Rename the decaf files to curve448 files

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

1 files changed, 726 insertions, 0 deletions

diff --git a/crypto/ec/curve448/curve448.c b/crypto/ec/curve448/curve448.c
new file mode 100644
index 0000000000..d5b684b3bd
--- /dev/null
+++ b/crypto/ec/curve448/curve448.c
@@ -0,0 +1,726 @@
+/**
+ * @file ed448goldilocks/decaf.c
+ * @author Mike Hamburg
+ *
+ * @copyright
+ *   Copyright (c) 2015-2016 Cryptography Research, Inc.  \n
+ *   Released under the MIT License.  See LICENSE.txt for license information.
+ *
+ * @brief Decaf high-level functions.
+ *
+ * @warning This file was automatically generated in Python.
+ * Please do not edit it.
+ */
+#include <openssl/crypto.h>
+#include "word.h"
+#include "field.h"
+
+#include "point_448.h"
+#include "ed448.h"
+#include "curve448_lcl.h"
+
+#define COFACTOR 4
+
+/* Comb config: number of combs, n, t, s. */
+#define COMBS_N 5
+#define COMBS_T 5
+#define COMBS_S 18
+#define DECAF_WINDOW_BITS 5
+#define DECAF_WNAF_FIXED_TABLE_BITS 5
+#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)
+}}};
+
+const uint8_t decaf_x448_base_point[DECAF_X448_PUBLIC_BYTES] = { 0x05 };
+
+#define RISTRETTO_FACTOR DECAF_448_RISTRETTO_FACTOR
+const gf RISTRETTO_FACTOR = {{{
+    0x42ef0f45572736, 0x7bf6aa20ce5296, 0xf4fd6eded26033, 0x968c14ba839a66, 0xb8d54b64a2d780, 0x6aa0a1f1a7b8a5, 0x683bf68d722fa2, 0x22d962fbeb24f7
+}}};
+
+
+#define TWISTED_D ((EDWARDS_D)-1)
+
+#define EFF_D (-(TWISTED_D))
+#define NEG_D 1
+
+/* End of template stuff */
+
+#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];
+
+/* Precomputed base */
+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;
+
+/** Inverse. */
+static void
+gf_invert(gf y, const gf x, int assert_nonzero) {
+    gf t1, t2;
+    gf_sqr(t1, x); // o^2
+    mask_t ret = gf_isr(t2, t1); // +-1/sqrt(o^2) = +-1/o
+    (void)ret;
+    if (assert_nonzero) assert(ret);
+    gf_sqr(t1, t2);
+    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}}}}};
+
+static void
+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 );
+}
+
+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
+) {
+    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 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 );
+}
+
+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
+) {
+    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 );
+}
+
+static void
+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 );
+}
+
+static void
+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 );
+}
+
+static void
+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 );
+}
+
+decaf_bool_t curve448_point_eq ( const curve448_point_t p, const curve448_point_t q ) {
+    /* equality mod 2-torsion compares x/y */
+    gf a, b;
+    gf_mul ( a, p->y, q->x );
+    gf_mul ( b, q->y, p->x );
+    mask_t succ = gf_eq(a,b);
+
+    return mask_to_bool(succ);
+}
+
+decaf_bool_t curve448_point_valid (
+    const curve448_point_t p
+) {
+    gf a,b,c;
+    gf_mul(a,p->x,p->y);
+    gf_mul(b,p->z,p->t);
+    mask_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(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
+) {
+    int i;
+    unsigned j,k;
+    const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;
+    
+    curve448_scalar_t scalar1x;
+    curve448_scalar_add(scalar1x, scalar, precomputed_scalarmul_adjustment);
+    curve448_scalar_halve(scalar1x,scalar1x);
+    
+    niels_t ni;
+    
+    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;
+         
+            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;
+                }
+            }
+            
+            mask_t invert = (tab>>(t-1))-1;
+            tab ^= invert;
+            tab &= (1<<(t-1)) - 1;
+
+            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);
+            } else {
+                niels_to_pt(out, ni);
