curve25519-donna-32bit.h

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/*
    Public domain by Andrew M. <liquidsun@gmail.com>
    See: https://github.com/floodyberry/curve25519-donna
 
    32 bit integer curve25519 implementation
*/
 
typedef uint32_t bignum25519[10];
typedef uint32_t bignum25519align16[12];
 
static const uint32_t reduce_mask_25 = (1 << 25) - 1;
static const uint32_t reduce_mask_26 = (1 << 26) - 1;
 
 
/* out = in */
DONNA_INLINE static void
curve25519_copy(bignum25519 out, const bignum25519 in) {
    out[0] = in[0];
    out[1] = in[1];
    out[2] = in[2];
    out[3] = in[3];
    out[4] = in[4];
    out[5] = in[5];
    out[6] = in[6];
    out[7] = in[7];
    out[8] = in[8];
    out[9] = in[9];
}
 
/* out = a + b */
DONNA_INLINE static void
curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
    out[0] = a[0] + b[0];
    out[1] = a[1] + b[1];
    out[2] = a[2] + b[2];
    out[3] = a[3] + b[3];
    out[4] = a[4] + b[4];
    out[5] = a[5] + b[5];
    out[6] = a[6] + b[6];
    out[7] = a[7] + b[7];
    out[8] = a[8] + b[8];
    out[9] = a[9] + b[9];
}
 
DONNA_INLINE static void 
curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
    uint32_t c;
    out[0] = a[0] + b[0]    ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
    out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
    out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
    out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
    out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
    out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
    out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
    out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
    out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
    out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
    out[0] += 19 * c;
}
 
DONNA_INLINE static void
curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
    uint32_t c;
    out[0] = a[0] + b[0]    ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
    out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
    out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
    out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
    out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
    out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
    out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
    out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
    out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
    out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
    out[0] += 19 * c;
}
 
/* multiples of p */
static const uint32_t twoP0       = 0x07ffffda;
static const uint32_t twoP13579   = 0x03fffffe;
static const uint32_t twoP2468    = 0x07fffffe;
static const uint32_t fourP0      = 0x0fffffb4;
static const uint32_t fourP13579  = 0x07fffffc;
static const uint32_t fourP2468   = 0x0ffffffc;
 
/* out = a - b */
DONNA_INLINE static void
curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
    uint32_t c;
    out[0] = twoP0     + a[0] - b[0]    ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
    out[1] = twoP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
    out[2] = twoP2468  + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
    out[3] = twoP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
    out[4] = twoP2468  + a[4] - b[4] + c;
    out[5] = twoP13579 + a[5] - b[5]    ;
    out[6] = twoP2468  + a[6] - b[6]    ;
    out[7] = twoP13579 + a[7] - b[7]    ;
    out[8] = twoP2468  + a[8] - b[8]    ;
    out[9] = twoP13579 + a[9] - b[9]    ;
}
 
/* out = a - b, where a is the result of a basic op (add,sub) */
DONNA_INLINE static void
curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
    uint32_t c;
    out[0] = fourP0     + a[0] - b[0]    ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
    out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
    out[2] = fourP2468  + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
    out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
    out[4] = fourP2468  + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
    out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
    out[6] = fourP2468  + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
    out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
    out[8] = fourP2468  + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
    out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
    out[0] += 19 * c;
}
 
DONNA_INLINE static void
curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
    uint32_t c;
    out[0] = fourP0     + a[0] - b[0]    ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
    out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
    out[2] = fourP2468  + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
    out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
    out[4] = fourP2468  + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
    out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
    out[6] = fourP2468  + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
    out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
    out[8] = fourP2468  + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
    out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
    out[0] += 19 * c;
}
 
/* out = -a */
DONNA_INLINE static void
curve25519_neg(bignum25519 out, const bignum25519 a) {
    uint32_t c;
    out[0] = twoP0     - a[0]    ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
    out[1] = twoP13579 - a[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
    out[2] = twoP2468  - a[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
    out[3] = twoP13579 - a[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
    out[4] = twoP2468  - a[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
    out[5] = twoP13579 - a[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
    out[6] = twoP2468  - a[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
    out[7] = twoP13579 - a[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
    out[8] = twoP2468  - a[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
    out[9] = twoP13579 - a[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
    out[0] += 19 * c;
}
 
