tweetnacl.cpp

#include "tweetnacl.h"
#include "randombytes.h"

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

static const u8 _0[16] = {}, _9[32] = {9};

static const gf gf0 = {}, gf1 = {1}, _121665 = {0xDB41, 1}, D = {0x78a3, 0x1359, 0x4dca, 0x75eb, 0xd8ab,
    0x4141, 0x0a4d, 0x0070, 0xe898, 0x7779, 0x4079, 0x8cc7, 0xfe73, 0x2b6f, 0x6cee, 0x5203}, 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}, I = {0xa0b0, 0x4a0e, 0x1b27, 0xc4ee, 0xe478, 0xad2f, 0x1806, 0x2f43, 0xd7a7, 0x3dfb, 0x0099, 0x2b4d, 0xdf0b, 0x4fc1, 0x2480, 0x2b83};

static
u32 L32(u32 x, int c){
    return (x << c) | (x >> (32 - c));
} 

static u32 
ld32(const u8 * x)
{
    u32 u = x[3];
    u = (u << 8) | x[2];
    u = (u << 8) | x[1];
    return (u << 8) | x[0];
} 

static u64 
dl64(const u8 * x)
{
    u64 i, u = 0;
    FOR(i, 8) u = (u << 8) | x[i];
    return u;
} 

sv 
st32(u8 * x, u32 u)
{
    int i;
    FOR(i, 4) {
        x[i] = u;
        u >>= 8;
    }
} 

sv 
ts64(u8 * x, u64 u)
{
    int i;
    for (i = 7; i >= 0; --i) {
        x[i] = u;
        u >>= 8;
    }
} 

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

int
crypto_verify_16(const u8 * x, const u8 * y){
    return vn(x, y, 16);
} 

int
crypto_verify_32(const u8 * x, const u8 * y){
    return vn(x, y, 32);
} 

sv 
core(u8 * out,
     const u8 * in, const u8 * k, const u8 * c, int h)
{
    u32 w[16], x[16], y[16], t[4];
    int i, j, m;
    FOR(i, 4) {
        x[5 * i] = ld32(c + 4 * i);
        x[1 + i] = ld32(k + 4 * i);
        x[6 + i] = ld32(in + 4 * i);
        x[11 + i] = ld32(k + 16 + 4 * i);
    }
    FOR(i, 16) y[i] = x[i];
    FOR(i, 20) {
        FOR(j, 4) {
            FOR(m, 4) t[m] = x[(5 * j + 4 * m) % 16];
            t[1] ^= L32(t[0] + t[3], 7);
            t[2] ^= L32(t[1] + t[0], 9);
            t[3] ^= L32(t[2] + t[1], 13);
            t[0] ^= L32(t[3] + t[2], 18);
            FOR(m, 4) w[4 * j + (j + m) % 4] = t[m];
        }
        FOR(m, 16) x[m] = w[m];
    }
    if (h) {
        FOR(i, 16) x[i] += y[i];
        FOR(i, 4) {
            x[5 * i] -= ld32(c + 4 * i);
            x[6 + i] -= ld32(in + 4 * i);
        }
        FOR(i, 4) {
            st32(out + 4 * i, x[5 * i]);
            st32(out + 16 + 4 * i, x[6 + i]);
        }
    } else {
        FOR(i, 16) st32(out + 4 * i, x[i] + y[i]);
    }
} 

int
crypto_core_salsa20(u8 * out, const u8 * in, const u8 * k, const u8 * c){
    core(out, in, k, c, 0);
    return 0;
} 

int 
crypto_core_hsalsa20(u8 * out, const u8 * in, const
                     u8 * k, const u8 * c)
{
    core(out, in, k, c, 1);
    return 0;
} 

static const u8 sigma[16] = "expand 32-bytek";

