, element_t a, mpz_t z) {
+  PBC_ASSERT_MATCH2(n, a);
+  n->field->mul_mpz(n, a, z);
+}
+
+/*@manual earith
+Set 'n' = 'a' 'z', that is 'a' + 'a' + ... + 'a' where there are 'z' 'a'#'s#.
+*/
+static inline void element_mul_si(element_t n, element_t a,
+                                  signed long int z) {
+  PBC_ASSERT_MATCH2(n, a);
+  n->field->mul_si(n, a, z);
+}
+
+/*@manual earith
+'z' must be an element of a integer mod ring (i.e. *Z*~n~ for some n).
+Set 'c' = 'a' 'z', that is 'a' + 'a' + ... + 'a'
+where there are 'z' 'a''s.
+*/
+static inline void element_mul_zn(element_t c, element_t a, element_t z) {
+  mpz_t z0;
+  PBC_ASSERT_MATCH2(c, a);
+  //TODO: check z->field is Zn
+  mpz_init(z0);
+  element_to_mpz(z0, z);
+  element_mul_mpz(c, a, z0);
+  mpz_clear(z0);
+}
+
+/*@manual earith
+Set 'n' = 'a' / 'b'.
+*/
+static inline void element_div(element_t n, element_t a, element_t b) {
+  PBC_ASSERT_MATCH3(n, a, b);
+  n->field->div(n, a, b);
+}
+
+/*@manual earith
+Set 'n' = 'a' + 'a'.
+*/
+static inline void element_double(element_t n, element_t a) {
+  PBC_ASSERT_MATCH2(n, a);
+  n->field->doub(n, a);
+}
+
+// Set n_i = a_i + a_i for all i at one time.
+// Uses multi_doub(), which only elliptic curves have at the moment.
+void element_multi_double(element_t n[], element_t a[], int m);
+
+// Set n_i =a_i + b_i for all i at one time.
+// Uses multi_add(), which only elliptic curves have at the moment.
+void element_multi_add(element_t n[], element_t a[],element_t b[], int m);
+
+/*@manual earith
+Set 'n' = 'a/2'
+*/
+static inline void element_halve(element_t n, element_t a) {
+  PBC_ASSERT_MATCH2(n, a);
+  n->field->halve(n, a);
+}
+
+/*@manual earith
+Set 'n' = 'a'^2^
+*/
+static inline void element_square(element_t n, element_t a) {
+  PBC_ASSERT_MATCH2(n, a);
+  n->field->square(n, a);
+}
+
+/*@manual epow
+Set 'x' = 'a'^'n'^, that is
+'a' times 'a' times ... times 'a' where there are 'n' 'a'#'s#.
+*/
+static inline void element_pow_mpz(element_t x, element_t a, mpz_t n) {
+  PBC_ASSERT_MATCH2(x, a);
+  x->field->pow_mpz(x, a, n);
+}
+
+/*@manual epow
+Set 'x' = 'a'^'n'^, where 'n' is an element of a ring *Z*~N~
+for some 'N' (typically the order of the algebraic structure 'x' lies in).
+*/
+static inline void element_pow_zn(element_t x, element_t a, element_t n) {
+  mpz_t z;
+  PBC_ASSERT_MATCH2(x, a);
+  mpz_init(z);
+  element_to_mpz(z, n);
+  element_pow_mpz(x, a, z);
+  mpz_clear(z);
+}
+
+/*@manual earith
+Set 'n' = -'a'.
+*/
+static inline void element_neg(element_t n, element_t a) {
+  PBC_ASSERT_MATCH2(n, a);
+  n->field->neg(n, a);
+}
+
+/*@manual earith
+Set 'n' to the inverse of 'a'.
+*/
+static inline void element_invert(element_t n, element_t a) {
+  PBC_ASSERT_MATCH2(n, a);
+  n->field->invert(n, a);
+}
+
+/*@manual erandom
+If the 'e' lies in a finite algebraic structure,
+assigns a uniformly random element to 'e'.
+*/
+static inline void element_random(element_t e) {
+  e->field->random(e);
+}
+
+/*@manual ecmp
+Returns true if 'n' is 1.
+*/
+static inline int element_is1(element_t n) {
+  return n->field->is1(n);
+}
+
+/*@manual ecmp
+Returns true if 'n' is 0.
+*/
+static inline int element_is0(element_t n) {
+  return n->field->is0(n);
+}
+
+/*@manual ecmp
+Returns 0 if 'a' and 'b' are the same, nonzero otherwise.
+*/
+static inline int element_cmp(element_t a, element_t b) {
+  PBC_ASSERT_MATCH2(a, b);
+  return a->field->cmp(a, b);
+}
+
+/*@manual ecmp
+Returns nonzero if 'a' is a perfect square (quadratic residue),
+zero otherwise.
+*/
+static inline int element_is_sqr(element_t a) {
+  return a->field->is_sqr(a);
+}
+
+/*@manual ecmp
+*/
+static inline int element_sgn(element_t a) {
+  return a->field->sign(a);
+}
+
+/*@manual ecmp
+If 'a' is zero, returns 0. For nozero 'a' the behaviour depends on
+the algebraic structure, but has the property that
+element_sgn('a') = -element_sgn(-'a')
+and
+element_sgn('a') = 0 implies 'a' = 0 with overwhelming probability.
+*/
+static inline int element_sign(element_t a) {
+  return a->field->sign(a);
+}
+
+static inline void element_sqrt(element_t a, element_t b) {
+  PBC_ASSERT_MATCH2(a, b);
+  a->field->sqrt(a, b);
+}
+
+/*@manual etrade
+Returns the length in bytes the element 'e' will take to represent
+*/
+static inline int element_length_in_bytes(element_t e) {
+  if (e->field->fixed_length_in_bytes < 0) {
+    return e->field->length_in_bytes(e);
+  } else {
+    return e->field->fixed_length_in_bytes;
+  }
+}
+
+/*@manual etrade
+Converts 'e' to byte, writing the result in the buffer 'data'.
