Add PrimeField::from_bytes_mod_order (#164)

* Add PrimeField::from_bytes_mod_order

CHANGELOG.md

@@ -45,6 +45,7 @@ The main features of this release are:
 - #96 (ark-ff) Make the `field_new` macro accept values in integer form, without requiring decomposition into limbs, and without requiring encoding in Montgomery form.
 - #106 (ark-ff, ark-ec) Add `Zeroize` trait bound to `Field, ProjectiveGroup, AffineGroup` traits.
 - #117 (ark-poly) Add operations to `SparsePolynomial`, so it implements `Polynomial`
+- #164 (ark-ff) Add methods `from_{be, le}_bytes_mod_order` to the `PrimeField` trait.
 
 ### Improvements
 - #22 (ark-ec) Speedup fixed-base MSMs

ff/Cargo.toml

@@ -29,6 +29,7 @@ rustc_version = "0.3"
 
 [dev-dependencies]
 rand_xorshift = "0.2"
+num-bigint = { version = "0.3.0", default-features = false }
 
 [features]
 default = []

ff/src/fields/mod.rs

@@ -9,6 +9,7 @@ use ark_serialize::{
     CanonicalSerializeWithFlags, EmptyFlags, Flags,
 };
 use ark_std::{
+    cmp::min,
     fmt::{Debug, Display},
     hash::Hash,
     ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
@@ -344,6 +345,40 @@ pub trait PrimeField:
     /// Returns the underlying representation of the prime field element.
     fn into_repr(&self) -> Self::BigInt;
 
