curve25519.c

/*
 * Dropbear - a SSH2 server
 * 
 * Copyright (c) 2002,2003 Matt Johnston
 * All rights reserved.
 * 
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 * 
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 * 
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE. */

#include "includes.h"
#include "dbrandom.h"
#include "curve25519.h"

#if DROPBEAR_CURVE25519 || DROPBEAR_ED25519

/* Modified TweetNaCl version 20140427, a self-contained public-domain C library.
 * https://tweetnacl.cr.yp.to/ */

#define FOR(i,n) for (i = 0;i < n;++i)
#define sv static void

typedef unsigned char u8;
typedef unsigned long u32;
typedef unsigned long long u64;
typedef long long i64;
typedef i64 gf[16];

#if DROPBEAR_CURVE25519
static const gf
  _121665 = {0xDB41,1};
#endif /* DROPBEAR_CURVE25519 */
#if DROPBEAR_ED25519
static const gf
  gf0,
  gf1 = {1},
  D2 = {0xf159, 0x26b2, 0x9b94, 0xebd6, 0xb156, 0x8283, 0x149a, 0x00e0, 0xd130, 0xeef3, 0x80f2, 0x198e, 0xfce7, 0x56df, 0xd9dc, 0x2406},
  X = {0xd51a, 0x8f25, 0x2d60, 0xc956, 0xa7b2, 0x9525, 0xc760, 0x692c, 0xdc5c, 0xfdd6, 0xe231, 0xc0a4, 0x53fe, 0xcd6e, 0x36d3, 0x2169},
  Y = {0x6658, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666};
#if DROPBEAR_SIGNKEY_VERIFY
static const gf
  D = {0x78a3, 0x1359, 0x4dca, 0x75eb, 0xd8ab, 0x4141, 0x0a4d, 0x0070, 0xe898, 0x7779, 0x4079, 0x8cc7, 0xfe73, 0x2b6f, 0x6cee, 0x5203},
  I = {0xa0b0, 0x4a0e, 0x1b27, 0xc4ee, 0xe478, 0xad2f, 0x1806, 0x2f43, 0xd7a7, 0x3dfb, 0x0099, 0x2b4d, 0xdf0b, 0x4fc1, 0x2480, 0x2b83};
#endif /* DROPBEAR_SIGNKEY_VERIFY */
#endif /* DROPBEAR_ED25519 */

#if DROPBEAR_ED25519
#if DROPBEAR_SIGNKEY_VERIFY
static int vn(const u8 *x,const u8 *y,u32 n)
{
  u32 i,d = 0;
  FOR(i,n) d |= x[i]^y[i];
  return (1 & ((d - 1) >> 8)) - 1;
}

static int crypto_verify_32(const u8 *x,const u8 *y)
{
  return vn(x,y,32);
}
#endif /* DROPBEAR_SIGNKEY_VERIFY */

sv set25519(gf r, const gf a)
{
  int i;
  FOR(i,16) r[i]=a[i];
}
#endif /* DROPBEAR_ED25519 */

sv car25519(gf o)
{
  int i;
  i64 c;
  FOR(i,16) {
    o[i]+=(1LL<<16);
    c=o[i]>>16;
    o[(i+1)*(i<15)]+=c-1+37*(c-1)*(i==15);
    o[i]-=c<<16;
  }
}

sv sel25519(gf p,gf q,int b)
{
  i64 t,i,c=~(b-1);
  FOR(i,16) {
    t= c&(p[i]^q[i]);
    p[i]^=t;
    q[i]^=t;
  }
}

sv pack25519(u8 *o,const gf n)
{
  int i,j,b;
  gf m,t;
  FOR(i,16) t[i]=n[i];
  car25519(t);
  car25519(t);
  car25519(t);
  FOR(j,2) {
    m[0]=t[0]-0xffed;
    for(i=1;i<15;i++) {
      m[i]=t[i]-0xffff-((m[i-1]>>16)&1);
      m[i-1]&=0xffff;
    }
    m[15]=t[15]-0x7fff-((m[14]>>16)&1);
    b=(m[15]>>16)&1;
    m[14]&=0xffff;
    sel25519(t,m,1-b);
  }
  FOR(i,16) {
    o[2*i]=t[i]&0xff;
    o[2*i+1]=t[i]>>8;
  }
}

