fix: bug in Falcon secret key basis order (#305)

src/dsa/rpo_falcon512/keys/mod.rs

@@ -33,7 +33,8 @@ mod tests {
         // test secret key serialization/deserialization
         let mut buffer = vec![];
         sk.write_into(&mut buffer);
-        let sk = SecretKey::read_from_bytes(&buffer).unwrap();
+        let sk_deserialized = SecretKey::read_from_bytes(&buffer).unwrap();
+        assert_eq!(sk.short_lattice_basis(), sk_deserialized.short_lattice_basis());
 
         // sign a random message
         let message: Word = [ONE; 4];

src/dsa/rpo_falcon512/keys/secret_key.rs

@@ -210,14 +210,14 @@ impl Serializable for SecretKey {
         let l = n.checked_ilog2().unwrap() as u8;
         let header: u8 = (5 << 4) | l;
 
-        let f = &basis[1];
+        let neg_f = &basis[1];
         let g = &basis[0];
-        let capital_f = &basis[3];
+        let neg_big_f = &basis[3];
 
         let mut buffer = Vec::with_capacity(1281);
         buffer.push(header);
 
-        let f_i8: Vec<i8> = f.coefficients.iter().map(|&a| -a as i8).collect();
+        let f_i8: Vec<i8> = neg_f.coefficients.iter().map(|&a| -a as i8).collect();
         let f_i8_encoded = encode_i8(&f_i8, WIDTH_SMALL_POLY_COEFFICIENT).unwrap();
         buffer.extend_from_slice(&f_i8_encoded);
 
@@ -225,7 +225,7 @@ impl Serializable for SecretKey {
         let g_i8_encoded = encode_i8(&g_i8, WIDTH_SMALL_POLY_COEFFICIENT).unwrap();
         buffer.extend_from_slice(&g_i8_encoded);
 
-        let big_f_i8: Vec<i8> = capital_f.coefficients.iter().map(|&a| -a as i8).collect();
+        let big_f_i8: Vec<i8> = neg_big_f.coefficients.iter().map(|&a| -a as i8).collect();
         let big_f_i8_encoded = encode_i8(&big_f_i8, WIDTH_BIG_POLY_COEFFICIENT).unwrap();
         buffer.extend_from_slice(&big_f_i8_encoded);
         target.write_bytes(&buffer);

src/dsa/rpo_falcon512/math/mod.rs

@@ -96,10 +96,10 @@ pub(crate) fn ntru_gen<R: Rng>(n: usize, rng: &mut R) -> [Polynomial<i16>; 4] {
             ntru_solve(&f.map(|&i| i.into()), &g.map(|&i| i.into()))
         {
             return [
-                f,
                 g,
-                capital_f.map(|i| i.try_into().unwrap()),
+                -f,
                 capital_g.map(|i| i.try_into().unwrap()),
+                -capital_f.map(|i| i.try_into().unwrap()),
             ];
         }
     }