Add DELTA generator of t-order multiplicative subgroup to Fp, Fq

src/arithmetic/fields.rs

@@ -64,6 +64,9 @@ pub trait Field:
     /// The value $t^{-1} \mod 2^S$.
     const UNROLL_S_EXPONENT: u64;
 
+    /// Generator of the $t-order$ multiplicative subgroup
+    const DELTA: Self;
+
     /// Inverse of $2$ in the field.
     const TWO_INV: Self;
 

src/arithmetic/fields/fp.rs

@@ -173,6 +173,20 @@ const ROOT_OF_UNITY: Fp = Fp::from_raw([
     0x2ae45117890ee2fc,
 ]);
 
+/// GENERATOR^{2^s} where t * 2^s + 1 = p
+/// with t odd. In other words, this
+/// is a t root of unity.
+///
+/// `GENERATOR = 5 mod p` is a generator
+/// of the p - 1 order multiplicative
+/// subgroup.
+const DELTA: Fp = Fp::from_raw([
+    0x1e9372724e80300d,
+    0x671383de08b5fe3c,
+    0xa99d8b67e918805e,
+    0x48796f6fde98a425,
+]);
+
 impl Default for Fp {
     #[inline]
     fn default() -> Self {
@@ -429,6 +443,7 @@ impl Field for Fp {
         0x0000000000000000,
         0x20000000,
     ];
+    const DELTA: Self = DELTA;
     const UNROLL_S_EXPONENT: u64 = 0x11cb54e91;
     const TWO_INV: Self = Fp::from_raw([
         0xd0a0327100000001,

src/arithmetic/fields/fq.rs

@@ -173,6 +173,20 @@ const ROOT_OF_UNITY: Fq = Fq::from_raw([
     0x113efc510dc03c0b,
 ]);
 
+/// GENERATOR^{2^s} where t * 2^s + 1 = q
+/// with t odd. In other words, this
+/// is a t root of unity.
+///
+/// `GENERATOR = 5 mod q` is a generator
+/// of the q - 1 order multiplicative
+/// subgroup.
+const DELTA: Fq = Fq::from_raw([
+    0x20daec44973be920,
+    0x4243423589e0a9b5,
+    0x5127e2ce24a8e69c,
+    0x83d2833d15f2bbf9,
+]);
+
 impl Default for Fq {
     #[inline]
     fn default() -> Self {
@@ -444,6 +458,7 @@ impl Field for Fq {
         0x0000000000000000,
         0x10000000,
     ];
+    const DELTA: Self = DELTA;
     const UNROLL_S_EXPONENT: u64 = 0x344cfe85d;
     const TWO_INV: Self = Fq::from_raw([
         0xc21657ea00000001,