sqrt(-d)

src/include/magic.h

@@ -47,6 +47,11 @@
  */
 extern const struct field_t sqrt_d_minus_1;
 
+/**
+ * @brief sqrt(-d), used for point formats and twisting.
+ */
+extern const struct field_t sqrt_minus_d;
+
 /**
  * @brief The base point for Goldilocks.
  */

src/p448/magic.c

@@ -79,3 +79,22 @@ sqrt_d_minus_1 = {{
     U56LE(0x12fec0c0b25b7a)
 #endif
 }};
+
+const struct field_t
+sqrt_minus_d = {{
+#ifdef USE_NEON_PERM
+    0x5572736,0x4a2d780,0x42ef0f4,0xb8d54b6,
+    0x0ce5296,0x1a7b8a5,0x7bf6aa2,0x6aa0a1f,
+    0xed26033,0xd722fa2,0xf4fd6ed,0x683bf68,
+    0xa839a66,0xbeb24f7,0x968c14b,0x22d962f
+#else
+    U56LE(0x42ef0f45572736),
+    U56LE(0x7bf6aa20ce5296),
+    U56LE(0xf4fd6eded26033),
+    U56LE(0x968c14ba839a66),
+    U56LE(0xb8d54b64a2d780),
+    U56LE(0x6aa0a1f1a7b8a5),
+    U56LE(0x683bf68d722fa2),
+    U56LE(0x22d962fbeb24f7)
+#endif
+}};

src/p480/magic.c

@@ -66,3 +66,15 @@ const struct field_t
 sqrt_d_minus_1 = {{
     232 /* Whoa, it comes out even. */
 }};
+
+const struct field_t
+sqrt_minus_d = {{
+    U60LE(0xf098fba8d880ec0),
+    U60LE(0x9d6ea1b2774d3e9),
+    U60LE(0x1a52c44c0154b38),
+    U60LE(0x9a7d2310c583efd),
+    U60LE(0xb548ed7aec18f2d),
+    U60LE(0xb9d4b5edcfee721),
+    U60LE(0x65275d687c7215d),
+    U60LE(0x3458ffa5bbfdea5)
+}};

src/p521/magic.c

@@ -109,3 +109,31 @@ sqrt_d_minus_1 = {{
     U58LE(0x0a9ea3ac10d6aed)
 #endif
 }};
+
+const struct field_t
+sqrt_minus_d = {{
+#ifdef USE_P521_3x3_TRANSPOSE
+    U58LE(0x375d668ef98910e),
+    U58LE(0x2e033a89e955dfc),
+    U58LE(0x11539170515b2da),
+    0,
+    U58LE(0x1d88a078877dc00),
+    U58LE(0x38dac4db4b0312c),
+    U58LE(0x009993c0e8ee528),
+    0,
+    U58LE(0x34829cd5d7c1584),
+    U58LE(0x2c688534aa9c317),
+    U58LE(0x0d07656ee612ae6),
+    0
+#else
+    U58LE(0x375d668ef98910e),
+    U58LE(0x1d88a078877dc00),
+    U58LE(0x34829cd5d7c1584),
+    U58LE(0x2e033a89e955dfc),
+    U58LE(0x38dac4db4b0312c),
+    U58LE(0x2c688534aa9c317),
+    U58LE(0x11539170515b2da),
+    U58LE(0x009993c0e8ee528),
+    U58LE(0x0d07656ee612ae6)
+#endif
+}};