/* out = a * b */
#define curve25519_mul_noinline curve25519_mul
static void
curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
    uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
    uint32_t s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
    uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
    uint32_t p;
 
    r0 = b[0];
    r1 = b[1];
    r2 = b[2];
    r3 = b[3];
    r4 = b[4];
    r5 = b[5];
    r6 = b[6];
    r7 = b[7];
    r8 = b[8];
    r9 = b[9];
 
    s0 = a[0];
    s1 = a[1];
    s2 = a[2];
    s3 = a[3];
    s4 = a[4];
    s5 = a[5];
    s6 = a[6];
    s7 = a[7];
    s8 = a[8];
    s9 = a[9];
 
    m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0);
    m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0);
    m5 = mul32x32_64(r0, s5) + mul32x32_64(r1, s4) + mul32x32_64(r2, s3) + mul32x32_64(r3, s2) + mul32x32_64(r4, s1) + mul32x32_64(r5, s0);
    m7 = mul32x32_64(r0, s7) + mul32x32_64(r1, s6) + mul32x32_64(r2, s5) + mul32x32_64(r3, s4) + mul32x32_64(r4, s3) + mul32x32_64(r5, s2) + mul32x32_64(r6, s1) + mul32x32_64(r7, s0);
    m9 = mul32x32_64(r0, s9) + mul32x32_64(r1, s8) + mul32x32_64(r2, s7) + mul32x32_64(r3, s6) + mul32x32_64(r4, s5) + mul32x32_64(r5, s4) + mul32x32_64(r6, s3) + mul32x32_64(r7, s2) + mul32x32_64(r8, s1) + mul32x32_64(r9, s0);
 
    r1 *= 2;
    r3 *= 2;
    r5 *= 2;
    r7 *= 2;
 
    m0 = mul32x32_64(r0, s0);
    m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0);
    m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0);
    m6 = mul32x32_64(r0, s6) + mul32x32_64(r1, s5) + mul32x32_64(r2, s4) + mul32x32_64(r3, s3) + mul32x32_64(r4, s2) + mul32x32_64(r5, s1) + mul32x32_64(r6, s0);
    m8 = mul32x32_64(r0, s8) + mul32x32_64(r1, s7) + mul32x32_64(r2, s6) + mul32x32_64(r3, s5) + mul32x32_64(r4, s4) + mul32x32_64(r5, s3) + mul32x32_64(r6, s2) + mul32x32_64(r7, s1) + mul32x32_64(r8, s0);
 
    r1 *= 19;
    r2 *= 19;
    r3 = (r3 / 2) * 19;
    r4 *= 19;
    r5 = (r5 / 2) * 19;
    r6 *= 19;
    r7 = (r7 / 2) * 19;
    r8 *= 19;
    r9 *= 19;
 
    m1 += (mul32x32_64(r9, s2) + mul32x32_64(r8, s3) + mul32x32_64(r7, s4) + mul32x32_64(r6, s5) + mul32x32_64(r5, s6) + mul32x32_64(r4, s7) + mul32x32_64(r3, s8) + mul32x32_64(r2, s9));
    m3 += (mul32x32_64(r9, s4) + mul32x32_64(r8, s5) + mul32x32_64(r7, s6) + mul32x32_64(r6, s7) + mul32x32_64(r5, s8) + mul32x32_64(r4, s9));
    m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9));
    m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9));
 
    r3 *= 2;
    r5 *= 2;
    r7 *= 2;
    r9 *= 2;
 
    m0 += (mul32x32_64(r9, s1) + mul32x32_64(r8, s2) + mul32x32_64(r7, s3) + mul32x32_64(r6, s4) + mul32x32_64(r5, s5) + mul32x32_64(r4, s6) + mul32x32_64(r3, s7) + mul32x32_64(r2, s8) + mul32x32_64(r1, s9));
    m2 += (mul32x32_64(r9, s3) + mul32x32_64(r8, s4) + mul32x32_64(r7, s5) + mul32x32_64(r6, s6) + mul32x32_64(r5, s7) + mul32x32_64(r4, s8) + mul32x32_64(r3, s9));
    m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9));
    m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9));
    m8 += (mul32x32_64(r9, s9));
 
                                 r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
    m1 += c;                     r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
    m2 += c;                     r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
    m3 += c;                     r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
    m4 += c;                     r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
    m5 += c;                     r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
    m6 += c;                     r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
    m7 += c;                     r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
    m8 += c;                     r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
    m9 += c;                     r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
    m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
    r1 += p;
 
    out[0] = r0;
    out[1] = r1;
    out[2] = r2;
    out[3] = r3;
    out[4] = r4;
    out[5] = r5;
    out[6] = r6;
    out[7] = r7;
    out[8] = r8;
    out[9] = r9;
}
 