+The number of bytes it will write can be determined from calling
+*element_length_in_bytes()*. Returns number of bytes written.
+*/
+static inline int element_to_bytes(unsigned char *data, element_t e) {
+  return e->field->to_bytes(data, e);
+}
+
+/*@manual etrade
+Reads 'e' from the buffer 'data', and returns the number of bytes read.
+*/
+static inline int element_from_bytes(element_t e, unsigned char *data) {
+  return e->field->from_bytes(e, data);
+}
+
+/*@manual epow
+Sets 'x' = 'a1'^'n1'^ 'a2'^'n2'^, and is generally faster than
+performing two separate exponentiations.
+*/
+void element_pow2_mpz(element_t x, element_t a1, mpz_t n1, element_t a2,
+                      mpz_t n2);
+/*@manual epow
+Also sets 'x' = 'a1'^'n1'^ 'a2'^'n2'^,
+but 'n1', 'n2' must be elements of a ring *Z*~n~ for some integer n.
+*/
+static inline void element_pow2_zn(element_t x, element_t a1, element_t n1,
+                                   element_t a2, element_t n2) {
+  mpz_t z1, z2;
+  mpz_init(z1);
+  mpz_init(z2);
+  element_to_mpz(z1, n1);
+  element_to_mpz(z2, n2);
+  element_pow2_mpz(x, a1, z1, a2, z2);
+  mpz_clear(z1);
+  mpz_clear(z2);
+}
+
+/*@manual epow
+Sets 'x' = 'a1'^'n1'^ 'a2'^'n2'^ 'a3'^'n3'^,
+generally faster than performing three separate exponentiations.
+*/
+void element_pow3_mpz(element_t x, element_t a1, mpz_t n1,
+                      element_t a2, mpz_t n2, element_t a3, mpz_t n3);
+
+/*@manual epow
+Also sets 'x' = 'a1'^'n1'^ 'a2'^'n2'^ 'a3'^'n3'^,
+but 'n1', 'n2', 'n3' must be elements of a ring *Z*~n~ for some integer n.
+*/
+static inline void element_pow3_zn(element_t x, element_t a1, element_t n1,
+                                   element_t a2, element_t n2,
+                                   element_t a3, element_t n3) {
+  mpz_t z1, z2, z3;
+  mpz_init(z1);
+  mpz_init(z2);
+  mpz_init(z3);
+  element_to_mpz(z1, n1);
+  element_to_mpz(z2, n2);
+  element_to_mpz(z3, n3);
+  element_pow3_mpz(x, a1, z1, a2, z2, a3, z3);
+  mpz_clear(z1);
+  mpz_clear(z2);
+  mpz_clear(z3);
+}
+
+void field_clear(field_ptr f);
+
+element_ptr field_get_nqr(field_ptr f);
+void field_set_nqr(field_ptr f, element_t nqr);
+void field_gen_nqr(field_ptr f);
+
+void field_init(field_ptr f);
+
+static inline int mpz_is0(mpz_t z) {
+  return !mpz_sgn(z);
+  //return !mpz_cmp_ui(z, 0);
+}
+
+/*@manual etrade
+Assumes 'e' is a point on an elliptic curve.
+Writes the x-coordinate of 'e' to the buffer 'data'
+*/
+int element_to_bytes_x_only(unsigned char *data, element_t e);
+/*@manual etrade
+Assumes 'e' is a point on an elliptic curve.
+Sets 'e' to a point with
+x-coordinate represented by the buffer 'data'. This is not unique.
+For each 'x'-coordinate, there exist two different points, at least
+for the elliptic curves in PBC. (They are inverses of each other.)
+*/
+int element_from_bytes_x_only(element_t e, unsigned char *data);
+/*@manual etrade
+Assumes 'e' is a point on an elliptic curve.
+Returns the length in bytes needed to hold the x-coordinate of 'e'.
+*/
+int element_length_in_bytes_x_only(element_t e);
+
+/*@manual etrade
+If possible, outputs a compressed form of the element 'e' to
+the buffer of bytes 'data'.
+Currently only implemented for points on an elliptic curve.
+*/
+int element_to_bytes_compressed(unsigned char *data, element_t e);
+
+/*@manual etrade
+Sets element 'e' to the element in compressed form in the buffer of bytes
+'data'.
+Currently only implemented for points on an elliptic curve.
+*/
+int element_from_bytes_compressed(element_t e, unsigned char *data);
+
+/*@manual etrade
+Returns the number of bytes needed to hold 'e' in compressed form.
+Currently only implemented for points on an elliptic curve.
+*/
+int element_length_in_bytes_compressed(element_t e);
+
+/*@manual epow
+Prepare to exponentiate an element 'in', and store preprocessing information
+in 'p'.
+*/
+static inline void element_pp_init(element_pp_t p, element_t in) {
+  p->field = in->field;
+  in->field->pp_init(p, in);
+}
+
+/*@manual epow
+Clear 'p'. Should be called after 'p' is no longer needed.
+*/
+static inline void element_pp_clear(element_pp_t p) {
+  p->field->pp_clear(p);
+}
+
+/*@manual epow
+Raise 'in' to 'power' and store the result in 'out', where 'in'
+is a previously preprocessed element, that is, the second argument
+passed to a previous *element_pp_init* call.
+*/
+static inline void element_pp_pow(element_t out, mpz_ptr power,
+                                  element_pp_t p) {
+  p->field->pp_pow(out, power, p);
+}
+
+/*@manual epow
+Same except 'power' is an element of *Z*~n~ for some integer n.
+*/
+static inline void element_pp_pow_zn(element_t out, element_t power,
+                                     element_pp_t p) {
+  mpz_t z;
+  mpz_init(z);
+  element_to_mpz(z, power);
+  element_pp_pow(out, z, p);
+  mpz_clear(z);
+}
+
+void pbc_mpz_out_raw_n(unsigned char *data, int n, mpz_t z);
+void pbc_mpz_from_hash(mpz_t z, mpz_t limit,
+                       unsigned char *data, unsigned int len);
+
+/*@manual etrade
+For points, returns the number of coordinates.
