diff --git a/include/decaf.h b/include/decaf.h
index 9eb5e78..b7f0ff2 100644
--- a/include/decaf.h
+++ b/include/decaf.h
@@ -63,6 +63,11 @@ typedef struct decaf_448_point_s {
     decaf_word_t x[DECAF_448_LIMBS],y[DECAF_448_LIMBS],z[DECAF_448_LIMBS],t[DECAF_448_LIMBS];
 } decaf_448_point_t[1];
 
+/** Precomputed table based on a point.  Can be trivial implementation. */
+typedef struct decaf_448_precomputed_s {
+    decaf_448_point_t p[1];
+} decaf_448_precomputed_t[1];
+
 /** Scalar is stored packed, because we don't need the speed. */
 typedef struct decaf_448_scalar_s {
     decaf_word_t limb[DECAF_448_SCALAR_LIMBS];
@@ -78,23 +83,26 @@ static const decaf_bool_t DECAF_SUCCESS = -(decaf_bool_t)1 /*DECAF_TRUE*/,
 /** The prime p, for debugging purposes.
  * TODO: prevent this scalar from actually being used for non-debugging purposes?
  */
-const decaf_448_scalar_t decaf_448_scalar_p API_VIS;
+extern const decaf_448_scalar_t decaf_448_scalar_p API_VIS;
 
 /** A scalar equal to 1. */
-const decaf_448_scalar_t decaf_448_scalar_one API_VIS;
+extern const decaf_448_scalar_t decaf_448_scalar_one API_VIS;
 
 /** A scalar equal to 0. */
-const decaf_448_scalar_t decaf_448_scalar_zero API_VIS;
+extern const decaf_448_scalar_t decaf_448_scalar_zero API_VIS;
 
 /** The identity point on the curve. */
-const decaf_448_point_t decaf_448_point_identity API_VIS;
+extern const decaf_448_point_t decaf_448_point_identity API_VIS;
 
 /**
  * An arbitrarily chosen base point on the curve.
  * Equal to Ed448-Goldilocks base point defined by DJB, except of course that
  * it's on the twist in this case.  TODO: choose a base point with nice encoding?
  */
-const decaf_448_point_t decaf_448_point_base API_VIS;
+extern const struct decaf_448_point_s *decaf_448_point_base API_VIS;
+
+/** Precomputed table for the base point on the curve. */
+extern const decaf_448_precomputed_t decaf_448_precomputed_base API_VIS;
 
 #ifdef __cplusplus
 extern "C" {
@@ -300,6 +308,37 @@ void decaf_448_point_scalarmul (
     const decaf_448_scalar_t scalar
 ) API_VIS NONNULL3;
 
+/**
+ * @brief Precompute a table for fast scalar multiplication.
+ * Some implementations do not include precomputed points; for
+ * those implementations, this implementation simply copies the
+ * point.
+ *
+ * @param [out] a A precomputed table of multiples of the point.
+ * @param [in] b Any point.
+ */
+void decaf_448_precompute (
+    decaf_448_precomputed_t a,
+    const decaf_448_point_t b
+) API_VIS NONNULL2;
+
+/**
+ * @brief Multiply a precomputed base point by a scalar:
+ * scaled = scalar*base.
+ * Some implementations do not include precomputed points; for
+ * those implementations, this function is the same as
+ * decaf_448_point_scalarmul
+ *
+ * @param [out] scaled The scaled point base*scalar
+ * @param [in] base The point to be scaled.
+ * @param [in] scalar The scalar to multiply by.
+ */
+void decaf_448_precomputed_scalarmul (
+    decaf_448_point_t scaled,
+    const decaf_448_precomputed_t base,
+    const decaf_448_scalar_t scalar
+) API_VIS NONNULL3;
+
 /**
  * @brief Multiply two base points by two scalars:
  * scaled = scalar1*base1 + scalar2*base2.
diff --git a/src/decaf.c b/src/decaf.c
index 0574186..b763bf9 100644
--- a/src/decaf.c
+++ b/src/decaf.c
@@ -66,7 +66,8 @@ static const decaf_448_scalar_t decaf_448_scalar_r2 = {{{
 static const decaf_word_t DECAF_MONTGOMERY_FACTOR = (decaf_word_t)(0x3bd440fae918bc5ull);
 