int 
crypto_stream_salsa20_xor(u8 * c, const u8 * m, u64
                          b, const u8 * n, const u8 * k)
{
    u8 z[16], x[64];
    u32 u, i;
    if (!b) {
        return 0;
    }
    FOR(i, 16) {
        z[i] = 0;
    }
    FOR(i, 8) {
        z[i] = n[i];
    }
    while (b >= 64) {
        crypto_core_salsa20(x, z, k, sigma);
        FOR(i, 64) {
            c[i] = (m ? m[i] : 0) ^ x[i];
        }
        u = 1;
        for (i = 8; i < 16; ++i) {
            u += (u32) z[i];
            z[i] = u;
            u >>= 8;
        }
        b -= 64;
        c += 64;
        if (m) {
            m += 64;
        }
    }
    if (b) {
        crypto_core_salsa20(x, z, k, sigma);
        FOR(i, b) {
            c[i] = (m ? m[i] : 0) ^ x[i];
        }
    }
    return 0;
} 

int 
crypto_stream_salsa20(u8 * c, u64 d, const u8 * n, const u8 * k)
{
    return crypto_stream_salsa20_xor(c, 0, d, n, k);
} 

int crypto_stream(u8 * c, u64 d, const u8 * n, const u8 * k){
    u8 s[32];
    crypto_core_hsalsa20(s, n, k, sigma);
    return crypto_stream_salsa20(c, d, n + 16, s);
} 

int 
crypto_stream_xor(u8 * c, const u8 * m, u64 d, const u8 * n, const u8 * k)
{
    u8 s[32];
    crypto_core_hsalsa20(s, n, k, sigma);
    return crypto_stream_salsa20_xor(c, m, d, n + 16, s);
} 

sv 
add1305(u32 * h, const u32 * c)
{
    u32 j, u = 0;
    FOR(j, 17) {
        u += h[j] + c[j];
        h[j] = u & 255;
        u >>= 8;
    }
}

static const u32 minusp[17] = {5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252};

int 
crypto_onetimeauth(u8 * out, const u8 * m, u64 n, const u8 * k)
{
    u32 s, i, j, u, x[17], r[17], h[17], c[17], g[17];
    FOR(j, 17) {
        r[j] = h[j] = 0;
    }
    FOR(j, 16) {
        r[j] = k[j];
    }
    r[3] &= 15;
    r[4] &= 252;
    r[7] &= 15;
    r[8] &= 252;
    r[11] &= 15;
    r[12] &= 252;
    r[15] &= 15;
    while (n > 0) {
        FOR(j, 17) {
            c[j] = 0;
        }
        for (j = 0; (j < 16) && (j < n); ++j) {
            c[j] = m[j];
        }
        c[j] = 1;
        m += j;
        n -= j;
        add1305(h, c);
        FOR(i, 17) {
            x[i] = 0;
            FOR(j, 17) {
                x[i] += h[j] * ((j <= i) ? r[i - j] : 320 * r[i + 17 - j]);
            }
        }
        FOR(i, 17) {
            h[i] = x[i];
        }
        u = 0;
        FOR(j, 16) {
            u += h[j];
            h[j] = u & 255;
            u >>= 8;
        }
        u += h[16];
        h[16] = u & 3;
        u = 5 * (u >> 2);
        FOR(j, 16) {
            u += h[j];
            h[j] = u & 255;
            u >>= 8;
        }
        u += h[16];
        h[16] = u;
    }
    FOR(j, 17) {
        g[j] = h[j];
    }
    add1305(h, minusp);
    s = -(h[16] >> 7);
    FOR(j, 17) {
        h[j] ^= s & (g[j] ^ h[j]);
    }
    FOR(j, 16) {
        c[j] = k[j + 16];
    }
    c[16] = 0;
    add1305(h, c);
    FOR(j, 16) {
        out[j] = h[j];
    }
    return 0;
} 

int 
crypto_onetimeauth_verify(const u8 * h, const u8 * m, u64 n, const u8 * k)
{
    u8 x[16];
    crypto_onetimeauth(x, m, n, k);
    return crypto_verify_16(h, x);
} 

int 
crypto_secretbox(u8 * c, const u8 * m, u64 d, const u8 * n, const u8 * k)
{
    int i;
    if (d < 32) {
        return -1;
    }
    crypto_stream_xor(c, m, d, n, k);
    crypto_onetimeauth(c + 16, c + 32, d - 32, c);
    FOR(i, 16) {
        c[i] = 0;
    }
    return 0;
} 

