diff --git a/src/crypto/ecdhe.c b/src/crypto/ecdhe.c
index 5481b02eb..592c8ca1a 100644
--- a/src/crypto/ecdhe.c
+++ b/src/crypto/ecdhe.c
@@ -55,7 +55,7 @@ int ecdhe_key ( struct elliptic_curve *curve, const void *partner,
 	}
 
 	/* Construct public key */
-	if ( ( rc = elliptic_multiply ( curve, NULL, private,
+	if ( ( rc = elliptic_multiply ( curve, curve->base, private,
 					public ) ) != 0 ) {
 		DBGC ( curve, "CURVE %s could not generate public key: %s\n",
 		       curve->name, strerror ( rc ) );
diff --git a/src/crypto/weierstrass.c b/src/crypto/weierstrass.c
index c149c7b21..4974e5252 100644
--- a/src/crypto/weierstrass.c
+++ b/src/crypto/weierstrass.c
@@ -762,7 +762,7 @@ static int weierstrass_verify_raw ( const struct weierstrass_curve *curve,
  * Multiply curve point by scalar
  *
  * @v curve		Weierstrass curve
- * @v base		Base point (or NULL to use generator)
+ * @v base		Base point
  * @v scalar		Scalar multiple
  * @v result		Result point to fill in
  * @ret rc		Return status code
@@ -806,10 +806,6 @@ int weierstrass_multiply ( struct weierstrass_curve *curve, const void *base,
 	if ( ! prime2->element[0] )
 		weierstrass_init ( curve );
 
-	/* Use generator if applicable */
-	if ( ! base )
-		base = curve->base;
-
 	/* Convert input to projective coordinates in Montgomery form */
 	DBGC ( curve, "WEIERSTRASS %s base (", curve->name );
 	for ( i = 0, offset = 0 ; i < WEIERSTRASS_AXES ; i++, offset += len ) {
diff --git a/src/crypto/x25519.c b/src/crypto/x25519.c
index 41bc5fc5e..00a791877 100644
--- a/src/crypto/x25519.c
+++ b/src/crypto/x25519.c
@@ -822,7 +822,7 @@ int x25519_key ( const struct x25519_value *base,
 /**
  * Multiply scalar by curve point
  *
- * @v base		Base point (or NULL to use generator)
+ * @v base		Base point
  * @v scalar		Scalar multiple
  * @v result		Result point to fill in
  * @ret rc		Return status code
@@ -830,10 +830,6 @@ int x25519_key ( const struct x25519_value *base,
 static int x25519_curve_multiply ( const void *base, const void *scalar,
 				   void *result ) {
 
-	/* Use base point if applicable */
-	if ( ! base )
-		base = &x25519_generator;
-
 	return x25519_key ( base, scalar, result );
 }
 
@@ -842,5 +838,6 @@ struct elliptic_curve x25519_curve = {
 	.name = "x25519",
 	.pointsize = sizeof ( struct x25519_value ),
 	.keysize = sizeof ( struct x25519_value ),
+	.base = x25519_generator.raw,
 	.multiply = x25519_curve_multiply,
 };
diff --git a/src/include/ipxe/crypto.h b/src/include/ipxe/crypto.h
index ee63423c9..d2adea5d6 100644
--- a/src/include/ipxe/crypto.h
+++ b/src/include/ipxe/crypto.h
@@ -181,9 +181,11 @@ struct elliptic_curve {
 	size_t pointsize;
 	/** Scalar (and private key) size */
 	size_t keysize;
+	/** Generator base point */
+	const void *base;
 	/** Multiply scalar by curve point
 	 *
-	 * @v base		Base point (or NULL to use generator)
+	 * @v base		Base point
 	 * @v scalar		Scalar multiple
 	 * @v result		Result point to fill in
 	 * @ret rc		Return status code
diff --git a/src/include/ipxe/weierstrass.h b/src/include/ipxe/weierstrass.h
index fb09fa6fa..e5e411499 100644
--- a/src/include/ipxe/weierstrass.h
+++ b/src/include/ipxe/weierstrass.h
@@ -160,6 +160,7 @@ extern int weierstrass_multiply ( struct weierstrass_curve *curve,
 		.name = #_name,						\
 		.pointsize = ( WEIERSTRASS_AXES * (_len) ),		\
 		.keysize = (_len),					\
+		.base = (_base),					\
 		.multiply = _name ## _multiply,				\
 	}
 
diff --git a/src/tests/elliptic_test.c b/src/tests/elliptic_test.c
index 4c42e5848..d8cdf2c0f 100644
--- a/src/tests/elliptic_test.c
+++ b/src/tests/elliptic_test.c
@@ -52,6 +52,7 @@ void elliptic_okx ( struct elliptic_test *test, const char *file,
 	size_t pointsize = curve->pointsize;
 	size_t keysize = curve->keysize;
 	uint8_t actual[pointsize];
+	const void *base;
 	int rc;
 
 	/* Sanity checks */
@@ -62,8 +63,8 @@ void elliptic_okx ( struct elliptic_test *test, const char *file,
 	      file, line );
 
 	/* Perform point multiplication */
-	rc = elliptic_multiply ( curve, ( test->base_len ? test->base : NULL ),
-				 test->scalar, actual );
+	base = ( test->base_len ? test->base : curve->base );
+	rc = elliptic_multiply ( curve, base, test->scalar, actual );
 	if ( test->expected_len ) {
 		okx ( rc == 0, file, line );
 	} else {