Use bit-reversal permutation

src/c_kzg.h

@@ -55,6 +55,7 @@ typedef struct {
     fr_t root_of_unity;            /**< The root of unity used to generate the lists in the structure. */
     fr_t *expanded_roots_of_unity; /**< Ascending powers of the root of unity, size `width + 1`. */
     fr_t *reverse_roots_of_unity;  /**< Descending powers of the root of unity, size `width + 1`. */
+    fr_t *bitrevp_roots_of_unity;  /**< Powers of the root of unity in bit-reversal permutation, size `width`. */
 } FFTSettings;
 
 C_KZG_RET new_fft_settings(FFTSettings *out, unsigned int max_scale);
@@ -87,9 +88,9 @@ typedef struct {
 } poly;
 
 typedef struct {
-    fr_t *values;    /**< `values[i]` is value of the polynomial at `ω^i`. */
+    fr_t *values;    /**< `values[i]` is value of the polynomial at `ω^brp(i)`. */
     uint64_t length; /**< One more than the polynomial's degree */
-} poly_l; // Lagrange form
+} poly_l; // Lagrange form, under bit-reversal permutation
 
 void eval_poly(fr_t *out, const poly *p, const fr_t *x);
 C_KZG_RET eval_poly_l(fr_t *out, const poly_l *p, const fr_t *x, const FFTSettings *fs);
@@ -117,7 +118,7 @@ void fr_vector_lincomb(fr_t out[], const fr_t *vectors, const fr_t *scalars, uin
 typedef struct {
     const FFTSettings *fs; /**< The corresponding settings for performing FFTs */
     g1_t *secret_g1;       /**< G1 group elements from the trusted setup */
-    g1_t *secret_g1_l;     /**< secret_g1 in Lagrange form */
+    g1_t *secret_g1_l;     /**< secret_g1 in Lagrange form, in bit-reversal permutation */
     g2_t *secret_g2;       /**< G2 group elements from the trusted setup */
     uint64_t length;       /**< The number of elements in secret_g1 and secret_g2 */
 } KZGSettings;

src/fft_common.c

@@ -20,8 +20,10 @@
  * Code shared between the FFTs over field elements and FFTs over G1 group elements.
  */
 
+#include <string.h> // memcpy
 #include "control.h"
 #include "c_kzg_alloc.h"
+#include "utility.h" // reverse_bit_order
 
 /**
  * The first 32 roots of unity in the finite field F_r.
@@ -131,6 +133,7 @@ C_KZG_RET new_fft_settings(FFTSettings *fs, unsigned int max_scale) {
     // Allocate space for the roots of unity
     TRY(new_fr_array(&fs->expanded_roots_of_unity, fs->max_width + 1));
     TRY(new_fr_array(&fs->reverse_roots_of_unity, fs->max_width + 1));
+    TRY(new_fr_array(&fs->bitrevp_roots_of_unity, fs->max_width));
 
     // Populate the roots of unity
     TRY(expand_root_of_unity(fs->expanded_roots_of_unity, &fs->root_of_unity, fs->max_width));
@@ -140,6 +143,10 @@ C_KZG_RET new_fft_settings(FFTSettings *fs, unsigned int max_scale) {
         fs->reverse_roots_of_unity[i] = fs->expanded_roots_of_unity[fs->max_width - i];
     }
 
+    // Permute the roots of unity
+    memcpy(fs->bitrevp_roots_of_unity, fs->expanded_roots_of_unity, sizeof(fr_t) * fs->max_width);
+    TRY(reverse_bit_order(fs->bitrevp_roots_of_unity, sizeof(fr_t), fs->max_width));
+
     return C_KZG_OK;
 }
 
@@ -151,6 +158,7 @@ C_KZG_RET new_fft_settings(FFTSettings *fs, unsigned int max_scale) {
 void free_fft_settings(FFTSettings *fs) {
     free(fs->expanded_roots_of_unity);
     free(fs->reverse_roots_of_unity);
+    free(fs->bitrevp_roots_of_unity);
     fs->max_width = 0;
 }
 
@@ -158,7 +166,6 @@ void free_fft_settings(FFTSettings *fs) {
 
 #include "../inc/acutest.h"
 #include "test_util.h"
-#include "utility.h"
 