+For polynomials, returns the number of coefficients.
+Otherwise returns zero.
+*/
+static inline int element_item_count(element_t e) {
+  return e->field->item_count(e);
+}
+
+/*@manual etrade
+For points, returns 'n'#th# coordinate.
+For polynomials, returns coefficient of 'x^n^'.
+Otherwise returns NULL.
+The element the return value points to may be modified.
+*/
+static inline element_ptr element_item(element_t e, int i) {
+  // TODO: Document the following:
+  // For polynomials, never zero the leading coefficient, e.g. never write:
+  //  element_set0(element_item(f, poly_degree(f)));
+  // Use poly_set_coeff0() to zero the leading coefficient.
+  return e->field->item(e, i);
+}
+
+// Returns the field containing the items.
+// Returns NULL if there are no items.
+static inline field_ptr element_item_field(element_t e) {
+  if (!element_item_count(e)) return NULL;
+  return element_item(e, 0)->field;
+}
+
+/*@manual etrade
+Equivalent to `element_item(a, 0)`.
+*/
+static inline element_ptr element_x(element_ptr a) {
+  return a->field->get_x(a);
+}
+/*@manual etrade
+Equivalent to `element_item(a, 1)`.
+*/
+static inline element_ptr element_y(element_ptr a) {
+  return a->field->get_y(a);
+}
+
+/*@manual epow
+Computes 'x' such that 'g^x^ = h' by brute force, where
+'x' lies in a field where `element_set_mpz()` makes sense.
+*/
+void element_dlog_brute_force(element_t x, element_t g, element_t h);
+
+/*@manual epow
+Computes 'x' such that 'g^x^ = h' using Pollard rho method, where
+'x' lies in a field where `element_set_mpz()` makes sense.
+*/
+void element_dlog_pollard_rho(element_t x, element_t g, element_t h);
+
+// Trial division up to a given limit. If limit == NULL, then there is no limit.
+// Call the callback for each factor found, abort and return 1 if the callback
+// returns nonzero, otherwise return 0.
+int pbc_trial_divide(int (*fun)(mpz_t factor,
+                                unsigned int multiplicity,
+                                void *scope_ptr),
+                     void *scope_ptr,
+                     mpz_t n,
+                     mpz_ptr limit);
+
+#endif  // __PBC_FIELD_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_fieldquadratic.h b/moon-abe/pbc-0.5.14/include/pbc_fieldquadratic.h
new file mode 100644
index 00000000..5a2111b3
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_fieldquadratic.h
@@ -0,0 +1,23 @@
+/*
+ * Quadratic field extensions.
+ */
+
+//requires
+// * field.h
+#ifndef __PBC_FIELDQUADRATIC_H__
+#define __PBC_FIELDQUADRATIC_H__
+
+// Initialize L as K[sqrt(a)], where a is a quadratic nonresidue of K. We
+// automatically randomly generate a if necessary (see field_get_nqr() in
+// field.c).
+void field_init_quadratic(field_ptr L, field_ptr K);
+
+// Initialize L as K[i], where i = sqrt(-1). Faster than the generic version.
+// Requires -1 to be a quadratic nonresidue in K.
+void field_init_fi(field_ptr L, field_ptr K);
+
+// Naturally map an element from a field K to K[a].
+void element_field_to_quadratic(element_ptr out, element_ptr in);
+void element_field_to_fi(element_ptr a, element_ptr b);
+
+#endif //__PBC_FIELDQUADRATIC_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_fp.h b/moon-abe/pbc-0.5.14/include/pbc_fp.h
new file mode 100644
index 00000000..3410cee1
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_fp.h
@@ -0,0 +1,26 @@
+/* There does not appear to be a succint name for rings of type Z/nZ.
+ * Sage calls it integer mod ring.
+ * NTL calls it ZZ_p.
+ * I'll call it fp, as it's the quickest to type.
+ * "zn" might be better since it can also handle composite numbers.
+ */
+// Requires:
+// * field.h
+// * gmp.h
+#ifndef __PBC_FP_H__
+#define __PBC_FP_H__
+
+void field_init_naive_fp(field_ptr f, mpz_t prime);
+void field_init_tiny_fp(field_ptr f, mpz_t prime);
+void field_init_fast_fp(field_ptr f, mpz_t prime);
+void field_init_faster_fp(field_ptr f, mpz_t prime);
+void field_init_mont_fp(field_ptr f, mpz_t prime);
+
+void pbc_tweak_use_fp(char *s);
+
+void element_tonelli(element_ptr x, element_ptr a);
+
+void field_init_fp(field_ptr f, mpz_t prime);
+
+int pbc_mpz_set_str(mpz_t z, const char *s, int base);
+#endif //__PBC_FP_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_g_param.h b/moon-abe/pbc-0.5.14/include/pbc_g_param.h
new file mode 100644
index 00000000..0b7bf45d
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_g_param.h
@@ -0,0 +1,28 @@
+// Type G pairings.
+
+// Requires:
+// * mnt.h
+// * param.h
+#ifndef __PBC_G_PARAM_H__
+#define __PBC_G_PARAM_H__
+
+struct symtab_s;
+int pbc_param_init_g(pbc_param_ptr par, struct symtab_s *tab);
+
+/*@manual gparam
+Type G curves are generated using the complex multiplication (CM) method.  This
+function sets 'p' to a type G pairing parameters from CM parameters 'cm'.
+They have embedding degree 10.
+
+To be secure, generic discrete log algorithms must be infeasible in groups of
+order r, and finite field discrete log algorithms must be infeasible in finite
+fields of order q^6^.  For usual CM parameters, r is a few bits smaller than q.