int 
crypto_secretbox_open(u8 * m, const u8 * c, u64 d, const u8 * n, const u8 * k)
{
    int i;
    u8 x[32];
    if (d < 32) {
        return -1;
    }
    crypto_stream(x, 32, n, k);
    if (crypto_onetimeauth_verify(c + 16, c + 32, d - 32, x) != 0) {
        return -1;
    }
    crypto_stream_xor(m, c, d, n, k);
    FOR(i, 32) {
        m[i] = 0;
    }
    return 0;
} 

sv 
set25519(gf r, const gf a)
{
    int i;
    FOR(i, 16) {
        r[i] = a[i];
    }
} 

sv 
car25519(gf o)
{
    int
        i;
    i64 c;
    FOR(i, 16) {
        o[i] += (1 << 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[15] &= 0xffff;
        sel25519(t, m, 1 - b);
    }
    FOR(i, 16) {
        o[2 * i] = t[i] & 0xff;
        o[2 * i + 1] = t[i] >> 8;
    }
} 

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);
} 

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

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];
    }
} 

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];
    }
} 

int
crypto_scalarmult(u8 * q, const u8 * n, const u8 * p)
{
    u8 z[32];
    i64 x[96], 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 + 32] = a[i];
        x[i + 48] = c[i];
        x[i + 64] = b[i];
        x[i + 80] = d[i];
    }
    inv25519(x + 48, x + 48);
    M(x + 32, x + 32, x + 48);
    pack25519(q, x + 32);
    return 0;
} 

int
crypto_scalarmult_base(u8 * q, const u8 * n){
    return crypto_scalarmult(q, n, _9);
} 

int
crypto_box_keypair(u8 * y, u8 * x) {
    randombytes(x, 32);
    return crypto_scalarmult_base(y, x);
} 

int 
crypto_box_beforenm(u8 * k, const u8 * y, const u8 * x)
{
    u8 s[32];
    crypto_scalarmult(s, x, y);
    return crypto_core_hsalsa20(k, _0, s, sigma);
} 

int 
crypto_box_afternm(u8 * c, const u8 * m, u64 d, const u8 * n, const u8 * k)
{
    return crypto_secretbox(c, m, d, n, k);
} 

int 
crypto_box_open_afternm(u8 * m, const u8 * c, u64 d, const u8 * n, const u8 * k)
{
    return crypto_secretbox_open(m, c, d, n, k);
} 

int
crypto_box(u8 * c, const u8 * m, u64 d, const u8 * n, const u8 * y, const u8 * x){
    u8 k[32];
    crypto_box_beforenm(k, y, x);
    return crypto_box_afternm(c, m, d, n, k);
} 

int 
crypto_box_open(u8 * m, const u8 * c, u64 d, const u8 * n, const u8 * y, const u8 * x)
{
    u8 k[32];
    crypto_box_beforenm(k, y, x);
    return crypto_box_open_afternm(m, c, d, n, k);
} 

