Run util/openssl-format-source on the Curve448 code

Reviewed-by: Bernd Edlinger <bernd.edlinger@hotmail.de>
(Merged from https://github.com/openssl/openssl/pull/5105)

1 files changed, 441 insertions, 419 deletions

diff --git a/crypto/ec/curve448/curve448.c b/crypto/ec/curve448/curve448.c
index 68085bf464..2a8678a40d 100644
--- a/crypto/ec/curve448/curve448.c
+++ b/crypto/ec/curve448/curve448.c
@@ -28,13 +28,20 @@
 #define DECAF_WNAF_VAR_TABLE_BITS 3
 
 static const int EDWARDS_D = -39081;
-static const curve448_scalar_t precomputed_scalarmul_adjustment = {{{
-    SC_LIMB(0xc873d6d54a7bb0cf), SC_LIMB(0xe933d8d723a70aad), SC_LIMB(0xbb124b65129c96fd), SC_LIMB(0x00000008335dc163)
-}}};
+static const curve448_scalar_t precomputed_scalarmul_adjustment = { {{
+                                                                      SC_LIMB
+                                                                      (0xc873d6d54a7bb0cf),
+                                                                      SC_LIMB
+                                                                      (0xe933d8d723a70aad),
+                                                                      SC_LIMB
+                                                                      (0xbb124b65129c96fd),
+                                                                      SC_LIMB
+                                                                      (0x00000008335dc163)
+                                                                      }}
+};
 
 const uint8_t decaf_x448_base_point[DECAF_X448_PUBLIC_BYTES] = { 0x05 };
 
-
 #define TWISTED_D ((EDWARDS_D)-1)
 
 #define EFF_D (-(TWISTED_D))
@@ -42,511 +49,507 @@ const uint8_t decaf_x448_base_point[DECAF_X448_PUBLIC_BYTES] = { 0x05 };
 
 /* End of template stuff */
 
-#define WBITS DECAF_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
+#define WBITS DECAF_WORD_BITS   /* NB this may be different from ARCH_WORD_BITS */
 
 /* Projective Niels coordinates */
-typedef struct { gf a, b, c; } niels_s, niels_t[1];
-typedef struct { niels_t n; gf z; } VECTOR_ALIGNED pniels_s, pniels_t[1];
+typedef struct {
+    gf a, b, c;
+} niels_s, niels_t[1];
+typedef struct {
+    niels_t n;
+    gf z;
+} VECTOR_ALIGNED pniels_s, pniels_t[1];
 
 /* Precomputed base */
-struct curve448_precomputed_s { niels_t table [COMBS_N<<(COMBS_T-1)]; };
+struct curve448_precomputed_s {
+    niels_t table[COMBS_N << (COMBS_T - 1)];
+};
 
 extern const gf curve448_precomputed_base_as_fe[];
 const curve448_precomputed_s *curve448_precomputed_base =
-    (const curve448_precomputed_s *) &curve448_precomputed_base_as_fe;
+    (const curve448_precomputed_s *)&curve448_precomputed_base_as_fe;
 
 /** Inverse. */
-static void
-gf_invert(gf y, const gf x, int assert_nonzero) {
+static void gf_invert(gf y, const gf x, int assert_nonzero)
+{
     mask_t ret;
 
     gf t1, t2;
-    gf_sqr(t1, x); /* o^2 */
-    ret = gf_isr(t2, t1); /* +-1/sqrt(o^2) = +-1/o */
+    gf_sqr(t1, x);              /* o^2 */
+    ret = gf_isr(t2, t1);       /* +-1/sqrt(o^2) = +-1/o */
     (void)ret;
-    if (assert_nonzero) assert(ret);
+    if (assert_nonzero)
+        assert(ret);
     gf_sqr(t1, t2);
-    gf_mul(t2, t1, x); /* not direct to y in case of alias. */
+    gf_mul(t2, t1, x);          /* not direct to y in case of alias. */
     gf_copy(y, t2);
 }
 
 /** identity = (0,1) */
-const curve448_point_t curve448_point_identity = {{{{{0}}},{{{1}}},{{{1}}},{{{0}}}}};
+const curve448_point_t curve448_point_identity =
+    { {{{{0}}}, {{{1}}}, {{{1}}}, {{{0}}}} };
 
 static void
-point_double_internal (
-    curve448_point_t p,
-    const curve448_point_t q,
-    int before_double
-) {
+point_double_internal(curve448_point_t p,
+                      const curve448_point_t q, int before_double)
+{
     gf a, b, c, d;
-    gf_sqr ( c, q->x );
-    gf_sqr ( a, q->y );
-    gf_add_nr ( d, c, a );             /* 2+e */
-    gf_add_nr ( p->t, q->y, q->x );    /* 2+e */
-    gf_sqr ( b, p->t );
-    gf_subx_nr ( b, b, d, 3 );         /* 4+e */
-    gf_sub_nr ( p->t, a, c );          /* 3+e */
-    gf_sqr ( p->x, q->z );
-    gf_add_nr ( p->z, p->x, p->x );    /* 2+e */
-    gf_subx_nr ( a, p->z, p->t, 4 );   /* 6+e */
-    if (GF_HEADROOM == 5) gf_weak_reduce(a); /* or 1+e */
-    gf_mul ( p->x, a, b );
-    gf_mul ( p->z, p->t, a );
-    gf_mul ( p->y, p->t, d );
-    if (!before_double) gf_mul ( p->t, b, d );
+    gf_sqr(c, q->x);
+    gf_sqr(a, q->y);
+    gf_add_nr(d, c, a);         /* 2+e */
+    gf_add_nr(p->t, q->y, q->x); /* 2+e */
+    gf_sqr(b, p->t);
+    gf_subx_nr(b, b, d, 3);     /* 4+e */
+    gf_sub_nr(p->t, a, c);      /* 3+e */
+    gf_sqr(p->x, q->z);
+    gf_add_nr(p->z, p->x, p->x); /* 2+e */
+    gf_subx_nr(a, p->z, p->t, 4); /* 6+e */
+    if (GF_HEADROOM == 5)
+        gf_weak_reduce(a);      /* or 1+e */
+    gf_mul(p->x, a, b);
+    gf_mul(p->z, p->t, a);
+    gf_mul(p->y, p->t, d);
+    if (!before_double)
+        gf_mul(p->t, b, d);
 }
 