#if DROPBEAR_ED25519
#if DROPBEAR_SIGNKEY_VERIFY
static int neq25519(const gf a, const gf b)
{
  u8 c[32],d[32];
  pack25519(c,a);
  pack25519(d,b);
  return crypto_verify_32(c,d);
}
#endif /* DROPBEAR_SIGNKEY_VERIFY */

static u8 par25519(const gf a)
{
  u8 d[32];
  pack25519(d,a);
  return d[0]&1;
}
#endif /* DROPBEAR_ED25519 */

sv unpack25519(gf o, const u8 *n)
{
  int i;
  FOR(i,16) o[i]=n[2*i]+((i64)n[2*i+1]<<8);
  o[15]&=0x7fff;
}

sv A(gf o,const gf a,const gf b)
{
  int i;
  FOR(i,16) o[i]=a[i]+b[i];
}

sv Z(gf o,const gf a,const gf b)
{
  int i;
  FOR(i,16) o[i]=a[i]-b[i];
}

sv M(gf o,const gf a,const gf b)
{
  i64 i,j,t[31];
  FOR(i,31) t[i]=0;
  FOR(i,16) FOR(j,16) t[i+j]+=a[i]*b[j];
  FOR(i,15) t[i]+=38*t[i+16];
  FOR(i,16) o[i]=t[i];
  car25519(o);
  car25519(o);
}

sv S(gf o,const gf a)
{
  M(o,a,a);
}

sv inv25519(gf o,const gf i)
{
  gf c;
  int a;
  FOR(a,16) c[a]=i[a];
  for(a=253;a>=0;a--) {
    S(c,c);
    if(a!=2&&a!=4) M(c,c,i);
  }
  FOR(a,16) o[a]=c[a];
}

#if DROPBEAR_ED25519 && DROPBEAR_SIGNKEY_VERIFY
sv pow2523(gf o,const gf i)
{
  gf c;
  int a;
  FOR(a,16) c[a]=i[a];
  for(a=250;a>=0;a--) {
    S(c,c);
    if(a!=1) M(c,c,i);
  }
  FOR(a,16) o[a]=c[a];
}
#endif /* DROPBEAR_ED25519 && DROPBEAR_SIGNKEY_VERIFY */

#if DROPBEAR_CURVE25519
void dropbear_curve25519_scalarmult(u8 *q,const u8 *n,const u8 *p)
{
  u8 z[32];
  i64 x[80],r,i;
  gf a,b,c,d,e,f;
  FOR(i,31) z[i]=n[i];
  z[31]=(n[31]&127)|64;
  z[0]&=248;
  unpack25519(x,p);
  FOR(i,16) {
    b[i]=x[i];
    d[i]=a[i]=c[i]=0;
  }
  a[0]=d[0]=1;
  for(i=254;i>=0;--i) {
    r=(z[i>>3]>>(i&7))&1;
    sel25519(a,b,r);
    sel25519(c,d,r);
    A(e,a,c);
    Z(a,a,c);
    A(c,b,d);
    Z(b,b,d);
    S(d,e);
    S(f,a);
    M(a,c,a);
    M(c,b,e);
    A(e,a,c);
    Z(a,a,c);
    S(b,a);
    Z(c,d,f);
    M(a,c,_121665);
    A(a,a,d);
    M(c,c,a);
    M(a,d,f);
    M(d,b,x);
    S(b,e);
    sel25519(a,b,r);
    sel25519(c,d,r);
  }
  FOR(i,16) {
    x[i+16]=a[i];
    x[i+32]=c[i];
    x[i+48]=b[i];
    x[i+64]=d[i];
  }
  inv25519(x+32,x+32);
  M(x+16,x+16,x+32);
  pack25519(q,x+16);
}
#endif /* DROPBEAR_CURVE25519 */

#if DROPBEAR_ED25519
static int crypto_hash(u8 *out,const u8 *m,u64 n)
{
  hash_state hs;

  sha512_init(&hs);
  sha512_process(&hs, m, n);
  return sha512_done(&hs, out);
}

sv add(gf p[4],gf q[4])
{
  gf a,b,c,d,t,e,f,g,h;
  
  Z(a, p[1], p[0]);
  Z(t, q[1], q[0]);
  M(a, a, t);
  A(b, p[0], p[1]);
  A(t, q[0], q[1]);
  M(b, b, t);
  M(c, p[3], q[3]);
  M(c, c, D2);
  M(d, p[2], q[2]);
  A(d, d, d);
  Z(e, b, a);
  Z(f, d, c);
  A(g, d, c);
  A(h, b, a);

  M(p[0], e, f);
  M(p[1], h, g);
  M(p[2], g, f);
  M(p[3], e, h);
}

sv cswap(gf p[4],gf q[4],u8 b)
{
  int i;
  FOR(i,4)
    sel25519(p[i],q[i],b);
}

sv pack(u8 *r,gf p[4])
{
  gf tx, ty, zi;
  inv25519(zi, p[2]); 
  M(tx, p[0], zi);
  M(ty, p[1], zi);
  pack25519(r, ty);
  r[31] ^= par25519(tx) << 7;
}

sv scalarmult(gf p[4],gf q[4],const u8 *s)
{
  int i;
  set25519(p[0],gf0);
  set25519(p[1],gf1);
  set25519(p[2],gf1);
  set25519(p[3],gf0);
  for (i = 255;i >= 0;--i) {
    u8 b = (s[i/8]>>(i&7))&1;
    cswap(p,q,b);
    add(q,p);
    add(p,p);
    cswap(p,q,b);
  }
}