static u64 R(u64 x, int c){
    return (x >> c) | (x << (64 - c));
} 

static u64 
Ch(u64 x, u64 y, u64 z)
{
    return (x & y) ^ (~x & z);
} 

static u64 Maj(u64 x, u64 y, u64 z) {
    return (x & y) ^ (x & z) ^ (y & z);
} 

static u64 Sigma0(u64 x) {
    return R(x, 28) ^ R(x, 34) ^ R(x, 39);
} 

static u64
       Sigma1(u64 x) {
    return R(x, 14) ^ R(x, 18) ^ R(x, 41);
} 

static u64 sigma0(u64 x) {
    return R(x, 1) ^ R(x, 8) ^ (x >> 7);
} 

static u64 
sigma1(u64 x)
{
    return R(x, 19) ^ R(x, 61) ^ (x >> 6);
} 

static const u64 K[80] = {0x428a2f98d728ae22ULL, 0x7137449123ef65cdULL, 0xb5c0fbcfec4d3b2fULL, 0xe9b5dba58189dbbcULL,
    0x3956c25bf348b538ULL, 0x59f111f1b605d019ULL, 0x923f82a4af194f9bULL, 0xab1c5ed5da6d8118ULL, 0xd807aa98a3030242ULL, 0x12835b0145706fbeULL,
    0x243185be4ee4b28cULL, 0x550c7dc3d5ffb4e2ULL, 0x72be5d74f27b896fULL, 0x80deb1fe3b1696b1ULL, 0x9bdc06a725c71235ULL, 0xc19bf174cf692694ULL,
    0xe49b69c19ef14ad2ULL, 0xefbe4786384f25e3ULL, 0x0fc19dc68b8cd5b5ULL, 0x240ca1cc77ac9c65ULL, 0x2de92c6f592b0275ULL, 0x4a7484aa6ea6e483ULL,
    0x5cb0a9dcbd41fbd4ULL, 0x76f988da831153b5ULL, 0x983e5152ee66dfabULL, 0xa831c66d2db43210ULL, 0xb00327c898fb213fULL, 0xbf597fc7beef0ee4ULL,
    0xc6e00bf33da88fc2ULL, 0xd5a79147930aa725ULL, 0x06ca6351e003826fULL, 0x142929670a0e6e70ULL, 0x27b70a8546d22ffcULL, 0x2e1b21385c26c926ULL,
    0x4d2c6dfc5ac42aedULL, 0x53380d139d95b3dfULL, 0x650a73548baf63deULL, 0x766a0abb3c77b2a8ULL, 0x81c2c92e47edaee6ULL, 0x92722c851482353bULL,
    0xa2bfe8a14cf10364ULL, 0xa81a664bbc423001ULL, 0xc24b8b70d0f89791ULL, 0xc76c51a30654be30ULL, 0xd192e819d6ef5218ULL, 0xd69906245565a910ULL,
    0xf40e35855771202aULL, 0x106aa07032bbd1b8ULL, 0x19a4c116b8d2d0c8ULL, 0x1e376c085141ab53ULL, 0x2748774cdf8eeb99ULL, 0x34b0bcb5e19b48a8ULL,
    0x391c0cb3c5c95a63ULL, 0x4ed8aa4ae3418acbULL, 0x5b9cca4f7763e373ULL, 0x682e6ff3d6b2b8a3ULL, 0x748f82ee5defb2fcULL, 0x78a5636f43172f60ULL,
    0x84c87814a1f0ab72ULL, 0x8cc702081a6439ecULL, 0x90befffa23631e28ULL, 0xa4506cebde82bde9ULL, 0xbef9a3f7b2c67915ULL, 0xc67178f2e372532bULL,
    0xca273eceea26619cULL, 0xd186b8c721c0c207ULL, 0xeada7dd6cde0eb1eULL, 0xf57d4f7fee6ed178ULL, 0x06f067aa72176fbaULL, 0x0a637dc5a2c898a6ULL,
    0x113f9804bef90daeULL, 0x1b710b35131c471bULL, 0x28db77f523047d84ULL, 0x32caab7b40c72493ULL, 0x3c9ebe0a15c9bebcULL, 0x431d67c49c100d4cULL,
    0x4cc5d4becb3e42b6ULL, 0x597f299cfc657e2aULL, 0x5fcb6fab3ad6faecULL, 0x6c44198c4a475817ULL};

int 
crypto_hashblocks(u8 * x, const u8 * m, u64 n)
{
    u64 z[8], b[8], a[8], w[16], t;
    int i, j;
    FOR(i, 8) {
        z[i] = a[i] = dl64(x + 8 * i);
    }
    while (n >= 128) {
        FOR(i, 16) {
            w[i] = dl64(m + 8 * i);
        }
        FOR(i, 80) {
            FOR(j, 8) {
                b[j] = a[j];
            }
            t = a[7] + Sigma1(a[4]) + Ch(a[4], a[5], a[6]) + K[i] + w[i % 16];
            b[7] = t + Sigma0(a[0]) + Maj(a[0], a[1], a[2]);
            b[3] += t;
            FOR(j, 8) a[(j + 1) % 8] = b[j];
            if (i % 16 == 15) {
                FOR(j, 16) w[j] += w[(j + 9) % 16] + sigma0(w[(j + 1) % 16]) + sigma1(w[(j + 14) % 16]);
            }
        }
        FOR(i, 8) {
            a[i] += z[i];
            z[i] = a[i];
        }
        m += 128;
        n -= 128;
    }
    FOR(i, 8) {
        ts64(x + 8 * i, z[i]);
    }
    return n;
} 