-void curve448_point_double(curve448_point_t p, const curve448_point_t q) {
-    point_double_internal(p,q,0);
+void curve448_point_double(curve448_point_t p, const curve448_point_t q)
+{
+    point_double_internal(p, q, 0);
 }
 
 /* Operations on [p]niels */
-static ossl_inline void
-cond_neg_niels (
-    niels_t n,
-    mask_t neg
-) {
+static ossl_inline void cond_neg_niels(niels_t n, mask_t neg)
+{
     gf_cond_swap(n->a, n->b, neg);
     gf_cond_neg(n->c, neg);
 }
 
-static void pt_to_pniels (
-    pniels_t b,
-    const curve448_point_t a
-) {
-    gf_sub ( b->n->a, a->y, a->x );
-    gf_add ( b->n->b, a->x, a->y );
-    gf_mulw ( b->n->c, a->t, 2*TWISTED_D );
-    gf_add ( b->z, a->z, a->z );
+static void pt_to_pniels(pniels_t b, const curve448_point_t a)
+{
+    gf_sub(b->n->a, a->y, a->x);
+    gf_add(b->n->b, a->x, a->y);
+    gf_mulw(b->n->c, a->t, 2 * TWISTED_D);
+    gf_add(b->z, a->z, a->z);
 }
 
-static void pniels_to_pt (
-    curve448_point_t e,
-    const pniels_t d
-) {
+static void pniels_to_pt(curve448_point_t e, const pniels_t d)
+{
     gf eu;
-    gf_add ( eu, d->n->b, d->n->a );
-    gf_sub ( e->y, d->n->b, d->n->a );
-    gf_mul ( e->t, e->y, eu);
-    gf_mul ( e->x, d->z, e->y );
-    gf_mul ( e->y, d->z, eu );
-    gf_sqr ( e->z, d->z );
+    gf_add(eu, d->n->b, d->n->a);
+    gf_sub(e->y, d->n->b, d->n->a);
+    gf_mul(e->t, e->y, eu);
+    gf_mul(e->x, d->z, e->y);
+    gf_mul(e->y, d->z, eu);
+    gf_sqr(e->z, d->z);
 }
 
-static void
-niels_to_pt (
-    curve448_point_t e,
-    const niels_t n
-) {
-    gf_add ( e->y, n->b, n->a );
-    gf_sub ( e->x, n->b, n->a );
-    gf_mul ( e->t, e->y, e->x );
-    gf_copy ( e->z, ONE );
+static void niels_to_pt(curve448_point_t e, const niels_t n)
+{
+    gf_add(e->y, n->b, n->a);
+    gf_sub(e->x, n->b, n->a);
+    gf_mul(e->t, e->y, e->x);
+    gf_copy(e->z, ONE);
 }
 
 static void
-add_niels_to_pt (
-    curve448_point_t d,
-    const niels_t e,
-    int before_double
-) {
+add_niels_to_pt(curve448_point_t d, const niels_t e, int before_double)
+{
     gf a, b, c;
-    gf_sub_nr ( b, d->y, d->x ); /* 3+e */
-    gf_mul ( a, e->a, b );
-    gf_add_nr ( b, d->x, d->y ); /* 2+e */
-    gf_mul ( d->y, e->b, b );
-    gf_mul ( d->x, e->c, d->t );
-    gf_add_nr ( c, a, d->y );    /* 2+e */
-    gf_sub_nr ( b, d->y, a );    /* 3+e */
-    gf_sub_nr ( d->y, d->z, d->x ); /* 3+e */
-    gf_add_nr ( a, d->x, d->z ); /* 2+e */
-    gf_mul ( d->z, a, d->y );
-    gf_mul ( d->x, d->y, b );
-    gf_mul ( d->y, a, c );
-    if (!before_double) gf_mul ( d->t, b, c );
+    gf_sub_nr(b, d->y, d->x);   /* 3+e */
+    gf_mul(a, e->a, b);
+    gf_add_nr(b, d->x, d->y);   /* 2+e */
+    gf_mul(d->y, e->b, b);
+    gf_mul(d->x, e->c, d->t);
+    gf_add_nr(c, a, d->y);      /* 2+e */
+    gf_sub_nr(b, d->y, a);      /* 3+e */
+    gf_sub_nr(d->y, d->z, d->x); /* 3+e */
+    gf_add_nr(a, d->x, d->z);   /* 2+e */
+    gf_mul(d->z, a, d->y);
+    gf_mul(d->x, d->y, b);
+    gf_mul(d->y, a, c);
+    if (!before_double)
+        gf_mul(d->t, b, c);
 }
 