 #define NUM_ROOTS 32
 

src/kzg_proofs.c

@@ -142,13 +142,13 @@ C_KZG_RET compute_proof_single_l(g1_t *out, const poly_l *p, const fr_t *x, cons
   TRY(new_fr_array(&inverses, p->length));
 
   for (i = 0; i < q.length; i++) {
-    if (fr_equal(x, &ks->fs->expanded_roots_of_unity[i])) {
+    if (fr_equal(x, &ks->fs->bitrevp_roots_of_unity[i])) {
       m = i + 1;
       continue;
     }
     // (p_i - y) / (ω_i - x)
     fr_sub(&q.values[i], &p->values[i], y);
-    fr_sub(&inverses_in[i], &ks->fs->expanded_roots_of_unity[i], x);
+    fr_sub(&inverses_in[i], &ks->fs->bitrevp_roots_of_unity[i], x);
   }
 
   TRY(fr_batch_inv(inverses, inverses_in, q.length));
@@ -161,14 +161,14 @@ C_KZG_RET compute_proof_single_l(g1_t *out, const poly_l *p, const fr_t *x, cons
     for (i=0; i < q.length; i++) {
       if (i == m) continue;
       // (p_i - y) * ω_i / (x * (x - ω_i))
-      fr_sub(&tmp, x, &ks->fs->expanded_roots_of_unity[i]);
+      fr_sub(&tmp, x, &ks->fs->bitrevp_roots_of_unity[i]);
       fr_mul(&inverses_in[i], &tmp, x);
     }
     TRY(fr_batch_inv(inverses, inverses_in, q.length));
     for (i=0; i < q.length; i++) {
       fr_sub(&tmp2, &p->values[i], y);
       fr_mul(&tmp, &tmp2, &inverses[i]);
-      fr_mul(&tmp, &tmp, &ks->fs->expanded_roots_of_unity[i]);
+      fr_mul(&tmp, &tmp, &ks->fs->bitrevp_roots_of_unity[i]);
       fr_add(&q.values[m], &q.values[m], &tmp);
     }
   }
@@ -318,8 +318,9 @@ C_KZG_RET new_kzg_settings(KZGSettings *ks, const g1_t *secret_g1, const g2_t *s
     }
     ks->fs = fs;
 
-    // Add Lagrange form (and return its success)
-    return fft_g1(ks->secret_g1_l, ks->secret_g1, true, length, fs);
+    // Add Lagrange form
+    TRY(fft_g1(ks->secret_g1_l, ks->secret_g1, true, length, fs));
+    return reverse_bit_order(ks->secret_g1_l, sizeof(g1_t), length);
 }
 
 /**

src/poly.c

@@ -117,19 +117,19 @@ C_KZG_RET eval_poly_l(fr_t *out, const poly_l *p, const fr_t *x, const FFTSettin
   TRY(new_fr_array(&inverses_in, p->length));
   TRY(new_fr_array(&inverses, p->length));
   for (i = 0; i < p->length; i++) {
-    if (fr_equal(x, &fs->expanded_roots_of_unity[i * stride])) {
+    if (fr_equal(x, &fs->bitrevp_roots_of_unity[i * stride])) {
       *out = p->values[i];
       free(inverses_in);
       free(inverses);
       return C_KZG_OK;
     }
-    fr_sub(&inverses_in[i], x, &fs->expanded_roots_of_unity[i * stride]);
+    fr_sub(&inverses_in[i], x, &fs->bitrevp_roots_of_unity[i * stride]);
   }
   TRY(fr_batch_inv(inverses, inverses_in, p->length));
 
   *out = fr_zero;
   for (i = 0; i < p->length; i++) {
-    fr_mul(&tmp, &inverses[i], &fs->expanded_roots_of_unity[i * stride]);
+    fr_mul(&tmp, &inverses[i], &fs->bitrevp_roots_of_unity[i * stride]);
     fr_mul(&tmp, &tmp, &p->values[i]);
     fr_add(out, out, &tmp);
   }
@@ -635,7 +635,7 @@ C_KZG_RET new_poly_with_coeffs(poly *out, const fr_t *coeffs, uint64_t length) {
 C_KZG_RET new_poly_l_from_poly(poly_l *out, const poly *in, const KZGSettings *ks) {
   TRY(new_poly_l(out, ks->length));
   if (out->length <= in->length) {
-    return fft_fr(out->values, in->coeffs, false, out->length, ks->fs);
+    fft_fr(out->values, in->coeffs, false, out->length, ks->fs);
   }
   else {
     int i;
@@ -649,8 +649,8 @@ C_KZG_RET new_poly_l_from_poly(poly_l *out, const poly *in, const KZGSettings *k
     }
     TRY(fft_fr(out->values, coeffs, false, out->length, ks->fs));
     free(coeffs);
-    return C_KZG_OK;
   }
+  return reverse_bit_order(out->values, sizeof(fr_t), out->length);
 }
 
 /**