sv scalarbase(gf p[4],const u8 *s)
{
  gf q[4];
  set25519(q[0],X);
  set25519(q[1],Y);
  set25519(q[2],gf1);
  M(q[3],X,Y);
  scalarmult(p,q,s);
}

void dropbear_ed25519_make_key(u8 *pk,u8 *sk)
{
  u8 d[64];
  gf p[4];

  genrandom(sk, 32);

  crypto_hash(d, sk, 32);
  d[0] &= 248;
  d[31] &= 127;
  d[31] |= 64;

  scalarbase(p,d);
  pack(pk,p);
}

static const u64 L[32] = {0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0x10};

sv modL(u8 *r,i64 x[64])
{
  i64 carry,i,j;
  for (i = 63;i >= 32;--i) {
    carry = 0;
    for (j = i - 32;j < i - 12;++j) {
      x[j] += carry - 16 * x[i] * L[j - (i - 32)];
      carry = (x[j] + 128) >> 8;
      x[j] -= carry << 8;
    }
    x[j] += carry;
    x[i] = 0;
  }
  carry = 0;
  FOR(j,32) {
    x[j] += carry - (x[31] >> 4) * L[j];
    carry = x[j] >> 8;
    x[j] &= 255;
  }
  FOR(j,32) x[j] -= carry * L[j];
  FOR(i,32) {
    x[i+1] += x[i] >> 8;
    r[i] = x[i] & 255;
  }
}

sv reduce(u8 *r)
{
  i64 x[64],i;
  FOR(i,64) x[i] = (u64) r[i];
  FOR(i,64) r[i] = 0;
  modL(r,x);
}

void dropbear_ed25519_sign(const u8 *m,u32 mlen,u8 *s,u32 *slen,const u8 *sk, const u8 *pk)
{
  hash_state hs;
  u8 d[64],h[64],r[64];
  i64 x[64];
  gf p[4];
  u32 i,j;

  crypto_hash(d, sk, 32);
  d[0] &= 248;
  d[31] &= 127;
  d[31] |= 64;

  *slen = 64;

  sha512_init(&hs);
  sha512_process(&hs,d + 32,32);
  sha512_process(&hs,m,mlen);
  sha512_done(&hs,r);
  reduce(r);
  scalarbase(p,r);
  pack(s,p);

  sha512_init(&hs);
  sha512_process(&hs,s,32);
  sha512_process(&hs,pk,32);
  sha512_process(&hs,m,mlen);
  sha512_done(&hs,h);
  reduce(h);

  FOR(i,64) x[i] = 0;
  FOR(i,32) x[i] = (u64) r[i];
  FOR(i,32) FOR(j,32) x[i+j] += h[i] * (u64) d[j];
  modL(s + 32,x);
}

#if DROPBEAR_SIGNKEY_VERIFY
static int unpackneg(gf r[4],const u8 p[32])
{
  gf t, chk, num, den, den2, den4, den6;
  set25519(r[2],gf1);
  unpack25519(r[1],p);
  S(num,r[1]);
  M(den,num,D);
  Z(num,num,r[2]);
  A(den,r[2],den);

  S(den2,den);
  S(den4,den2);
  M(den6,den4,den2);
  M(t,den6,num);
  M(t,t,den);

  pow2523(t,t);
  M(t,t,num);
  M(t,t,den);
  M(t,t,den);
  M(r[0],t,den);

  S(chk,r[0]);
  M(chk,chk,den);
  if (neq25519(chk, num)) M(r[0],r[0],I);

  S(chk,r[0]);
  M(chk,chk,den);
  if (neq25519(chk, num)) return -1;

  if (par25519(r[0]) == (p[31]>>7)) Z(r[0],gf0,r[0]);

  M(r[3],r[0],r[1]);
  return 0;
}

int dropbear_ed25519_verify(const u8 *m,u32 mlen,const u8 *s,u32 slen,const u8 *pk)
{
  hash_state hs;
  u8 t[32],h[64];
  gf p[4],q[4];

  if (slen < 64) return -1;

  if (unpackneg(q,pk)) return -1;

  sha512_init(&hs);
  sha512_process(&hs,s,32);
  sha512_process(&hs,pk,32);
  sha512_process(&hs,m,mlen);
  sha512_done(&hs,h);

  reduce(h);
  scalarmult(p,q,h);

  scalarbase(q,s + 32);
  add(p,q);
  pack(t,p);

  if (crypto_verify_32(s, t))
    return -1;

  return 0;
}
#endif /* DROPBEAR_SIGNKEY_VERIFY */

#endif /* DROPBEAR_ED25519 */

#endif /* DROPBEAR_CURVE25519 || DROPBEAR_ED25519 */