 static void
-sub_niels_from_pt (
-    curve448_point_t d,
-    const niels_t e,
-    int before_double
-) {
+sub_niels_from_pt(curve448_point_t d, const niels_t e, int before_double)
+{
     gf a, b, c;
-    gf_sub_nr ( b, d->y, d->x ); /* 3+e */
-    gf_mul ( a, e->b, b );
-    gf_add_nr ( b, d->x, d->y ); /* 2+e */
-    gf_mul ( d->y, e->a, b );
-    gf_mul ( d->x, e->c, d->t );
-    gf_add_nr ( c, a, d->y );    /* 2+e */
-    gf_sub_nr ( b, d->y, a );    /* 3+e */
-    gf_add_nr ( d->y, d->z, d->x ); /* 2+e */
-    gf_sub_nr ( a, d->z, d->x ); /* 3+e */
-    gf_mul ( d->z, a, d->y );
-    gf_mul ( d->x, d->y, b );
-    gf_mul ( d->y, a, c );
-    if (!before_double) gf_mul ( d->t, b, c );
+    gf_sub_nr(b, d->y, d->x);   /* 3+e */
+    gf_mul(a, e->b, b);
+    gf_add_nr(b, d->x, d->y);   /* 2+e */
+    gf_mul(d->y, e->a, b);
+    gf_mul(d->x, e->c, d->t);
+    gf_add_nr(c, a, d->y);      /* 2+e */
+    gf_sub_nr(b, d->y, a);      /* 3+e */
+    gf_add_nr(d->y, d->z, d->x); /* 2+e */
+    gf_sub_nr(a, d->z, d->x);   /* 3+e */
+    gf_mul(d->z, a, d->y);
+    gf_mul(d->x, d->y, b);
+    gf_mul(d->y, a, c);
+    if (!before_double)
+        gf_mul(d->t, b, c);
 }
 
 static void
-add_pniels_to_pt (
-    curve448_point_t p,
-    const pniels_t pn,
-    int before_double
-) {
+add_pniels_to_pt(curve448_point_t p, const pniels_t pn, int before_double)
+{
     gf L0;
-    gf_mul ( L0, p->z, pn->z );
-    gf_copy ( p->z, L0 );
-    add_niels_to_pt( p, pn->n, before_double );
+    gf_mul(L0, p->z, pn->z);
+    gf_copy(p->z, L0);
+    add_niels_to_pt(p, pn->n, before_double);
 }
 
 static void
-sub_pniels_from_pt (
-    curve448_point_t p,
-    const pniels_t pn,
-    int before_double
-) {
+sub_pniels_from_pt(curve448_point_t p, const pniels_t pn, int before_double)
+{
     gf L0;
-    gf_mul ( L0, p->z, pn->z );
-    gf_copy ( p->z, L0 );
-    sub_niels_from_pt( p, pn->n, before_double );
+    gf_mul(L0, p->z, pn->z);
+    gf_copy(p->z, L0);
+    sub_niels_from_pt(p, pn->n, before_double);
 }
 
-decaf_bool_t curve448_point_eq ( const curve448_point_t p, const curve448_point_t q ) {
+decaf_bool_t curve448_point_eq(const curve448_point_t p,
+                               const curve448_point_t q)
+{
     mask_t succ;
 
     /* equality mod 2-torsion compares x/y */
     gf a, b;
-    gf_mul ( a, p->y, q->x );
-    gf_mul ( b, q->y, p->x );
-    succ = gf_eq(a,b);
+    gf_mul(a, p->y, q->x);
+    gf_mul(b, q->y, p->x);
+    succ = gf_eq(a, b);
 
     return mask_to_bool(succ);
 }
 
-decaf_bool_t curve448_point_valid (
-    const curve448_point_t p
-) {
+decaf_bool_t curve448_point_valid(const curve448_point_t p)
+{
     mask_t out;
 
-    gf a,b,c;
-    gf_mul(a,p->x,p->y);
-    gf_mul(b,p->z,p->t);
-    out = gf_eq(a,b);
-    gf_sqr(a,p->x);
-    gf_sqr(b,p->y);
-    gf_sub(a,b,a);
-    gf_sqr(b,p->t);
-    gf_mulw(c,b,TWISTED_D);
-    gf_sqr(b,p->z);
-    gf_add(b,b,c);
-    out &= gf_eq(a,b);
-    out &= ~gf_eq(p->z,ZERO);
+    gf a, b, c;
+    gf_mul(a, p->x, p->y);
+    gf_mul(b, p->z, p->t);
+    out = gf_eq(a, b);
+    gf_sqr(a, p->x);
+    gf_sqr(b, p->y);
+    gf_sub(a, b, a);
+    gf_sqr(b, p->t);
+    gf_mulw(c, b, TWISTED_D);
+    gf_sqr(b, p->z);
+    gf_add(b, b, c);
+    out &= gf_eq(a, b);
+    out &= ~gf_eq(p->z, ZERO);
     return mask_to_bool(out);
 }
 
 static ossl_inline void
-constant_time_lookup_niels (
-    niels_s *__restrict__ ni,
-    const niels_t *table,
-    int nelts,
-    int idx
-) {
+constant_time_lookup_niels(niels_s * __restrict__ ni,
+                           const niels_t * table, int nelts, int idx)
+{
     constant_time_lookup(ni, table, sizeof(niels_s), nelts, idx);
 }
 
