Add Pallas and Vesta curves (#21)

Co-authored-by: Ying Tong Lai <yingtong@electriccoin.co>
Co-authored-by: Daira Hopwood <daira@jacaranda.org>
Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>
Co-authored-by: therealyingtong <yingtong@z.cash>

pallas/src/fields/fq.rs

@@ -0,0 +1,90 @@
+use ark_ff::{
+    biginteger::BigInteger256 as BigInteger,
+    fields::{FftParameters, Fp256, Fp256Parameters},
+};
+
+pub type Fq = Fp256<FqParameters>;
+
+pub struct FqParameters;
+
+impl Fp256Parameters for FqParameters {}
+impl FftParameters for FqParameters {
+    type BigInt = BigInteger;
+
+    const TWO_ADICITY: u32 = 32;
+
+    // TWO_ADIC_ROOT_OF_UNITY = GENERATOR^T
+    // Encoded in Montgomery form, so the value here is (5^T)R mod p.
+    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
+        0xa28db849bad6dbf0,
+        0x9083cd03d3b539df,
+        0xfba6b9ca9dc8448e,
+        0x3ec928747b89c6da,
+    ]);
+}
+
+impl ark_ff::fields::FpParameters for FqParameters {
+    // 28948022309329048855892746252171976963363056481941560715954676764349967630337
+    const MODULUS: BigInteger = BigInteger([
+        0x992d30ed00000001,
+        0x224698fc094cf91b,
+        0x0000000000000000,
+        0x4000000000000000,
+    ]);
+
+    // R = 2^256 mod p
+    const R: BigInteger = BigInteger([
+        0x34786d38fffffffd,
+        0x992c350be41914ad,
+        0xffffffffffffffff,
+        0x3fffffffffffffff,
+    ]);
+
+    // R2 = (2^256)^2 mod p
+    const R2: BigInteger = BigInteger([
+        0x8c78ecb30000000f,
+        0xd7d30dbd8b0de0e7,
+        0x7797a99bc3c95d18,
+        0x096d41af7b9cb714,
+    ]);
+
+    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
+        0xcc96987680000000,
+        0x11234c7e04a67c8d,
+        0x0000000000000000,
+        0x2000000000000000,
+    ]);
+
+    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
+    const T: BigInteger = BigInteger([
+        0x094cf91b992d30ed,
+        0x00000000224698fc,
+        0x0000000000000000,
+        0x0000000040000000,
+    ]);
+
+    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
+        0x04a67c8dcc969876,
+        0x0000000011234c7e,
+        0x0000000000000000,
+        0x0000000020000000,
+    ]);
+
+    // GENERATOR = 5
+    // Encoded in Montgomery form, so the value here is 5R mod p.
+    const GENERATOR: BigInteger = BigInteger([
+        0xa1a55e68ffffffed,
+        0x74c2a54b4f4982f3,
+        0xfffffffffffffffd,
+        0x3fffffffffffffff,
+    ]);
+
+    const MODULUS_BITS: u32 = 255;
+
+    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
+
+    const REPR_SHAVE_BITS: u32 = 1;
+
+    // INV = -p^{-1} (mod 2^64)
+    const INV: u64 = 11037532056220336127;
+}