+
+They are quite slow at the moment so for now type F is a better choice.
+
+The file `param/g149.param` contains parameters for a
+type G pairing with 149-bit group and field sizes.
+*/
+void pbc_param_init_g_gen(pbc_param_t p, pbc_cm_ptr cm);
+
+#endif //__PBC_G_PARAM_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_hilbert.h b/moon-abe/pbc-0.5.14/include/pbc_hilbert.h
new file mode 100644
index 00000000..64bdf9c1
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_hilbert.h
@@ -0,0 +1,13 @@
+// Requires:
+// * gmp.h
+#ifndef __PBC_HILBERT_H__
+#define __PBC_HILBERT_H__
+
+// Allocate an array of mpz_t and fill it with the coefficients of the Hilbert
+// polynomial H_D(x). Returns the size of array.
+size_t pbc_hilbert(mpz_t **arr, int D);
+
+// Free an array allocated by `pbc_hilbert()`.
+void pbc_hilbert_free(mpz_t *arr, size_t n);
+
+#endif //__PBC_HILBERT_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_i_param.h b/moon-abe/pbc-0.5.14/include/pbc_i_param.h
new file mode 100644
index 00000000..3f0dde58
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_i_param.h
@@ -0,0 +1,23 @@
+// Eta_T pairing over ternary extension field
+//
+// Requires:
+// * pbc_param.h
+#ifndef __PBC_I_PARAM_H__
+#define __PBC_I_PARAM_H__
+
+struct symtab_s;
+int pbc_param_init_i(pbc_param_ptr par, struct symtab_s *);
+
+/*@manual aparam
+Generate type I pairing parameters and store them in 'p',
+where the group order is at least 2^'group_size'.
+
+To be as secure as 64 bit symmetric encryption, 'group_size' may be 150.
+To get 128 bit symmetric secure level, 'group_size' may be 696.
+
+The file `param/i.param` contains parameters for a type I pairing suitable for
+cryptographic use.
+*/
+void pbc_param_init_i_gen(pbc_param_ptr par, int group_size);
+
+#endif //__PBC_I_PARAM_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_memory.h b/moon-abe/pbc-0.5.14/include/pbc_memory.h
new file mode 100644
index 00000000..4c71a2e0
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_memory.h
@@ -0,0 +1,24 @@
+// Requires:
+// * stdlib.h
+#ifndef __PBC_MEMORY_H__
+#define __PBC_MEMORY_H__
+
+// Memory allocation functions used by PBC.
+extern void *(*pbc_malloc)(size_t);
+extern void *(*pbc_realloc)(void *, size_t);
+extern void (*pbc_free)(void *);
+
+void *pbc_calloc(size_t, size_t);
+
+/*@manual alloc
+Set custom allocation functions.  The parameters must be function pointers to
+drop-in replacements for malloc, realloc and free, except that malloc and
+realloc should terminate the program on failure: they must not return in this
+case.
+*/
+void pbc_set_memory_functions(void *(*malloc_fn)(size_t),
+        void *(*realloc_fn)(void *, size_t), void (*free_fn)(void *));
+
+char *pbc_strdup(const char *s);
+
+#endif //__PBC_MEMORY_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_mnt.h b/moon-abe/pbc-0.5.14/include/pbc_mnt.h
new file mode 100644
index 00000000..82e4993b
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_mnt.h
@@ -0,0 +1,49 @@
+//requires
+// * gmp.h
+#ifndef __PBC_MNT_H__
+#define __PBC_MNT_H__
+
+struct pbc_cm_s {
+  mpz_t q; //curve defined over F_q
+  mpz_t n; //has order n (= q - t + 1) in F_q (and r^2 in F_q^k)
+  mpz_t h; //h * r = n, r is prime
+  mpz_t r;
+  int D; //discrminant needed to find j-invariant
+  int k; //embedding degree
+};
+
+typedef struct pbc_cm_s *pbc_cm_ptr;
+typedef struct pbc_cm_s pbc_cm_t[1];
+
+/*@manual cminfo
+Initializes 'cm'.
+*/
+void pbc_cm_init(pbc_cm_t cm);
+/*@manual cminfo
+Clears 'cm'.
+*/
+void pbc_cm_clear(pbc_cm_t cm);
+
+/*@manual cminfo
+For a given discriminant D, searches for type D pairings suitable for
+cryptography (MNT curves of embedding degree 6).
+The group order is at most 'bitlimit' bits. For each set of CM parameters
+found, call 'callback' with +pbc_cm_t+ and given +void *+. If the callback
+returns nonzero, stops search and returns that value.
+Otherwise returns 0.
+*/
+int pbc_cm_search_d(int (*callback)(pbc_cm_ptr, void *), void *data,
+  unsigned int D, unsigned int bitlimit);
+
+/*@manual cminfo
+For a given discriminant D, searches for type G pairings suitable for
+cryptography (Freeman curve).
+The group order is at most 'bitlimit' bits. For each set of CM parameters
+found, call 'callback' with +pbc_cm_t+ and given +void *+. If the callback
+returns nonzero, stops search and returns that value.
+Otherwise returns 0.
+*/
+int pbc_cm_search_g(int (*callback)(pbc_cm_ptr, void *), void *data,
+  unsigned int D, unsigned int bitlimit);
+
+#endif //__PBC_MNT_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_multiz.h b/moon-abe/pbc-0.5.14/include/pbc_multiz.h
new file mode 100644
index 00000000..17657779
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_multiz.h
@@ -0,0 +1,20 @@
+// Multinomnials with integer coefficients.