+            }
+        }
+    }
+    
+    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
+) {
+    
+    /* 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);
+
+    {
+        /* 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));
+    }
+
+    /* Affinize */
+    gf_invert(z,z,1);
+    gf_mul(t,x,z);
+    gf_mul(x,y,z);
+    
+    /* Encode */
+    enc[DECAF_EDDSA_448_PRIVATE_BYTES-1] = 0;
+    gf_serialize(enc, x, 1);
+    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));
+    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]
+) {
+    uint8_t enc2[DECAF_EDDSA_448_PUBLIC_BYTES];
+    memcpy(enc2,enc,sizeof(enc2));
+
+    mask_t low = ~word_is_zero(enc2[DECAF_EDDSA_448_PRIVATE_BYTES-1] & 0x80);
+    enc2[DECAF_EDDSA_448_PRIVATE_BYTES-1] &= ~0x80;
+    
+    mask_t succ = gf_deserialize(p->y, enc2, 1, 0);
+#if 0 == 0
+    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);
+  
+    {
+        /* 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));
+    }
+    
+    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]
+) {
+    gf x1, x2, z2, x3, z3, t1, t2;
+    ignore_result(gf_deserialize(x1,base,1,0));
+    gf_copy(x2,ONE);
+    gf_copy(z2,ZERO);
+    gf_copy(x3,x1);
+    gf_copy(z3,ONE);
+    
+    int t;
+    mask_t swap = 0;
+    
+    for (t = X_PRIVATE_BITS-1; t>=0; t--) {
+        uint8_t sb = scalar[t/8];
+        
+        /* Scalar conditioning */
+        if (t/8==0) sb &= -(uint8_t)COFACTOR;
+        else if (t == X_PRIVATE_BITS-1) sb = -1;
+        
+        mask_t 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);
+        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) */
+    }
+    
+    /* 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);
+    mask_t 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]
+) {
+    gf y;
+    const uint8_t mask = (uint8_t)(0xFE<<(7));
+    ignore_result(gf_deserialize(y, ed, 1, mask));
+    
+    {
+        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));
+    }
+}
+
+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_destroy(q);
+}
+
+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];
+    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_t the_scalar;
+    curve448_scalar_decode_long(the_scalar,scalar2,sizeof(scalar2));
+    
+    /* Compensate for the encoding ratio */
+    for (unsigned i=1; i<DECAF_X448_ENCODE_RATIO; i<<=1) {
+        curve448_scalar_halve(the_scalar,the_scalar);
+    }
+    curve448_point_t 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);
+}
+
+/**
+ * @cond internal
+ * Control for variable-time scalar multiply algorithms.
+ */
+struct smvt_control {
+  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;
+    int position = table_size - 1; /* at the end */
+    
+    /* place the end marker */
+    control[position].power = -1;
+    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.
+     */
+    
+    uint64_t current = scalar->limb[0] & 0xFFFF;
+    uint32_t mask = (1<<(table_bits+1))-1;
+
+    unsigned int w;
+    const unsigned int B_OVER_16 = sizeof(scalar->limb[0]) / 2;
+    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);
+        }
+        
+        while (current & 0xFFFF) {
+            assert(position >= 0);
+            uint32_t pos = __builtin_ctz((uint32_t)current), odd = (uint32_t)current >> pos;
+            int32_t delta = odd & mask;
+            if (odd & 1<<(table_bits+1)) delta -= (1<<(table_bits+1));
+            current -= delta << pos;
+            control[position].power = pos + 16*(w-1);
+            control[position].addend = delta;
+            position--;
+        }
+        current >>= 16;
+    }
+    assert(current==0);
+    
+    position++;
+    unsigned int n = table_size - position;
+    unsigned int i;
+    for (i=0; i<n; i++) {
+        control[i] = control[i+position];
+    }
+    return n-1;
+}
+
+static void
