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diff --git a/moon-abe/pbc-0.5.14/include/pbc_curve.h b/moon-abe/pbc-0.5.14/include/pbc_curve.h
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+// 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__