-void curve448_precomputed_scalarmul (
-    curve448_point_t out,
-    const curve448_precomputed_s *table,
-    const curve448_scalar_t scalar
-) {
+void curve448_precomputed_scalarmul(curve448_point_t out,
+                                    const curve448_precomputed_s * table,
+                                    const curve448_scalar_t scalar)
+{
     int i;
-    unsigned j,k;
+    unsigned j, k;
     const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;
     niels_t ni;
-    
+
     curve448_scalar_t scalar1x;
     curve448_scalar_add(scalar1x, scalar, precomputed_scalarmul_adjustment);
-    curve448_scalar_halve(scalar1x,scalar1x);
-    
-    for (i=s-1; i>=0; i--) {
-        if (i != (int)s-1) point_double_internal(out,out,0);
-        
-        for (j=0; j<n; j++) {
+    curve448_scalar_halve(scalar1x, scalar1x);
+
+    for (i = s - 1; i >= 0; i--) {
+        if (i != (int)s - 1)
+            point_double_internal(out, out, 0);
+
+        for (j = 0; j < n; j++) {
             int tab = 0;
             mask_t invert;
-         
-            for (k=0; k<t; k++) {
-                unsigned int bit = i + s*(k + j*t);
+
+            for (k = 0; k < t; k++) {
+                unsigned int bit = i + s * (k + j * t);
                 if (bit < DECAF_448_SCALAR_BITS) {
-                    tab |= (scalar1x->limb[bit/WBITS] >> (bit%WBITS) & 1) << k;
+                    tab |=
+                        (scalar1x->limb[bit / WBITS] >> (bit % WBITS) & 1) << k;
                 }
             }
-            
-            invert = (tab>>(t-1))-1;
+
+            invert = (tab >> (t - 1)) - 1;
             tab ^= invert;
-            tab &= (1<<(t-1)) - 1;
+            tab &= (1 << (t - 1)) - 1;
 
-            constant_time_lookup_niels(ni, &table->table[j<<(t-1)], 1<<(t-1), tab);
+            constant_time_lookup_niels(ni, &table->table[j << (t - 1)],
+                                       1 << (t - 1), tab);
 
             cond_neg_niels(ni, invert);
-            if ((i!=(int)s-1)||j) {
-                add_niels_to_pt(out, ni, j==n-1 && i);
+            if ((i != (int)s - 1) || j) {
+                add_niels_to_pt(out, ni, j == n - 1 && i);
             } else {
                 niels_to_pt(out, ni);
             }
         }
     }
-    
-    OPENSSL_cleanse(ni,sizeof(ni));
-    OPENSSL_cleanse(scalar1x,sizeof(scalar1x));
+
+    OPENSSL_cleanse(ni, sizeof(ni));
+    OPENSSL_cleanse(scalar1x, sizeof(scalar1x));
 }
 
-void curve448_point_mul_by_ratio_and_encode_like_eddsa (
-    uint8_t enc[DECAF_EDDSA_448_PUBLIC_BYTES],
-    const curve448_point_t p
-) {
-    
+void curve448_point_mul_by_ratio_and_encode_like_eddsa(uint8_t
+                                                       enc
+                                                       [DECAF_EDDSA_448_PUBLIC_BYTES],
+                                                       const curve448_point_t p)
+{
+
     /* The point is now on the twisted curve.  Move it to untwisted. */
     gf x, y, z, t;
     curve448_point_t q;
-    curve448_point_copy(q,p);
+    curve448_point_copy(q, p);
 
     {
         /* 4-isogeny: 2xy/(y^+x^2), (y^2-x^2)/(2z^2-y^2+x^2) */
         gf u;
-        gf_sqr ( x, q->x );
-        gf_sqr ( t, q->y );
-        gf_add( u, x, t );
-        gf_add( z, q->y, q->x );
-        gf_sqr ( y, z);
-        gf_sub ( y, y, u );
-        gf_sub ( z, t, x );
-        gf_sqr ( x, q->z );
-        gf_add ( t, x, x); 
-        gf_sub ( t, t, z);
-        gf_mul ( x, t, y );
-        gf_mul ( y, z, u );
-        gf_mul ( z, u, t );
-        OPENSSL_cleanse(u,sizeof(u));
+        gf_sqr(x, q->x);
+        gf_sqr(t, q->y);
+        gf_add(u, x, t);
+        gf_add(z, q->y, q->x);
+        gf_sqr(y, z);
+        gf_sub(y, y, u);
+        gf_sub(z, t, x);
+        gf_sqr(x, q->z);
+        gf_add(t, x, x);
+        gf_sub(t, t, z);
+        gf_mul(x, t, y);
+        gf_mul(y, z, u);
+        gf_mul(z, u, t);
+        OPENSSL_cleanse(u, sizeof(u));
     }
 
     /* Affinize */
-    gf_invert(z,z,1);
-    gf_mul(t,x,z);
-    gf_mul(x,y,z);
-    
+    gf_invert(z, z, 1);
+    gf_mul(t, x, z);
+    gf_mul(x, y, z);
+
     /* Encode */
-    enc[DECAF_EDDSA_448_PRIVATE_BYTES-1] = 0;
+    enc[DECAF_EDDSA_448_PRIVATE_BYTES - 1] = 0;
     gf_serialize(enc, x, 1);
-    enc[DECAF_EDDSA_448_PRIVATE_BYTES-1] |= 0x80 & gf_lobit(t);
+    enc[DECAF_EDDSA_448_PRIVATE_BYTES - 1] |= 0x80 & gf_lobit(t);
 
-    OPENSSL_cleanse(x,sizeof(x));
-    OPENSSL_cleanse(y,sizeof(y));
-    OPENSSL_cleanse(z,sizeof(z));
-    OPENSSL_cleanse(t,sizeof(t));
+    OPENSSL_cleanse(x, sizeof(x));
+    OPENSSL_cleanse(y, sizeof(y));
+    OPENSSL_cleanse(z, sizeof(z));
+    OPENSSL_cleanse(t, sizeof(t));
     curve448_point_destroy(q);
 }
 