+prepare_wnaf_table(
+    pniels_t *output,
+    const curve448_point_t working,
+    unsigned int tbits
+) {
+    curve448_point_t tmp;
+    int i;
+    pt_to_pniels(output[0], working);
+
+    if (tbits == 0) return;
+
+    curve448_point_double(tmp,working);
+    pniels_t twop;
+    pt_to_pniels(twop, tmp);
+
+    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);
+        pt_to_pniels(output[i], tmp);
+    }
+    
+    curve448_point_destroy(tmp);
+    OPENSSL_cleanse(twop,sizeof(twop));
+}
+
+extern const gf curve448_precomputed_wnaf_as_fe[];
+static const niels_t *curve448_wnaf_base = (const niels_t *)curve448_precomputed_wnaf_as_fe;
+
+void curve448_base_double_scalarmul_non_secret (
+    curve448_point_t combo,
+    const curve448_scalar_t scalar1,
+    const curve448_point_t base2,
+    const curve448_scalar_t scalar2
+) {
+    const int table_bits_var = DECAF_WNAF_VAR_TABLE_BITS,
+        table_bits_pre = DECAF_WNAF_FIXED_TABLE_BITS;
+    struct smvt_control control_var[DECAF_448_SCALAR_BITS/(table_bits_var+1)+3];
+    struct smvt_control control_pre[DECAF_448_SCALAR_BITS/(table_bits_pre+1)+3];
+    
+    int ncb_pre = recode_wnaf(control_pre, scalar1, table_bits_pre);
+    int ncb_var = recode_wnaf(control_var, scalar2, table_bits_var);
+  
+    pniels_t precmp_var[1<<table_bits_var];
+    prepare_wnaf_table(precmp_var, base2, table_bits_var);
+  
+    int contp=0, contv=0, i = control_var[0].power;
+
+    if (i < 0) {
+        curve448_point_copy(combo, curve448_point_identity);
+        return;
+    } else if (i > control_pre[0].power) {
+        pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
+        contv++;
+    } else if (i == control_pre[0].power && i >=0 ) {
+        pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
+        add_niels_to_pt(combo, curve448_wnaf_base[control_pre[0].addend >> 1], i);
+        contv++; contp++;
+    } else {
+        i = control_pre[0].power;
+        niels_to_pt(combo, curve448_wnaf_base[control_pre[0].addend >> 1]);
+        contp++;
+    }
+    
+    for (i--; i >= 0; i--) {
+        int cv = (i==control_var[contv].power), cp = (i==control_pre[contp].power);
+        point_double_internal(combo,combo,i && !(cv||cp));
+
+        if (cv) {
+            assert(control_var[contv].addend);
+
+            if (control_var[contv].addend > 0) {
+                add_pniels_to_pt(combo, precmp_var[control_var[contv].addend >> 1], i&&!cp);
+            } else {
+                sub_pniels_from_pt(combo, precmp_var[(-control_var[contv].addend) >> 1], i&&!cp);
+            }
+            contv++;
+        }
+
+        if (cp) {
+            assert(control_pre[contp].addend);
+
+            if (control_pre[contp].addend > 0) {
+                add_niels_to_pt(combo, curve448_wnaf_base[control_pre[contp].addend >> 1], i);
+            } else {
+                sub_niels_from_pt(combo, curve448_wnaf_base[(-control_pre[contp].addend) >> 1], i);
+            }
+            contp++;
+        }
+    }
+    
+    /* This function is non-secret, but whatever this is cheap. */
+    OPENSSL_cleanse(control_var,sizeof(control_var));
+    OPENSSL_cleanse(control_pre,sizeof(control_pre));
+    OPENSSL_cleanse(precmp_var,sizeof(precmp_var));
+
+    assert(contv == ncb_var); (void)ncb_var;
+    assert(contp == ncb_pre); (void)ncb_pre;
+}
+
+void curve448_point_destroy (
+    curve448_point_t point
+) {
+    OPENSSL_cleanse(point, sizeof(curve448_point_t));
+}
+
+int X448(uint8_t out_shared_key[56], const uint8_t private_key[56],
+         const uint8_t peer_public_value[56])
+{
+  return decaf_x448(out_shared_key, peer_public_value, private_key)
+         == DECAF_SUCCESS;
+}
+
+void X448_public_from_private(uint8_t out_public_value[56],
+                              const uint8_t private_key[56])
+{
+    decaf_x448_derive_public_key(out_public_value, private_key);
+}