+
+//requires
+// * field.h
+
+#ifndef __PBC_FIELDMULTI_H__
+#define __PBC_FIELDMULTI_H__
+
+void field_init_multiz(field_ptr f);
+
+element_ptr multiz_new_list(element_ptr e);
+void multiz_append(element_ptr l, element_ptr m);
+
+void multiz_to_mpz(mpz_ptr z, multiz ep);
+int multiz_is_z(multiz m);
+multiz multiz_at(multiz m, int i);
+int multiz_count(multiz m);
+int multiz_is0(multiz m);
+
+#endif //__PBC_FIELDMULTI_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_pairing.h b/moon-abe/pbc-0.5.14/include/pbc_pairing.h
new file mode 100644
index 00000000..1f127fb1
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_pairing.h
@@ -0,0 +1,280 @@
+// Requires:
+// * stdio.h
+// * gmp.h
+// * utils.h
+// * field.h
+// * param.h
+#ifndef __PBC_PAIRING_H__
+#define __PBC_PAIRING_H__
+
+struct pairing_pp_s {
+  struct pairing_s *pairing;
+  void *data;
+};
+typedef struct pairing_pp_s pairing_pp_t[1];
+typedef struct pairing_pp_s *pairing_pp_ptr;
+
+struct pairing_s {
+  mpz_t r; // order of G1, G2, GT
+  field_t Zr; // the field Z_r
+  field_ptr G1, G2;
+  field_t GT; // group of rth roots of unity
+
+  mpz_t phikonr;
+  // Phi_k(q)/r where Phi_k is the kth cyclotomic polynomial,
+  // q as in F_q, is the base field
+
+  void (*phi)(element_ptr out, element_ptr in, struct pairing_s *pairing); //isomorphism G2 --> G1
+  void (*map)(element_ptr out, element_ptr in1, element_ptr in2,
+      struct pairing_s *p);
+  void (*prod_pairings)(element_ptr out, element_t in1[], element_t in2[], int n_prod,
+            struct pairing_s *p);  //calculate a product of pairings at one time.
+  // is_almost coddh returns true given (g, g^x, h, h^x) or (g, g^x, h, h^-x)
+  // order is important: a, b are from G1, c, d are from G2
+  int (*is_almost_coddh)(element_ptr a, element_ptr b,
+      element_ptr c, element_ptr d,
+      struct pairing_s *p);
+  void (*clear_func)(struct pairing_s *);
+  void (*pp_init)(pairing_pp_t p, element_t in1, struct pairing_s *);
+  void (*pp_clear)(pairing_pp_t p);
+  void (*pp_apply)(element_t out, element_t in2, pairing_pp_t p);
+  void (*finalpow)(element_t e);
+  void (*option_set)(struct pairing_s *, char *key, char *value);
+  void *data;
+};
+
+typedef struct pairing_s pairing_t[1];
+typedef struct pairing_s *pairing_ptr;
+
+// TODO: The 'pairing' argument is redundant.
+/*@manual pairing_apply
+Get ready to perform a pairing whose first input is 'in1',
+and store the results of time-saving precomputation in 'p'.
+*/
+static inline void pairing_pp_init(pairing_pp_t p, element_t in1, pairing_t pairing) {
+  if (element_is0(in1)) {
+    p->pairing = NULL;
+    return;
+  }
+  p->pairing = pairing;
+  pairing->pp_init(p, in1, pairing);
+}
+
+/*@manual pairing_apply
+Clear 'p'. This should be called after 'p' is no longer needed.
+*/
+static inline void pairing_pp_clear(pairing_pp_t p) {
+  if (!p->pairing) {
+    // happens when p was initialized with identity
+    return;
+  }
+  p->pairing->pp_clear(p);
+}
+
+/*@manual pairing_apply
+Compute a pairing using 'in2' and the preprocessed information stored in 'p'
+and store the output in 'out'. The inputs to the pairing are the element
+previously used to initialize 'p' and the element 'in2'.
+*/
+static inline void pairing_pp_apply(element_t out, element_t in2, pairing_pp_t p) {
+  if (!p->pairing) {
+    element_set0(out);
+    return;
+  }
+  if (element_is0(in2)) {
+    element_set0(out);
+    return;
+  }
+  p->pairing->pp_apply((element_ptr) out->data, in2, p);
+}
+
+/*@manual pairing_init
+Initialize pairing from parameters in a ASCIIZ string 'str'
+Returns 0 on success, 1 on failure.
+*/
+int pairing_init_set_str(pairing_t pairing, const char *s);
+
+/*@manual pairing_init
+Same, but read at most 'len' bytes.
+If 'len' is 0, it behaves as the previous function.
+Returns 0 on success, 1 on failure.
+*/
+int pairing_init_set_buf(pairing_t pairing, const char *s, size_t len);
+
+/*@manual pairing_init
+Initialize a pairing with pairing parameters 'p'.
+*/
+void pairing_init_pbc_param(struct pairing_s *pairing, pbc_param_ptr p);
+
+/*@manual pairing_init
+Free the space occupied by 'pairing'. Call
+whenever a +pairing_t+ variable is no longer needed.
+Only call this after all elements associated with 'pairing'
+have been cleared, as they need information stored in the 'pairing'
+structure.
+*/
+void pairing_clear(pairing_t pairing);
+
+static inline void pairing_apply(element_t out, element_t in1, element_t in2,
+    pairing_t pairing) {
+  PBC_ASSERT(pairing->GT == out->field, "pairing output mismatch");
+  PBC_ASSERT(pairing->G1 == in1->field, "pairing 1st input mismatch");
+  PBC_ASSERT(pairing->G2 == in2->field, "pairing 2nd input mismatch");
+  if (element_is0(in1)) {
+    element_set0(out);
+    return;
+  }
+  if (element_is0(in2)) {
+    element_set0(out);
+    return;
+  }
+  // TODO: 'out' is an element of a multiplicative subgroup, but the
+  // pairing routine expects it to be an element of the full group, hence
+  // the 'out->data'. I should make this clearer.
+  pairing->map((element_ptr) out->data, in1, in2, pairing);
+}
+
+/*@manual pairing_apply
+Computes a pairing: 'out' = 'e'('in1', 'in2'),
+where 'in1', 'in2', 'out' must be in the groups G1, G2, GT.