+    /// Reads bytes in big-endian, and converts them to a field element.
+    /// If the bytes are larger than the modulus, it will reduce them.
+    fn from_be_bytes_mod_order(bytes: &[u8]) -> Self {
+        let num_modulus_bytes = ((Self::Params::MODULUS_BITS + 7) / 8) as usize;
+        let num_bytes_to_directly_convert = min(num_modulus_bytes - 1, bytes.len());
+        // Copy the leading big-endian bytes directly into a field element.
+        // The number of bytes directly converted must be less than the
+        // number of bytes needed to represent the modulus, as we must begin
+        // modular reduction once the data is of the same number of bytes as the modulus.
+        let mut bytes_to_directly_convert = Vec::new();
+        bytes_to_directly_convert.extend(bytes[..num_bytes_to_directly_convert].iter().rev());
+        // Guaranteed to not be None, as the input is less than the modulus size.
+        let mut res = Self::from_random_bytes(&bytes_to_directly_convert).unwrap();
+
+        // Update the result, byte by byte.
+        // We go through existing field arithmetic, which handles the reduction.
+        // TODO: If we need higher speeds, parse more bytes at once, or implement
+        // modular multiplication by a u64
+        let window_size = Self::from(256u64);
+        for byte in bytes[num_bytes_to_directly_convert..].iter() {
+            res *= window_size;
+            res += Self::from(*byte);
+        }
+        res
+    }
+
+    /// Reads bytes in little-endian, and converts them to a field element.
+    /// If the bytes are larger than the modulus, it will reduce them.
+    fn from_le_bytes_mod_order(bytes: &[u8]) -> Self {
+        let mut bytes_copy = bytes.to_vec();
+        bytes_copy.reverse();
+        Self::from_be_bytes_mod_order(&bytes_copy)
+    }
+
     /// Return the QNR^t, for t defined by
     /// `2^s * t = MODULUS - 1`, and t coprime to 2.
     fn qnr_to_t() -> Self {
@@ -569,6 +604,7 @@ fn serial_batch_inversion_and_mul<F: Field>(v: &mut [F], coeff: &F) {
 #[cfg(all(test, feature = "std"))]
 mod std_tests {
     use super::BitIteratorLE;
+
     #[test]
     fn bit_iterator_le() {
         let bits = BitIteratorLE::new(&[0, 1 << 10]).collect::<Vec<_>>();
@@ -614,4 +650,107 @@ mod no_std_tests {
             );
         }
     }
+
+    #[test]
+    fn test_from_be_bytes_mod_order() {
+        // Each test vector is a byte array,
+        // and its tested by parsing it with from_bytes_mod_order, and the num-bigint library.
+        // The bytes are currently generated from scripts/test_vectors.py.
+        // TODO: Eventually generate all the test vector bytes via computation with the modulus
+        use ark_std::string::ToString;
+        use num_bigint::BigUint;
+        use rand::Rng;
+
+        let ref_modulus =
+            BigUint::from_bytes_be(&<Fr as PrimeField>::Params::MODULUS.to_bytes_be());
+
+        let mut test_vectors = vec![
+            // 0
+            vec![0u8],
+            // 1
+            vec![1u8],
+            // 255
+            vec![255u8],
+            // 256
+            vec![1u8, 0u8],
+            // 65791
+            vec![1u8, 0u8, 255u8],
+            // 204827637402836681560342736360101429053478720705186085244545541796635082752
+            vec![
+                115u8, 237u8, 167u8, 83u8, 41u8, 157u8, 125u8, 72u8, 51u8, 57u8, 216u8, 8u8, 9u8,
+                161u8, 216u8, 5u8, 83u8, 189u8, 164u8, 2u8, 255u8, 254u8, 91u8, 254u8, 255u8,
+                255u8, 255u8, 255u8, 0u8, 0u8, 0u8,
+            ],
+            // 204827637402836681560342736360101429053478720705186085244545541796635082753
+            vec![
+                115u8, 237u8, 167u8, 83u8, 41u8, 157u8, 125u8, 72u8, 51u8, 57u8, 216u8, 8u8, 9u8,
+                161u8, 216u8, 5u8, 83u8, 189u8, 164u8, 2u8, 255u8, 254u8, 91u8, 254u8, 255u8,
+                255u8, 255u8, 255u8, 0u8, 0u8, 1u8,
+            ],
+            // 52435875175126190479447740508185965837690552500527637822603658699938581184512
+            vec![
+                115u8, 237u8, 167u8, 83u8, 41u8, 157u8, 125u8, 72u8, 51u8, 57u8, 216u8, 8u8, 9u8,
+                161u8, 216u8, 5u8, 83u8, 189u8, 164u8, 2u8, 255u8, 254u8, 91u8, 254u8, 255u8,
+                255u8, 255u8, 255u8, 0u8, 0u8, 0u8, 0u8,
+            ],
+            // 52435875175126190479447740508185965837690552500527637822603658699938581184513
+            vec![
+                115u8, 237u8, 167u8, 83u8, 41u8, 157u8, 125u8, 72u8, 51u8, 57u8, 216u8, 8u8, 9u8,
+                161u8, 216u8, 5u8, 83u8, 189u8, 164u8, 2u8, 255u8, 254u8, 91u8, 254u8, 255u8,
+                255u8, 255u8, 255u8, 0u8, 0u8, 0u8, 1u8,
+            ],
+            // 52435875175126190479447740508185965837690552500527637822603658699938581184514
+            vec![
+                115u8, 237u8, 167u8, 83u8, 41u8, 157u8, 125u8, 72u8, 51u8, 57u8, 216u8, 8u8, 9u8,
+                161u8, 216u8, 5u8, 83u8, 189u8, 164u8, 2u8, 255u8, 254u8, 91u8, 254u8, 255u8,
+                255u8, 255u8, 255u8, 0u8, 0u8, 0u8, 2u8,
+            ],
+            // 104871750350252380958895481016371931675381105001055275645207317399877162369026
+            vec![
+                231u8, 219u8, 78u8, 166u8, 83u8, 58u8, 250u8, 144u8, 102u8, 115u8, 176u8, 16u8,
+                19u8, 67u8, 176u8, 10u8, 167u8, 123u8, 72u8, 5u8, 255u8, 252u8, 183u8, 253u8,
+                255u8, 255u8, 255u8, 254u8, 0u8, 0u8, 0u8, 2u8,
+            ],
+            // 13423584044832304762738621570095607254448781440135075282586536627184276783235328
+            vec![
+                115u8, 237u8, 167u8, 83u8, 41u8, 157u8, 125u8, 72u8, 51u8, 57u8, 216u8, 8u8, 9u8,
+                161u8, 216u8, 5u8, 83u8, 189u8, 164u8, 2u8, 255u8, 254u8, 91u8, 254u8, 255u8,
+                255u8, 255u8, 255u8, 0u8, 0u8, 0u8, 1u8, 0u8,
+            ],
+            // 115792089237316195423570985008687907853269984665640564039457584007913129639953
+            vec![
+                1u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8,
+                0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8, 0u8,
+                17u8,
+            ],
+            // 168227964412442385903018725516873873690960537166168201862061242707851710824468
+            vec![
+                1u8, 115u8, 237u8, 167u8, 83u8, 41u8, 157u8, 125u8, 72u8, 51u8, 57u8, 216u8, 8u8,
+                9u8, 161u8, 216u8, 5u8, 83u8, 189u8, 164u8, 2u8, 255u8, 254u8, 91u8, 254u8, 255u8,
+                255u8, 255u8, 255u8, 0u8, 0u8, 0u8, 20u8,
+            ],
+            // 29695210719928072218913619902732290376274806626904512031923745164725699769008210
+            vec![
+                1u8, 0u8, 115u8, 237u8, 167u8, 83u8, 41u8, 157u8, 125u8, 72u8, 51u8, 57u8, 216u8,
+                8u8, 9u8, 161u8, 216u8, 5u8, 83u8, 189u8, 164u8, 2u8, 255u8, 254u8, 91u8, 254u8,
+                255u8, 255u8, 255u8, 255u8, 0u8, 0u8, 0u8, 82u8,
+            ],
+        ];
+        // Add random bytestrings to the test vector list
+        for i in 1..512 {
+            let mut rng = test_rng();
+            let data: Vec<u8> = (0..i).map(|_| rng.gen()).collect();
+            test_vectors.push(data);
+        }
+        for i in test_vectors {
+            let mut expected_biguint = BigUint::from_bytes_be(&i);
+            // Reduce expected_biguint using modpow API
+            expected_biguint =
+                expected_biguint.modpow(&BigUint::from_bytes_be(&[1u8]), &ref_modulus);
+            let expected_string = expected_biguint.to_string();
+            let expected = Fr::from_str(&expected_string).unwrap();
+            let actual = Fr::from_be_bytes_mod_order(&i);
+            assert_eq!(expected, actual, "failed on test {:?}", i);
+        }
+    }
 }