 /** base = twist of Goldilocks base point (~,19). */
-const decaf_448_point_t decaf_448_point_base = {{
+
+const decaf_448_precomputed_t decaf_448_precomputed_base = {{{{{
     { LIMB(0xb39a2d57e08c7b),LIMB(0xb38639c75ff281),
       LIMB(0x2ec981082b3288),LIMB(0x99fe8607e5237c),
       LIMB(0x0e33fbb1fadd1f),LIMB(0xe714f67055eb4a),
@@ -80,7 +81,9 @@ const decaf_448_point_t decaf_448_point_base = {{
       LIMB(0x0d79c0a7729a69),LIMB(0xc18d3f24aebc1c),
       LIMB(0x1fbb5389b3fda5),LIMB(0xbb24f674635948),
       LIMB(0x723a55709a3983),LIMB(0xe1c0107a823dd4) }
-}};
+}}}}};
+
+const struct decaf_448_point_s *decaf_448_point_base = decaf_448_precomputed_base->p[0];
 
 #if (defined(__OPTIMIZE__) && !defined(__OPTIMIZE_SIZE__)) || defined(DECAF_FORCE_UNROLL)
     #if DECAF_448_LIMBS==8
@@ -698,3 +701,18 @@ decaf_bool_t decaf_448_point_valid (
     out &= ~gf_eq(p->z,ZERO);
     return out;
 }
+
+void decaf_448_precompute (
+    decaf_448_precomputed_t a,
+    const decaf_448_point_t b
+) {
+    decaf_448_point_copy(a->p[0],b);
+}
+
+void decaf_448_precomputed_scalarmul (
+    decaf_448_point_t a,
+    const decaf_448_precomputed_t b,
+    const decaf_448_scalar_t scalar
+) {
+    decaf_448_point_scalarmul(a,b->p[0],scalar);
+}
diff --git a/test/test_scalarmul.c b/test/test_scalarmul.c
index 79266e4..43c4057 100644
--- a/test/test_scalarmul.c
+++ b/test/test_scalarmul.c
@@ -111,10 +111,22 @@ single_scalarmul_compatibility_test (
         scalarmul_vt(&work, scalar, nbits);
         untwist_and_double_and_serialize(vt, &work);
         
-        decaf_448_point_t ed2;
+        decaf_448_point_t ed2, ed3;
+        decaf_448_precomputed_t dpre;
     	tw_extended_a_t ed;
         convert_tw_extensible_to_tw_extended(ed, &text);
-        decaf_448_point_scalarmul(ed2, (struct decaf_448_point_s *)ed, (struct decaf_448_scalar_s *)scalar);
+        decaf_448_point_scalarmul(
+            ed2,
+            (struct decaf_448_point_s *)ed,
+            (struct decaf_448_scalar_s *)scalar
+        );
+        decaf_448_precompute(dpre, (struct decaf_448_point_s *)ed);
+        decaf_448_precomputed_scalarmul(
+            ed3,
+            dpre,
+            (struct decaf_448_scalar_s *)scalar
+        );
+        
 
         scalarmul_ed(ed, scalar);
         field_copy(work.x, ed->x);
@@ -124,9 +136,11 @@ single_scalarmul_compatibility_test (
         field_set_ui(work.u, 1);
         untwist_and_double_and_serialize(sced, &work);
 
-        uint8_t ser1[(FIELD_BITS+6)/8], ser2[(FIELD_BITS+6)/8];
+        uint8_t ser1[DECAF_448_SER_BYTES], ser2[DECAF_448_SER_BYTES],
+            ser3[DECAF_448_SER_BYTES];
         decaf_448_point_encode(ser1, (struct decaf_448_point_s *)ed);
         decaf_448_point_encode(ser2, ed2);
+        decaf_448_point_encode(ser3, ed3);
 
         /* check consistency mont vs window */
         consistent &= field_eq(mont, ct);
@@ -134,6 +148,7 @@ single_scalarmul_compatibility_test (
         consistent &= field_eq(mont, vt);
         consistent &= field_eq(mont, sced);
         consistent &= memcmp(ser1,ser2,sizeof(ser1)) ? 0 : -1;
+        consistent &= memcmp(ser1,ser3,sizeof(ser1)) ? 0 : -1;
     }
     
     /* check consistency mont vs combs */