-
-decaf_error_t curve448_point_decode_like_eddsa_and_mul_by_ratio (
-    curve448_point_t p,
-    const uint8_t enc[DECAF_EDDSA_448_PUBLIC_BYTES]
-) {
+decaf_error_t curve448_point_decode_like_eddsa_and_mul_by_ratio(curve448_point_t
+                                                                p,
+                                                                const uint8_t
+                                                                enc
+                                                                [DECAF_EDDSA_448_PUBLIC_BYTES]
+    )
+{
     uint8_t enc2[DECAF_EDDSA_448_PUBLIC_BYTES];
     mask_t low;
     mask_t succ;
 
-    memcpy(enc2,enc,sizeof(enc2));
+    memcpy(enc2, enc, sizeof(enc2));
+
+    low = ~word_is_zero(enc2[DECAF_EDDSA_448_PRIVATE_BYTES - 1] & 0x80);
+    enc2[DECAF_EDDSA_448_PRIVATE_BYTES - 1] &= ~0x80;
 
-    low = ~word_is_zero(enc2[DECAF_EDDSA_448_PRIVATE_BYTES-1] & 0x80);
-    enc2[DECAF_EDDSA_448_PRIVATE_BYTES-1] &= ~0x80;
-    
     succ = gf_deserialize(p->y, enc2, 1, 0);
 #if 0 == 0
-    succ &= word_is_zero(enc2[DECAF_EDDSA_448_PRIVATE_BYTES-1]);
+    succ &= word_is_zero(enc2[DECAF_EDDSA_448_PRIVATE_BYTES - 1]);
 #endif
 
-    gf_sqr(p->x,p->y);
-    gf_sub(p->z,ONE,p->x); /* num = 1-y^2 */
-    gf_mulw(p->t,p->x,EDWARDS_D); /* dy^2 */
-    gf_sub(p->t,ONE,p->t); /* denom = 1-dy^2 or 1-d + dy^2 */
-    
-    gf_mul(p->x,p->z,p->t);
-    succ &= gf_isr(p->t,p->x); /* 1/sqrt(num * denom) */
-    
-    gf_mul(p->x,p->t,p->z); /* sqrt(num / denom) */
-    gf_cond_neg(p->x,gf_lobit(p->x)^low);
-    gf_copy(p->z,ONE);
-  
+    gf_sqr(p->x, p->y);
+    gf_sub(p->z, ONE, p->x);    /* num = 1-y^2 */
+    gf_mulw(p->t, p->x, EDWARDS_D); /* dy^2 */
+    gf_sub(p->t, ONE, p->t);    /* denom = 1-dy^2 or 1-d + dy^2 */
+
+    gf_mul(p->x, p->z, p->t);
+    succ &= gf_isr(p->t, p->x); /* 1/sqrt(num * denom) */
+
+    gf_mul(p->x, p->t, p->z);   /* sqrt(num / denom) */
+    gf_cond_neg(p->x, gf_lobit(p->x) ^ low);
+    gf_copy(p->z, ONE);
+
     {
         /* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */
         gf a, b, c, d;
-        gf_sqr ( c, p->x );
-        gf_sqr ( a, p->y );
-        gf_add ( d, c, a );
-        gf_add ( p->t, p->y, p->x );
-        gf_sqr ( b, p->t );
-        gf_sub ( b, b, d );
-        gf_sub ( p->t, a, c );
-        gf_sqr ( p->x, p->z );
-        gf_add ( p->z, p->x, p->x );
-        gf_sub ( a, p->z, d );
-        gf_mul ( p->x, a, b );
-        gf_mul ( p->z, p->t, a );
-        gf_mul ( p->y, p->t, d );
-        gf_mul ( p->t, b, d );
-        OPENSSL_cleanse(a,sizeof(a));
-        OPENSSL_cleanse(b,sizeof(b));
-        OPENSSL_cleanse(c,sizeof(c));
-        OPENSSL_cleanse(d,sizeof(d));
+        gf_sqr(c, p->x);
+        gf_sqr(a, p->y);
+        gf_add(d, c, a);
+        gf_add(p->t, p->y, p->x);
+        gf_sqr(b, p->t);
+        gf_sub(b, b, d);
+        gf_sub(p->t, a, c);
+        gf_sqr(p->x, p->z);
+        gf_add(p->z, p->x, p->x);
+        gf_sub(a, p->z, d);
+        gf_mul(p->x, a, b);
+        gf_mul(p->z, p->t, a);
+        gf_mul(p->y, p->t, d);
+        gf_mul(p->t, b, d);
+        OPENSSL_cleanse(a, sizeof(a));
+        OPENSSL_cleanse(b, sizeof(b));
+        OPENSSL_cleanse(c, sizeof(c));
+        OPENSSL_cleanse(d, sizeof(d));
     }
-    
-    OPENSSL_cleanse(enc2,sizeof(enc2));
+
+    OPENSSL_cleanse(enc2, sizeof(enc2));
     assert(curve448_point_valid(p) || ~succ);
-    
+
     return decaf_succeed_if(mask_to_bool(succ));
 }
 
-decaf_error_t decaf_x448 (
-    uint8_t out[X_PUBLIC_BYTES],
-    const uint8_t base[X_PUBLIC_BYTES],
-    const uint8_t scalar[X_PRIVATE_BYTES]
-) {
+decaf_error_t decaf_x448(uint8_t out[X_PUBLIC_BYTES],
+                         const uint8_t base[X_PUBLIC_BYTES],
+                         const uint8_t scalar[X_PRIVATE_BYTES]
+    )
+{
     gf x1, x2, z2, x3, z3, t1, t2;
     int t;
     mask_t swap = 0;
     mask_t nz;
 