scripts/test_vectors.py

@@ -0,0 +1,46 @@
+
+def generate_from_bytes_mod_order_test_vector(modulus):
+    def gen_vector(number):
+        byte_arr = convert_int_to_byte_vec(number)
+        # s = str(number % modulus)
+        # return "(" + byte_arr + ", \"" + s + "\"),"
+        return byte_arr + ","
+    data = ["vec!["]
+
+    small_values_to_test = [0, 1, 255, 256, 256*256 + 255]
+    modulus_bits = int((len(bin(modulus)[2:]) + 7) / 8) * 8
+    values_to_test = small_values_to_test + [
+        modulus >> 8, 
+        (modulus >> 8) + 1, 
+        modulus - 1,
+        modulus,
+        modulus + 1,
+        modulus * 2,
+        modulus * 256,
+        17 + (1 << modulus_bits),
+        19 + (1 << modulus_bits) + modulus,
+        81 + (1 << modulus_bits) * 256 + modulus]
+
+    for i in values_to_test:
+        data += ["// " + str(i)]
+        data += [gen_vector(i)]
+
+    data += ["];"]
+    return '\n'.join(data)
+
+def convert_int_to_byte_vec(number):
+    s = bin(number)[2:]
+    num_bytes = int((len(s) + 7) / 8)
+    s = s.zfill(num_bytes * 8)
+
+    byte_arr = []
+    for i in range(num_bytes):
+        byte = s[i*8: (i+1)*8]
+        i = int(byte, 2)
+        byte_arr += [str(i) + "u8"]
+
+    data = ', '.join(byte_arr)
+    return "vec![" + data + "]"
+
+bls12_fr_mod = 52435875175126190479447740508185965837690552500527637822603658699938581184513
+print(generate_from_bytes_mod_order_test_vector(bls12_fr_mod))