static
const u8 iv[64] = {0x6a, 0x09, 0xe6, 0x67, 0xf3, 0xbc, 0xc9, 0x08, 0xbb, 0x67, 0xae, 0x85, 0x84, 0xca, 0xa7, 0x3b, 0x3c, 0x6e, 0xf3, 0x72, 0xfe, 0x94, 0xf8, 0x2b,
    0xa5, 0x4f, 0xf5, 0x3a, 0x5f, 0x1d, 0x36, 0xf1, 0x51, 0x0e, 0x52, 0x7f, 0xad, 0xe6, 0x82, 0xd1, 0x9b, 0x05, 0x68, 0x8c, 0x2b, 0x3e, 0x6c, 0x1f, 0x1f, 0x83, 0xd9, 0xab,
    0xfb, 0x41, 0xbd, 0x6b, 0x5b, 0xe0, 0xcd, 0x19, 0x13, 0x7e, 0x21, 0x79};

int 
crypto_hash(u8 * out, const u8 * m, u64 n)
{
    u8 h[64], x[256];
    u64 i, b = n;
    FOR(i, 64) {
        h[i] = iv[i];
    }
    crypto_hashblocks(h, m, n);
    m += n;
    n &= 127;
    m -= n;
    FOR(i, 256) {
        x[i] = 0;
    }
    FOR(i, n) {
        x[i] = m[i];
    }
    x[n] = 128;
    n = 256 - 128 * (n < 112);
    x[n - 9] = b >> 61;
    ts64(x + n - 8, b << 3);
    crypto_hashblocks(h, x, n);
    FOR(i, 64) {
        out[i] = h[i];
    }
    return 0;
} 

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);
} 

int
crypto_sign_keypair(u8 * pk, u8 * sk) {
    u8 d[64];
    gf p[4];
    int i;
    randombytes(sk, 32);
    crypto_hash(d, sk, 32);
    d[0] &= 248;
    d[31] &= 127;
    d[31] |= 64;
    scalarbase(p, d);
    pack(pk, p);
    FOR(i, 32) {
        sk[32 + i] = pk[i];
    }
    return 0;
} 

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);
} 

int 
crypto_sign(u8 * sm, u64 * smlen, const u8 * m, u64 n, const u8 * sk)
{
    u8 d[64], h[64], r[64];
    i64 i, j, x[64];
    gf p[4];
    crypto_hash(d, sk, 32);
    d[0] &= 248;
    d[31] &= 127;
    d[31] |= 64;
    *smlen = n + 64;
    FOR(i, n) {
        sm[64 + i] = m[i];
    }
    FOR(i, 32) {
        sm[32 + i] = d[32 + i];
    }
    crypto_hash(r, sm + 32, n + 32);
    reduce(r);
    scalarbase(p, r);
    pack(sm, p);
    FOR(i, 32) {
        sm[i + 32] = sk[i + 32];
    }
    crypto_hash(h, sm, n + 64);
    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(sm + 32, x);
    return 0;
} 

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 
crypto_sign_open(u8 * m, u64 * mlen, const u8 * sm, u64 n, const u8 * pk)
{
    int i;
    u8 t[32], h[64];
    gf p[4], q[4];
    *mlen = -1;
    if (n < 64) {
        return -1;
    }
    if (unpackneg(q, pk)) {
        return -1;
    }
    FOR(i, n) {
        m[i] = sm[i];
    }
    FOR(i, 32) {
        m[i + 32] = pk[i];
    }
    crypto_hash(h, m, n);
    reduce(h);
    scalarmult(p, q, h);
    scalarbase(q, sm + 32);
    add(p, q);
    pack(t, p);
    n -= 64;
    if (crypto_verify_32(sm, t)) {
        FOR(i, n) {
            m[i] = 0;
        }
        return -1;
    }
    FOR(i, n) {
        m[i] = sm[i + 64];
    }
    *mlen = n;
    return 0;
}