-    ignore_result(gf_deserialize(x1,base,1,0));
-    gf_copy(x2,ONE);
-    gf_copy(z2,ZERO);
-    gf_copy(x3,x1);
-    gf_copy(z3,ONE);
-    
-    for (t = X_PRIVATE_BITS-1; t>=0; t--) {
-        uint8_t sb = scalar[t/8];
+    ignore_result(gf_deserialize(x1, base, 1, 0));
+    gf_copy(x2, ONE);
+    gf_copy(z2, ZERO);
+    gf_copy(x3, x1);
+    gf_copy(z3, ONE);
+
+    for (t = X_PRIVATE_BITS - 1; t >= 0; t--) {
+        uint8_t sb = scalar[t / 8];
         mask_t k_t;
-        
+
         /* Scalar conditioning */
-        if (t/8==0) sb &= -(uint8_t)COFACTOR;
-        else if (t == X_PRIVATE_BITS-1) sb = -1;
-        
-        k_t = (sb>>(t%8)) & 1;
-        k_t = -k_t; /* set to all 0s or all 1s */
-        
+        if (t / 8 == 0)
+            sb &= -(uint8_t)COFACTOR;
+        else if (t == X_PRIVATE_BITS - 1)
+            sb = -1;
+
+        k_t = (sb >> (t % 8)) & 1;
+        k_t = -k_t;             /* set to all 0s or all 1s */
+
         swap ^= k_t;
-        gf_cond_swap(x2,x3,swap);
-        gf_cond_swap(z2,z3,swap);
+        gf_cond_swap(x2, x3, swap);
+        gf_cond_swap(z2, z3, swap);
         swap = k_t;
-        
-        gf_add_nr(t1,x2,z2); /* A = x2 + z2 */        /* 2+e */
-        gf_sub_nr(t2,x2,z2); /* B = x2 - z2 */        /* 3+e */
-        gf_sub_nr(z2,x3,z3); /* D = x3 - z3 */        /* 3+e */
-        gf_mul(x2,t1,z2);    /* DA */
-        gf_add_nr(z2,z3,x3); /* C = x3 + z3 */        /* 2+e */
-        gf_mul(x3,t2,z2);    /* CB */
-        gf_sub_nr(z3,x2,x3); /* DA-CB */              /* 3+e */
-        gf_sqr(z2,z3);       /* (DA-CB)^2 */
-        gf_mul(z3,x1,z2);    /* z3 = x1(DA-CB)^2 */
-        gf_add_nr(z2,x2,x3); /* (DA+CB) */            /* 2+e */
-        gf_sqr(x3,z2);       /* x3 = (DA+CB)^2 */
-        
-        gf_sqr(z2,t1);       /* AA = A^2 */
-        gf_sqr(t1,t2);       /* BB = B^2 */
-        gf_mul(x2,z2,t1);    /* x2 = AA*BB */
-        gf_sub_nr(t2,z2,t1); /* E = AA-BB */          /* 3+e */
-        
-        gf_mulw(t1,t2,-EDWARDS_D); /* E*-d = a24*E */
-        gf_add_nr(t1,t1,z2); /* AA + a24*E */         /* 2+e */
-        gf_mul(z2,t2,t1); /* z2 = E(AA+a24*E) */
+
+        gf_add_nr(t1, x2, z2);  /* A = x2 + z2 *//* 2+e */
+        gf_sub_nr(t2, x2, z2);  /* B = x2 - z2 *//* 3+e */
+        gf_sub_nr(z2, x3, z3);  /* D = x3 - z3 *//* 3+e */
+        gf_mul(x2, t1, z2);     /* DA */
+        gf_add_nr(z2, z3, x3);  /* C = x3 + z3 *//* 2+e */
+        gf_mul(x3, t2, z2);     /* CB */
+        gf_sub_nr(z3, x2, x3);  /* DA-CB *//* 3+e */
+        gf_sqr(z2, z3);         /* (DA-CB)^2 */
+        gf_mul(z3, x1, z2);     /* z3 = x1(DA-CB)^2 */
+        gf_add_nr(z2, x2, x3);  /* (DA+CB) *//* 2+e */
+        gf_sqr(x3, z2);         /* x3 = (DA+CB)^2 */
+
+        gf_sqr(z2, t1);         /* AA = A^2 */
+        gf_sqr(t1, t2);         /* BB = B^2 */
+        gf_mul(x2, z2, t1);     /* x2 = AA*BB */
+        gf_sub_nr(t2, z2, t1);  /* E = AA-BB *//* 3+e */
+
+        gf_mulw(t1, t2, -EDWARDS_D); /* E*-d = a24*E */
+        gf_add_nr(t1, t1, z2);  /* AA + a24*E *//* 2+e */
+        gf_mul(z2, t2, t1);     /* z2 = E(AA+a24*E) */
     }
-    
+
     /* Finish */
-    gf_cond_swap(x2,x3,swap);
-    gf_cond_swap(z2,z3,swap);
-    gf_invert(z2,z2,0);
-    gf_mul(x1,x2,z2);
-    gf_serialize(out,x1,1);
-    nz = ~gf_eq(x1,ZERO);
-    
-    OPENSSL_cleanse(x1,sizeof(x1));
-    OPENSSL_cleanse(x2,sizeof(x2));
-    OPENSSL_cleanse(z2,sizeof(z2));
-    OPENSSL_cleanse(x3,sizeof(x3));
-    OPENSSL_cleanse(z3,sizeof(z3));
-    OPENSSL_cleanse(t1,sizeof(t1));
-    OPENSSL_cleanse(t2,sizeof(t2));
-    
+    gf_cond_swap(x2, x3, swap);
+    gf_cond_swap(z2, z3, swap);
+    gf_invert(z2, z2, 0);
+    gf_mul(x1, x2, z2);
+    gf_serialize(out, x1, 1);
+    nz = ~gf_eq(x1, ZERO);
+
+    OPENSSL_cleanse(x1, sizeof(x1));
+    OPENSSL_cleanse(x2, sizeof(x2));
+    OPENSSL_cleanse(z2, sizeof(z2));
+    OPENSSL_cleanse(x3, sizeof(x3));
+    OPENSSL_cleanse(z3, sizeof(z3));
+    OPENSSL_cleanse(t1, sizeof(t1));
+    OPENSSL_cleanse(t2, sizeof(t2));
+
     return decaf_succeed_if(mask_to_bool(nz));
 }
 