/* out = in*in */
static void
curve25519_square(bignum25519 out, const bignum25519 in) {
    uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
    uint32_t d6,d7,d8,d9;
    uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
    uint32_t p;
 
    r0 = in[0];
    r1 = in[1];
    r2 = in[2];
    r3 = in[3];
    r4 = in[4];
    r5 = in[5];
    r6 = in[6];
    r7 = in[7];
    r8 = in[8];
    r9 = in[9];
 
    m0 = mul32x32_64(r0, r0);
    r0 *= 2;
    m1 = mul32x32_64(r0, r1);
    m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
    r1 *= 2;
    m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2    );
    m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
    r2 *= 2;
    m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4    ) + mul32x32_64(r2, r3);
    m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
    r3 *= 2;
    m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6    ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4    );
    m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4    );
    m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8    ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6    ) + mul32x32_64(r4, r5 * 2);
 
    d6 = r6 * 19;
    d7 = r7 * 2 * 19;
    d8 = r8 * 19;
    d9 = r9 * 2 * 19;
 
    m0 += (mul32x32_64(d9, r1    ) + mul32x32_64(d8, r2    ) + mul32x32_64(d7, r3    ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
    m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3    ) + mul32x32_64(d7, r4    ) + mul32x32_64(d6, r5 * 2));
    m2 += (mul32x32_64(d9, r3    ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6    ));
    m3 += (mul32x32_64(d9, r4    ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6    ));
    m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7    ));
    m5 += (mul32x32_64(d9, r6    ) + mul32x32_64(d8, r7 * 2));
    m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8    ));
    m7 += (mul32x32_64(d9, r8    ));
    m8 += (mul32x32_64(d9, r9    ));
 
                                 r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
    m1 += c;                     r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
    m2 += c;                     r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
    m3 += c;                     r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
    m4 += c;                     r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
    m5 += c;                     r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
    m6 += c;                     r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
    m7 += c;                     r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
    m8 += c;                     r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
    m9 += c;                     r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
    m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
    r1 += p;
 
    out[0] = r0;
    out[1] = r1;
    out[2] = r2;
    out[3] = r3;
    out[4] = r4;
    out[5] = r5;
    out[6] = r6;
    out[7] = r7;
    out[8] = r8;
    out[9] = r9;
}
 
 
/* out = in ^ (2 * count) */
static void
curve25519_square_times(bignum25519 out, const bignum25519 in, int count) {
    uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
    uint32_t d6,d7,d8,d9;
    uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
    uint32_t p;
 
    r0 = in[0];
    r1 = in[1];
    r2 = in[2];
    r3 = in[3];
    r4 = in[4];
    r5 = in[5];
    r6 = in[6];
    r7 = in[7];
    r8 = in[8];
    r9 = in[9];
 
    do {
        m0 = mul32x32_64(r0, r0);
        r0 *= 2;
        m1 = mul32x32_64(r0, r1);
        m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
        r1 *= 2;
        m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2    );
        m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
        r2 *= 2;
        m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4    ) + mul32x32_64(r2, r3);
        m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
        r3 *= 2;
        m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6    ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4    );
        m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4    );
        m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8    ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6    ) + mul32x32_64(r4, r5 * 2);
 
        d6 = r6 * 19;
        d7 = r7 * 2 * 19;
        d8 = r8 * 19;
        d9 = r9 * 2 * 19;
 
        m0 += (mul32x32_64(d9, r1    ) + mul32x32_64(d8, r2    ) + mul32x32_64(d7, r3    ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
        m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3    ) + mul32x32_64(d7, r4    ) + mul32x32_64(d6, r5 * 2));
        m2 += (mul32x32_64(d9, r3    ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6    ));
        m3 += (mul32x32_64(d9, r4    ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6    ));
        m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7    ));
        m5 += (mul32x32_64(d9, r6    ) + mul32x32_64(d8, r7 * 2));
        m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8    ));
        m7 += (mul32x32_64(d9, r8    ));
        m8 += (mul32x32_64(d9, r9    ));
 
