diff --git a/src/lib/math/pcurves/pcurves_secp256k1/pcurves_secp256k1.cpp b/src/lib/math/pcurves/pcurves_secp256k1/pcurves_secp256k1.cpp
index 3f66142da64..d3c3d6ce152 100644
--- a/src/lib/math/pcurves/pcurves_secp256k1/pcurves_secp256k1.cpp
+++ b/src/lib/math/pcurves/pcurves_secp256k1/pcurves_secp256k1.cpp
@@ -49,13 +49,145 @@ class Params final : public EllipticCurveParameters<
 };
 
 // clang-format on
-
 #if BOTAN_MP_WORD_BITS == 64
-class Curve final : public EllipticCurve<Params, Secp256k1Rep> {};
+typedef EllipticCurve<Params, Secp256k1Rep> Secp256k1Base;
 #else
-class Curve final : public EllipticCurve<Params> {};
+typedef EllipticCurve<Params> Secp256k1Base;
 #endif
 
+class Curve final : public Secp256k1Base {
+   public:
+      // Return the square of the inverse of x
+      static FieldElement fe_invert2(const FieldElement& x) {
+         auto z = x.square();
+         z *= x;
+         auto t0 = z;
+         t0.square_n(2);
+         t0 *= z;
+         auto t1 = t0.square();
+         auto t2 = t1 * x;
+         t1 = t2;
+         t1.square_n(2);
+         t1 *= z;
+         auto t3 = t1;
+         t3.square_n(4);
+         t0 *= t3;
+         t3 = t0;
+         t3.square_n(11);
+         t0 *= t3;
+         t3 = t0;
+         t3.square_n(5);
+         t2 *= t3;
+         t3 = t2;
+         t3.square_n(27);
+         t2 *= t3;
+         t3 = t2;
+         t3.square_n(54);
+         t2 *= t3;
+         t3 = t2;
+         t3.square_n(108);
+         t2 *= t3;
+         t2.square_n(7);
+         t1 *= t2;
+         t1.square_n(23);
+         t0 *= t1;
+         t0.square_n(5);
+         t0 *= x;
+         t0.square_n(3);
+         z *= t0;
+         z.square_n(2);
+         return z;
+      }
+
+      static Scalar scalar_invert(const Scalar& x) {
+         auto z = x.square();
+         auto t2 = x * z;
+         auto t6 = t2 * z;
+         auto t5 = t6 * z;
+         auto t0 = t5 * z;
+         auto t3 = t0 * z;
+         auto t1 = t3 * z;
+         z = t1;
+         z.square_n(2);
+         z *= t3;
+         auto t4 = z.square();
+         auto t7 = t4 * x;
+         t4 = t7.square();
+         t4 *= x;
+         auto t9 = t4;
+         t9.square_n(3);
+         auto t10 = t9;
+         t10.square_n(2);
+         auto t11 = t10.square();
+         auto t8 = t11.square();
+         auto t12 = t8;
+         t12.square_n(7);
+         t11 *= t12;
+         t11.square_n(9);
+         t8 *= t11;
+         t11 = t8;
+         t11.square_n(6);
+         t10 *= t11;
+         t10.square_n(26);
+         t8 *= t10;
+         t10 = t8;
+         t10.square_n(4);
+         t9 *= t10;
+         t9.square_n(60);
+         t8 *= t9;
+         t7 *= t8;
+         t7.square_n(5);
+         t7 *= t3;
+         t7.square_n(3);
+         t7 *= t6;
+         t7.square_n(4);
+         t7 *= t6;
+         t7.square_n(4);
+         t7 *= t5;
+         t7.square_n(5);
+         t7 *= t1;
+         t7.square_n(2);
+         t7 *= t2;
+         t7.square_n(5);
+         t7 *= t5;
+         t7.square_n(6);
+         t7 *= t1;
+         t7.square_n(5);
+         t7 *= t3;
+         t7.square_n(4);
+         t7 *= t1;
+         t7.square_n(3);
+         t7 *= x;
+         t7.square_n(6);
+         t6 *= t7;
+         t6.square_n(10);
+         t6 *= t5;
+         t6.square_n(4);
+         t5 *= t6;
+         t5.square_n(9);
+         t4 *= t5;
+         t4.square_n(5);
+         t4 *= t0;
+         t4.square_n(6);
+         t3 *= t4;
+         t3.square_n(4);
+         t3 *= t1;
+         t3.square_n(5);
+         t2 *= t3;
+         t2.square_n(6);
+         t2 *= t1;
+         t2.square_n(10);
+         t1 *= t2;
+         t1.square_n(4);
+         t0 *= t1;
+         t0.square_n(6);
+         t0 *= x;
+         t0.square_n(8);
+         z *= t0;
+         return z;
+      }
+};
+
 }  // namespace secp256k1
 
 }  // namespace
diff --git a/src/lib/math/pcurves/pcurves_secp256r1/pcurves_secp256r1.cpp b/src/lib/math/pcurves/pcurves_secp256r1/pcurves_secp256r1.cpp
index 618410d89af..51bddadca52 100644
--- a/src/lib/math/pcurves/pcurves_secp256r1/pcurves_secp256r1.cpp
+++ b/src/lib/math/pcurves/pcurves_secp256r1/pcurves_secp256r1.cpp
@@ -165,6 +165,80 @@ class Curve final : public EllipticCurve<Params, Secp256r1Rep> {
 
          return r;
       }
+
+      static Scalar scalar_invert(const Scalar& x) {
+         auto t1 = x.square();
+         auto t5 = t1.square();
+         auto t2 = t5 * x;
+         auto t10 = t2 * x;
+         auto t3 = t2 * t5;
+         auto z = t10 * t3;
+         auto t9 = t3.square();
+         auto t4 = t10 * z;
+         auto t0 = t10 * t9;
+         auto t13 = t0 * t1;
+         auto t8 = t13 * t4;
+         t4 = t3 * t8;
+         auto t7 = t2 * t4;
+         t2 = t1 * t7;
+         auto t6 = t7 * t9;
+         t3 = t6 * t9;
+         t1 *= t3;
+         auto t12 = t3 * t9;
+         t5 *= t12;
+         auto t11 = t10 * t5;
+         t0 *= t11;
+         t9 *= t0;
+         t10 *= t9;
+         t4 *= t10;
+         t13 *= t4;
+         auto t14 = t13;
+         t14.square_n(8);
+         t13 *= t14;
+         t14 = t13;
+         t14.square_n(16);
+         t14 *= t13;
+         t14.square_n(48);
+         t14 *= t13;
+         t14.square_n(16);
+         t14 *= t13;
+         t14.square_n(16);
+         t14 *= t13;
+         t14.square_n(16);
+         t13 *= t14;
+         t13.square_n(6);
+         t13 *= t8;
+         t13.square_n(9);
+         t12 *= t13;
+         t12.square_n(8);
+         t11 *= t12;
+         t11.square_n(9);
+         t10 *= t11;
+         t10.square_n(8);
+         t9 *= t10;
+         t9.square_n(9);
+         t8 *= t9;
+         t8.square_n(8);
+         t7 *= t8;
+         t7.square_n(11);
+         t6 *= t7;
+         t6.square_n(9);
+         t5 *= t6;
+         t5.square_n(10);
+         t4 *= t5;
+         t4.square_n(8);
+         t3 *= t4;
+         t3.square_n(7);
+         t2 *= t3;
+         t2.square_n(10);
+         t1 *= t2;
+         t1.square_n(10);
+         t0 *= t1;
+         t0.square_n(6);
+         z *= t0;
+
+         return z;
+      }
 };
 
 }  // namespace secp256r1