+*/
+static inline void element_pairing(element_t out, element_t in1, element_t in2) {
+  pairing_ptr pairing = out->field->pairing;
+  PBC_ASSERT(pairing != NULL, "pairing output mismatch");
+  pairing_apply(out, in1, in2, pairing);
+}
+
+/*@manual pairing_apply
+Computes the product of pairings, that is
+'out' = 'e'('in1'[0], 'in2'[0]) ... 'e'('in1'[n-1], 'in2'[n-1]).
+The arrays 'in1', 'in2' must have at least 'n' elements belonging to
+the groups G1, G2 respectively, and 'out' must belong to the group GT.
+*/
+static inline void element_prod_pairing(
+    element_t out, element_t in1[], element_t in2[], int n) {
+  pairing_ptr pairing = out->field->pairing;
+  int i;
+  PBC_ASSERT(pairing->GT == out->field, "pairing output mismatch");
+  for(i = 0; i < n; i++) {
+    PBC_ASSERT(pairing->G1 == in1[i]->field, "pairing 1st input mismatch");
+    PBC_ASSERT(pairing->G2 == in2[i]->field, "pairing 2nd input mismatch");
+    if (element_is0(in1[i])) {
+      element_set0(out);
+      return;
+    }
+    if (element_is0(in2[i])) {
+      element_set0(out);
+      return;
+    }
+  }
+  pairing->prod_pairings((element_ptr) out->data, in1, in2, n, pairing);
+}
+
+/*@manual pairing_op
+Returns true if G1 and G2 are the same group.
+*/
+static inline int pairing_is_symmetric(pairing_t pairing) {
+  return pairing->G1 == pairing->G2;
+}
+
+/*@manual pairing_op
+Returns the length in bytes needed to represent an element of G1.
+*/
+static inline int pairing_length_in_bytes_G1(pairing_t pairing) {
+  return pairing->G1->fixed_length_in_bytes;
+}
+
+/*@manual pairing_op
+Returns the length in bytes needed to represent the x-coordinate of
+an element of G1.
+*/
+static inline int pairing_length_in_bytes_x_only_G1(pairing_t pairing) {
+  return pairing->G1->fixed_length_in_bytes / 2;
+}
+
+/*@manual pairing_op
+Returns the length in bytes needed to represent a compressed form of
+an element of G1. There is some overhead in decompressing.
+*/
+static inline int pairing_length_in_bytes_compressed_G1(pairing_t pairing) {
+  return pairing->G1->fixed_length_in_bytes / 2 + 1;
+}
+
+/*@manual pairing_op
+Returns the length in bytes needed to represent an element of G2.
+*/
+static inline int pairing_length_in_bytes_G2(pairing_t pairing) {
+  return pairing->G2->fixed_length_in_bytes;
+}
+
+/*@manual pairing_op
+Returns the length in bytes needed to represent a compressed form of
+an element of G2. There is some overhead in decompressing.
+*/
+static inline int pairing_length_in_bytes_compressed_G2(pairing_t pairing) {
+  return pairing->G2->fixed_length_in_bytes / 2 + 1;
+}
+
+/*@manual pairing_op
+Returns the length in bytes needed to represent the x-coordinate of
+an element of G2.
+*/
+static inline int pairing_length_in_bytes_x_only_G2(pairing_t pairing) {
+  return pairing->G2->fixed_length_in_bytes / 2;
+}
+
+/*@manual pairing_op
+Returns the length in bytes needed to represent an element of GT.
+*/
+static inline int pairing_length_in_bytes_GT(pairing_t pairing) {
+  return pairing->GT->fixed_length_in_bytes;
+}
+
+/*@manual pairing_op
+Returns the length in bytes needed to represent an element of Zr.
+*/
+static inline int pairing_length_in_bytes_Zr(pairing_t pairing) {
+  return pairing->Zr->fixed_length_in_bytes;
+}
+
+static inline int is_almost_coddh(element_t a, element_t b,
+    element_t c, element_t d, pairing_t pairing) {
+  return pairing->is_almost_coddh(a, b, c, d, pairing);
+}
+
+/*@manual einit.1
+*/
+static inline void element_init_G1(element_t e, pairing_t pairing) {
+  element_init(e, pairing->G1);
+}
+
+/*@manual einit.1
+*/
+static inline void element_init_G2(element_t e, pairing_t pairing) {
+  element_init(e, pairing->G2);
+}
+
+/*@manual einit.1
+Initialize 'e' to be an element of the group G1, G2 or GT of 'pairing'.
+*/
+static inline void element_init_GT(element_t e, pairing_t pairing) {
+  element_init(e, pairing->GT);
+}
+
+/*@manual einit.1
+Initialize 'e' to be an element of the ring Z_r of 'pairing'.
+r is the order of the groups G1, G2 and GT that are involved in the pairing.
+*/
+static inline void element_init_Zr(element_t e, pairing_t pairing) {
+  element_init(e, pairing->Zr);
+}
+
+static inline void pairing_option_set(pairing_t pairing, char *key, char *value) {
+  pairing->option_set(pairing, key, value);
+}
+
+// Initialize GT = group of rth roots of unity in f.
+// Requires pairing->r has been set.
+void pairing_GT_init(pairing_ptr pairing, field_t f);
+
+#endif //__PBC_PAIRING_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_param.h b/moon-abe/pbc-0.5.14/include/pbc_param.h
new file mode 100644
index 00000000..143ab73c
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_param.h
@@ -0,0 +1,49 @@
+// Requires:
+// * gmp.h
+#ifndef __PBC_PARAM_H__
+#define __PBC_PARAM_H__
+
+struct pairing_s;
+struct pbc_param_interface_s {
+  void (*clear)(void *);
+  void (*init_pairing)(struct pairing_s *, void *);
+  void (*out_str)(FILE *stream, void *data);
+};
+typedef struct pbc_param_interface_s pbc_param_interface_t[1];
+typedef struct pbc_param_interface_s *pbc_param_interface_ptr;
+
+struct pbc_param_s {
+  pbc_param_interface_ptr api;
+  void *data;
+};
+typedef struct pbc_param_s *pbc_param_ptr;
+typedef struct pbc_param_s pbc_param_t[1];
+
+/*@manual param
+Initializes pairing parameters from the string 's'.
