diff --git a/src/scalar_low.h b/src/scalar_low.h
index 67051bd30b788..2711eb932dc6d 100644
--- a/src/scalar_low.h
+++ b/src/scalar_low.h
@@ -1,5 +1,5 @@
 /***********************************************************************
- * Copyright (c) 2015 Andrew Poelstra                                  *
+ * Copyright (c) 2015, 2022 Andrew Poelstra, Pieter Wuille             *
  * Distributed under the MIT software license, see the accompanying    *
  * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
  ***********************************************************************/
@@ -12,6 +12,13 @@
 /** A scalar modulo the group order of the secp256k1 curve. */
 typedef uint32_t secp256k1_scalar;
 
-#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) (d0)
+/* A compile-time constant equal to 2^32 (modulo order). */
+#define SCALAR_2P32 ((0xffffffffUL % EXHAUSTIVE_TEST_ORDER) + 1U)
+
+/* Compute a*2^32 + b (modulo order). */
+#define SCALAR_HORNER(a, b) (((uint64_t)(a) * SCALAR_2P32 + (b)) % EXHAUSTIVE_TEST_ORDER)
+
+/* Evaluates to the provided 256-bit constant reduced modulo order. */
+#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) SCALAR_HORNER(SCALAR_HORNER(SCALAR_HORNER(SCALAR_HORNER(SCALAR_HORNER(SCALAR_HORNER(SCALAR_HORNER((d7), (d6)), (d5)), (d4)), (d3)), (d2)), (d1)), (d0))
 
 #endif /* SECP256K1_SCALAR_REPR_H */