 /* Thanks Johan Pascal */
-void decaf_ed448_convert_public_key_to_x448 (
-    uint8_t x[DECAF_X448_PUBLIC_BYTES],
-    const uint8_t ed[DECAF_EDDSA_448_PUBLIC_BYTES]
-) {
+void decaf_ed448_convert_public_key_to_x448(uint8_t x[DECAF_X448_PUBLIC_BYTES],
+                                            const uint8_t
+                                            ed[DECAF_EDDSA_448_PUBLIC_BYTES]
+    )
+{
     gf y;
-    const uint8_t mask = (uint8_t)(0xFE<<(7));
+    const uint8_t mask = (uint8_t)(0xFE << (7));
     ignore_result(gf_deserialize(y, ed, 1, mask));
-    
+
     {
-        gf n,d;
-        
+        gf n, d;
+
         /* u = y^2 * (1-dy^2) / (1-y^2) */
-        gf_sqr(n,y); /* y^2*/
-        gf_sub(d,ONE,n); /* 1-y^2*/
-        gf_invert(d,d,0); /* 1/(1-y^2)*/
-        gf_mul(y,n,d); /* y^2 / (1-y^2) */
-        gf_mulw(d,n,EDWARDS_D); /* dy^2*/
-        gf_sub(d, ONE, d); /* 1-dy^2*/
-        gf_mul(n, y, d); /* y^2 * (1-dy^2) / (1-y^2) */
-        gf_serialize(x,n,1);
-        
-        OPENSSL_cleanse(y,sizeof(y));
-        OPENSSL_cleanse(n,sizeof(n));
-        OPENSSL_cleanse(d,sizeof(d));
+        gf_sqr(n, y);           /* y^2 */
+        gf_sub(d, ONE, n);      /* 1-y^2 */
+        gf_invert(d, d, 0);     /* 1/(1-y^2) */
+        gf_mul(y, n, d);        /* y^2 / (1-y^2) */
+        gf_mulw(d, n, EDWARDS_D); /* dy^2 */
+        gf_sub(d, ONE, d);      /* 1-dy^2 */
+        gf_mul(n, y, d);        /* y^2 * (1-dy^2) / (1-y^2) */
+        gf_serialize(x, n, 1);
+
+        OPENSSL_cleanse(y, sizeof(y));
+        OPENSSL_cleanse(n, sizeof(n));
+        OPENSSL_cleanse(d, sizeof(d));
     }
 }
 
-void curve448_point_mul_by_ratio_and_encode_like_x448 (
-    uint8_t out[X_PUBLIC_BYTES],
-    const curve448_point_t p
-) {
+void curve448_point_mul_by_ratio_and_encode_like_x448(uint8_t
+                                                      out[X_PUBLIC_BYTES],
+                                                      const curve448_point_t p)
+{
     curve448_point_t q;
-    curve448_point_copy(q,p);
-    gf_invert(q->t,q->x,0); /* 1/x */
-    gf_mul(q->z,q->t,q->y); /* y/x */
-    gf_sqr(q->y,q->z); /* (y/x)^2 */
-    gf_serialize(out,q->y,1);
+    curve448_point_copy(q, p);
+    gf_invert(q->t, q->x, 0);   /* 1/x */
+    gf_mul(q->z, q->t, q->y);   /* y/x */
+    gf_sqr(q->y, q->z);         /* (y/x)^2 */
+    gf_serialize(out, q->y, 1);
     curve448_point_destroy(q);
 }
 
-void decaf_x448_derive_public_key (
-    uint8_t out[X_PUBLIC_BYTES],
-    const uint8_t scalar[X_PRIVATE_BYTES]
-) {
+void decaf_x448_derive_public_key(uint8_t out[X_PUBLIC_BYTES],
+                                  const uint8_t scalar[X_PRIVATE_BYTES]
+    )
+{
     /* Scalar conditioning */
     uint8_t scalar2[X_PRIVATE_BYTES];
     curve448_scalar_t the_scalar;
     curve448_point_t p;
     unsigned int i;
 