+Returns 0 if successful, 1 otherwise.
+*/
+int pbc_param_init_set_str(pbc_param_t par, const char *s);
+
+/*@manual param
+Same, but read at most 'len' bytes.
+If 'len' is 0, it behaves as the previous function.
+Returns 0 if successful, 1 otherwise.
+*/
+int pbc_param_init_set_buf(pbc_param_t par, const char *s, size_t len);
+
+/*@manual param
+Write pairing parameters to ''stream'' in a text format.
+*/
+static inline void pbc_param_out_str(FILE *stream, pbc_param_ptr p) {
+  p->api->out_str(stream, p->data);
+}
+
+/*@manual param
+Clear 'p'. Call after 'p' is no longer needed.
+*/
+static inline void pbc_param_clear(pbc_param_ptr p) {
+  p->api->clear(p->data);
+}
+
+#endif //__PBC_PARAM_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_poly.h b/moon-abe/pbc-0.5.14/include/pbc_poly.h
new file mode 100644
index 00000000..bca8e108
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_poly.h
@@ -0,0 +1,57 @@
+// Polynomial rings R[x], and polynomial rings modulo polynomials,
+// i.e. R[x]_{f(x)}.
+
+// Requires:
+// * gmp.h
+// * field.h
+#ifndef __PBC_POLY_H__
+#define __PBC_POLY_H__
+
+// Initializes a polynomial ring.
+void field_init_poly(field_ptr f, field_ptr base_field);
+
+// Initializes a polynomial modulo ring.
+// Requires poly to be monic.
+void field_init_polymod(field_ptr f, element_ptr poly);
+
+#pragma GCC visibility push(hidden)
+// Internal library functions:
+
+// Returns deg f.
+static inline int poly_degree(element_ptr f) {
+  return element_item_count(f) - 1;
+}
+
+// Returns base field of f (where the coefficients live).
+field_ptr poly_base_field(element_t f);
+
+// Sets the coefficient of x^n to 0.
+void poly_set_coeff0(element_ptr f, int n);
+
+// Sets the coefficient of x^n to 1.
+void poly_set_coeff1(element_ptr f, int n);
+
+// Sets the coefficient of x^n to a.
+void poly_set_coeff(element_ptr f, element_ptr a, int n);
+
+// Sets f = x.
+void poly_setx(element_ptr f);
+void poly_const_mul(element_ptr res, element_ptr a, element_ptr poly);
+
+// Returns 0 when a root exists and sets root to one of the roots.
+int poly_findroot(element_ptr root, element_ptr poly);
+
+// Returns 1 if polynomial is irreducible, 0 otherwise.
+// Requires the polynomial to be monic.
+int poly_is_irred(element_ptr f);
+void poly_random_monic(element_ptr f, int deg);
+
+void element_field_to_poly(element_t poly, element_t constant);
+void element_field_to_polymod(element_ptr f, element_ptr a);
+
+void polymod_const_mul(element_ptr res, element_ptr a, element_ptr e);
+int polymod_field_degree(field_t f);
+
+#pragma GCC visibility pop
+
+#endif //__PBC_POLY_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_random.h b/moon-abe/pbc-0.5.14/include/pbc_random.h
new file mode 100644
index 00000000..df688b9a
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_random.h
@@ -0,0 +1,32 @@
+// Requires:
+// * gmp.h
+#ifndef __PBC_RANDOM_H__
+#define __PBC_RANDOM_H__
+
+/*@manual pbcrandom
+Sets 'filename' as a source of random bytes. For example,
+on Linux one might use `/dev/random`.
+*/
+void pbc_random_set_file(char *filename);
+
+/*@manual pbcrandom
+Uses a determinstic random number generator, seeded with 'seed'.
+*/
+void pbc_random_set_deterministic(unsigned int seed);
+
+/*@manual pbcrandom
+Uses given function as a random number generator.
+*/
+void pbc_random_set_function(void (*fun)(mpz_t, mpz_t, void *), void *data);
+
+/*@manual pbcrandom
+Selects a random 'z' that is less than 'limit'.
+*/
+void pbc_mpz_random(mpz_t z, mpz_t limit);
+
+/*@manual pbcrandom
+Selects a random 'bits'-bit integer 'z'.
+*/
+void pbc_mpz_randomb(mpz_t z, unsigned int bits);
+
+#endif //__PBC_RANDOM_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_singular.h b/moon-abe/pbc-0.5.14/include/pbc_singular.h
new file mode 100644
index 00000000..afa6156f
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_singular.h
@@ -0,0 +1,11 @@
+//requires
+// * stdio.h
+// * gmp.h
+// * field.h
+#ifndef __PBC_SINGULAR_H__
+#define __PBC_SINGULAR_H__
+
+void field_init_curve_singular_with_node(field_t c, field_t field);
+void pairing_init_singular_with_node(pairing_t pairing, mpz_t q);
+
+#endif //__PBC_SINGULAR_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_ternary_extension_field.h b/moon-abe/pbc-0.5.14/include/pbc_ternary_extension_field.h
new file mode 100644
index 00000000..8effc16a
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_ternary_extension_field.h
@@ -0,0 +1,22 @@
+// some ternary extension fields,
+// including $GF(3^m) = GF(3)[x]/(x^m + x^t + 2)$,
+//           $GF(3^{2*m}) = GF(3^m)[x]/(x^2 + 1)$,
+//           $GF(3^{3*m}) = GF(3^m)[x]/(x^3 - x - 1)$,
+//           and $GF(3^{6*m}) = GF(3^{2*m})[x]/(x^3 - x - 1)$
+//
+// Requires:
+// * pbc_field.h
+
+#ifndef __PBC_TERNARY_EXTENSION_FIELD_H__
+#define __PBC_TERNARY_EXTENSION_FIELD_H__
+
+/* initialize $f$ as $GF(3)[x]/(x^m + x^t + 2)$ */
+void field_init_gf3m(field_t f, unsigned m, unsigned t);
+
+/* initialize $f$ as $base_field[x]/(x^2 + 1)$ */
+void field_init_gf32m(field_t f, field_t base_field);
+
+/* initialize $f$ as $base_field[x]/(x^3 - x - 1)$ */
+void field_init_gf33m(field_t f, field_t base_field);
+
+#endif //__PBC_TERNARY_EXTENSION_FIELD_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_test.h b/moon-abe/pbc-0.5.14/include/pbc_test.h
new file mode 100644
index 00000000..35d6f754
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_test.h
@@ -0,0 +1,42 @@
+// Useful for tests.
+
+#ifndef __PBC_TEST_H__
+#define __PBC_TEST_H__
+
+/*@manual test
+Initializes pairing from file specified as first argument, or from standard
+input if there is no first argument.
+*/
+static inline void pbc_demo_pairing_init(pairing_t pairing, int argc, char **argv) {
+  char s[16384];
+  FILE *fp = stdin;
+
+  if (argc > 1) {
+    fp = fopen(argv[1], "r");
+    if (!fp) pbc_die("error opening %s", argv[1]);
+  }
+  size_t count = fread(s, 1, 16384, fp);
+  if (!count) pbc_die("input error");
+  fclose(fp);
+
+  if (pairing_init_set_buf(pairing, s, count)) pbc_die("pairing init failed");
+}
+
+/*@manual test
+Returns seconds elapsed since the first call to this function.
+Returns 0 the first time.
+*/
+double pbc_get_time(void);
+
+/*@manual test
+Macro: if `condition` evaluates to 0 then print an error.
+*/
+#define EXPECT(condition) \
+  if (condition); else pbc_err_count++, fprintf(stderr, "\n*** FAIL ***\n  %s:%d: %s\n\n", __FILE__, __LINE__, #condition)
+
+/*@manual test
+Total number of failed EXPECT checks.
+*/
+int pbc_err_count;
+
+#endif //__PBC_TEST_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_utils.h b/moon-abe/pbc-0.5.14/include/pbc_utils.h
new file mode 100644
index 00000000..62c02b07
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_utils.h
@@ -0,0 +1,86 @@
+#ifndef __PBC_UTILS_H__
+#define __PBC_UTILS_H__
+
+#ifdef PBC_DEBUG
+
+/*@manual debug
+Macro: if `expr` evaluates to 0, print `msg` and exit.
+*/
+#define PBC_ASSERT(expr, msg) \
+    (pbc_assert(expr, msg, __func__))
+
+/*@manual debug
+Macro: if elements `a` and `b` are from different fields then exit.
+*/
+#define PBC_ASSERT_MATCH2(a, b) \
+    (pbc_assert_match2(a, b, __func__))
+
+/*@manual debug
+Macro: if elements `a`, `b` and `c` are from different fields then exit.
+*/
+#define PBC_ASSERT_MATCH3(a, b, c) \
+    (pbc_assert_match3(a, b, c, __func__))
+
+#else
+
+#define PBC_ASSERT(expr, msg) ((void) (0))
+#define PBC_ASSERT_MATCH2(a, b) ((void) (0))
+#define PBC_ASSERT_MATCH3(a, b, c) ((void) (0))
+
+#endif
+
+// die, warn and info based on Git code.
+
+/*@manual log
+By default error messages are printed to standard error.
+Call `pbc_set_msg_to_stderr(0)` to suppress messages.
+*/
+int pbc_set_msg_to_stderr(int i);
+
+/*@manual log
+Reports error message and exits with code 128.
+*/
+void pbc_die(const char *err, ...)
+    __attribute__((__noreturn__))
+    __attribute__((format (printf, 1, 2)));
+
+/*@manual log
+Reports informational message.
+*/
+void pbc_info(const char *err, ...)
+    __attribute__((format (printf, 1, 2)));
+
+/*@manual log
+Reports warning message.
+*/
+void pbc_warn(const char *err, ...)
+    __attribute__((format (printf, 1, 2)));
+
+/*@manual log
+Reports error message.
+*/
+void pbc_error(const char *err, ...)
+    __attribute__((format (printf, 1, 2)));
+
+#ifndef UNUSED_VAR
+#if defined(__GNUC__)
+// We could use __attribute__((unused)) instead.
+#define UNUSED_VAR(a) (void) a
+#else
+// From the ACE project: http://www.cs.wustl.edu/~schmidt/ACE.html
+// silences warnings, and generates no code for many compilers
+// See ACE_wrappers/ace/ace/config-macros.h:391
+//
+// Not anymore: gcc no longer likes it -blynn
+#define UNUSED_VAR(a) do { /* nothing */ } while (&a == 0)
+#endif
+#endif
+
+// For storing small integers in void *
+// C99 standard introduced the intptr_t and uintptr_t types,
+// guaranteed to be able to hold pointers
+static inline void *int_to_voidp(intptr_t i) {
+  return (void *) i;
+}
+
+#endif //__PBC_UTILS_H__
diff --git a/moon-abe/pbc-0.5.14/include/pbc_z.h b/moon-abe/pbc-0.5.14/include/pbc_z.h
new file mode 100644
index 00000000..2ec54af3
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/include/pbc_z.h
@@ -0,0 +1,12 @@
+// ring of integers Z
+// wrappers around GMP's mpz_t
+
+//requires
+// * field.h
+
+#ifndef __PBC_FIELDMPZ_H__
+#define __PBC_FIELDMPZ_H__
+
+void field_init_z(field_ptr f);
+
+#endif //__PBC_FIELDMPZ_H__