-    memcpy(scalar2,scalar,sizeof(scalar2));
+    memcpy(scalar2, scalar, sizeof(scalar2));
     scalar2[0] &= -(uint8_t)COFACTOR;
-    
-    scalar2[X_PRIVATE_BYTES-1] &= ~(-1u<<((X_PRIVATE_BITS+7)%8));
-    scalar2[X_PRIVATE_BYTES-1] |= 1<<((X_PRIVATE_BITS+7)%8);
-    
-    curve448_scalar_decode_long(the_scalar,scalar2,sizeof(scalar2));
-    
+
+    scalar2[X_PRIVATE_BYTES - 1] &= ~(-1u << ((X_PRIVATE_BITS + 7) % 8));
+    scalar2[X_PRIVATE_BYTES - 1] |= 1 << ((X_PRIVATE_BITS + 7) % 8);
+
+    curve448_scalar_decode_long(the_scalar, scalar2, sizeof(scalar2));
+
     /* Compensate for the encoding ratio */
-    for (i=1; i<DECAF_X448_ENCODE_RATIO; i<<=1) {
-        curve448_scalar_halve(the_scalar,the_scalar);
+    for (i = 1; i < DECAF_X448_ENCODE_RATIO; i <<= 1) {
+        curve448_scalar_halve(the_scalar, the_scalar);
     }
-    curve448_precomputed_scalarmul(p,curve448_precomputed_base,the_scalar);
-    curve448_point_mul_by_ratio_and_encode_like_x448(out,p);
+    curve448_precomputed_scalarmul(p, curve448_precomputed_base, the_scalar);
+    curve448_point_mul_by_ratio_and_encode_like_x448(out, p);
     curve448_point_destroy(p);
 }
 
@@ -555,18 +558,17 @@ void decaf_x448_derive_public_key (
  * Control for variable-time scalar multiply algorithms.
  */
 struct smvt_control {
-  int power, addend;
+    int power, addend;
 };
 
-static int recode_wnaf (
-    struct smvt_control *control, /* [nbits/(table_bits+1) + 3] */
-    const curve448_scalar_t scalar,
-    unsigned int table_bits
-) {
-    unsigned int table_size = DECAF_448_SCALAR_BITS/(table_bits+1) + 3;
+static int recode_wnaf(struct smvt_control *control, /* [nbits/(table_bits+1) +
+                                                      * 3] */
+                       const curve448_scalar_t scalar, unsigned int table_bits)
+{
+    unsigned int table_size = DECAF_448_SCALAR_BITS / (table_bits + 1) + 3;
     int position = table_size - 1; /* at the end */
     uint64_t current = scalar->limb[0] & 0xFFFF;
-    uint32_t mask = (1<<(table_bits+1))-1;
+    uint32_t mask = (1 << (table_bits + 1)) - 1;
     unsigned int w;
     const unsigned int B_OVER_16 = sizeof(scalar->limb[0]) / 2;
     unsigned int n, i;
@@ -576,86 +578,94 @@ static int recode_wnaf (
     control[position].addend = 0;
     position--;
 
-    /* PERF: Could negate scalar if it's large.  But then would need more cases
-     * in the actual code that uses it, all for an expected reduction of like 1/5 op.
-     * Probably not worth it.
+    /*
+     * PERF: Could negate scalar if it's large.  But then would need more cases
+     * in the actual code that uses it, all for an expected reduction of like
+     * 1/5 op. Probably not worth it.
      */
 
-    for (w = 1; w<(DECAF_448_SCALAR_BITS-1)/16+3; w++) {
-        if (w < (DECAF_448_SCALAR_BITS-1)/16+1) {
+    for (w = 1; w < (DECAF_448_SCALAR_BITS - 1) / 16 + 3; w++) {
+        if (w < (DECAF_448_SCALAR_BITS - 1) / 16 + 1) {
             /* Refill the 16 high bits of current */
-            current += (uint32_t)((scalar->limb[w/B_OVER_16]>>(16*(w%B_OVER_16)))<<16);
+            current +=
+                (uint32_t)((scalar->limb[w / B_OVER_16] >> (16 *
+                                                            (w %
+                                                             B_OVER_16))) <<
+                           16);
         }
-        
+
         while (current & 0xFFFF) {
-            uint32_t pos = __builtin_ctz((uint32_t)current), odd = (uint32_t)current >> pos;
+            uint32_t pos = __builtin_ctz((uint32_t)current), odd =
+                (uint32_t)current >> pos;
             int32_t delta = odd & mask;
 
             assert(position >= 0);
-            if (odd & 1<<(table_bits+1)) delta -= (1<<(table_bits+1));
+            if (odd & 1 << (table_bits + 1))
+                delta -= (1 << (table_bits + 1));
             current -= delta << pos;
-            control[position].power = pos + 16*(w-1);
+            control[position].power = pos + 16 * (w - 1);
             control[position].addend = delta;
             position--;
         }
         current >>= 16;
     }
-    assert(current==0);
-    
+    assert(current == 0);
+
     position++;
     n = table_size - position;
-    for (i=0; i<n; i++) {
-        control[i] = control[i+position];
+    for (i = 0; i < n; i++) {
+        control[i] = control[i + position];
     }
-    return n-1;
+    return n - 1;
 }
 
 static void
-prepare_wnaf_table(
-    pniels_t *output,
-    const curve448_point_t working,
-    unsigned int tbits
-) {
+prepare_wnaf_table(pniels_t * output,
+                   const curve448_point_t working, unsigned int tbits)
+{
     curve448_point_t tmp;
     int i;
     pniels_t twop;
 
     pt_to_pniels(output[0], working);
 
-    if (tbits == 0) return;
+    if (tbits == 0)
+        return;
 
-    curve448_point_double(tmp,working);
+    curve448_point_double(tmp, working);
     pt_to_pniels(twop, tmp);
 
-    add_pniels_to_pt(tmp, output[0],0);
+    add_pniels_to_pt(tmp, output[0], 0);
     pt_to_pniels(output[1], tmp);
 
-    for (i=2; i < 1<<tbits; i++) {
-        add_pniels_to_pt(tmp, twop,0);
+    for (i = 2; i < 1 << tbits; i++) {
+        add_pniels_to_pt(tmp, twop, 0);
         pt_to_pniels(output[i], tmp);
     }
-    
+
     curve448_point_destroy(tmp);