                                     r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
        m1 += c;                     r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
        m2 += c;                     r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
        m3 += c;                     r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
        m4 += c;                     r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
        m5 += c;                     r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
        m6 += c;                     r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
        m7 += c;                     r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
        m8 += c;                     r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
        m9 += c;                     r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
        m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
        r1 += p;
    } while (--count);
 
    out[0] = r0;
    out[1] = r1;
    out[2] = r2;
    out[3] = r3;
    out[4] = r4;
    out[5] = r5;
    out[6] = r6;
    out[7] = r7;
    out[8] = r8;
    out[9] = r9;
}
 
/* Take a little-endian, 32-byte number and expand it into polynomial form */
static void
curve25519_expand(bignum25519 out, const unsigned char in[32]) {
    static const union { uint8_t b[2]; uint16_t s; } endian_check = {{1,0}};
    uint32_t x0,x1,x2,x3,x4,x5,x6,x7;
 
    if (endian_check.s == 1) {
        x0 = *(uint32_t *)(in + 0);
        x1 = *(uint32_t *)(in + 4);
        x2 = *(uint32_t *)(in + 8);
        x3 = *(uint32_t *)(in + 12);
        x4 = *(uint32_t *)(in + 16);
        x5 = *(uint32_t *)(in + 20);
        x6 = *(uint32_t *)(in + 24);
        x7 = *(uint32_t *)(in + 28);
    } else {
        #define F(s)                         \
            ((((uint32_t)in[s + 0])      ) | \
             (((uint32_t)in[s + 1]) <<  8) | \
             (((uint32_t)in[s + 2]) << 16) | \
             (((uint32_t)in[s + 3]) << 24))
        x0 = F(0);
        x1 = F(4);
        x2 = F(8);
        x3 = F(12);
        x4 = F(16);
        x5 = F(20);
        x6 = F(24);
        x7 = F(28);
        #undef F
    }
 
    out[0] = (                        x0       ) & 0x3ffffff;
    out[1] = ((((uint64_t)x1 << 32) | x0) >> 26) & 0x1ffffff;
    out[2] = ((((uint64_t)x2 << 32) | x1) >> 19) & 0x3ffffff;
    out[3] = ((((uint64_t)x3 << 32) | x2) >> 13) & 0x1ffffff;
    out[4] = ((                       x3) >>  6) & 0x3ffffff;
    out[5] = (                        x4       ) & 0x1ffffff;
    out[6] = ((((uint64_t)x5 << 32) | x4) >> 25) & 0x3ffffff;
    out[7] = ((((uint64_t)x6 << 32) | x5) >> 19) & 0x1ffffff;
    out[8] = ((((uint64_t)x7 << 32) | x6) >> 12) & 0x3ffffff;
    out[9] = ((                       x7) >>  6) & 0x1ffffff;
}
 
/* Take a fully reduced polynomial form number and contract it into a
 * little-endian, 32-byte array
 */
static void
curve25519_contract(unsigned char out[32], const bignum25519 in) {
    bignum25519 f;
    curve25519_copy(f, in);
 
    #define carry_pass() \
        f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \
        f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \
        f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \
        f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \
        f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \
        f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \
        f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \
        f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \
        f[9] += f[8] >> 26; f[8] &= reduce_mask_26;
 
    #define carry_pass_full() \
        carry_pass() \
        f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25;
 
    #define carry_pass_final() \
        carry_pass() \
        f[9] &= reduce_mask_25;
 
    carry_pass_full()
    carry_pass_full()
 
    /* now t is between 0 and 2^255-1, properly carried. */
    /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
    f[0] += 19;
    carry_pass_full()
 
    /* now between 19 and 2^255-1 in both cases, and offset by 19. */
    f[0] += (reduce_mask_26 + 1) - 19;
    f[1] += (reduce_mask_25 + 1) - 1;
    f[2] += (reduce_mask_26 + 1) - 1;
    f[3] += (reduce_mask_25 + 1) - 1;
    f[4] += (reduce_mask_26 + 1) - 1;
    f[5] += (reduce_mask_25 + 1) - 1;
    f[6] += (reduce_mask_26 + 1) - 1;
    f[7] += (reduce_mask_25 + 1) - 1;
    f[8] += (reduce_mask_26 + 1) - 1;
    f[9] += (reduce_mask_25 + 1) - 1;
 
    /* now between 2^255 and 2^256-20, and offset by 2^255. */
    carry_pass_final()
 
    #undef carry_pass
    #undef carry_full
    #undef carry_final
 
    f[1] <<= 2;
    f[2] <<= 3;
    f[3] <<= 5;
    f[4] <<= 6;
    f[6] <<= 1;
    f[7] <<= 3;
    f[8] <<= 4;
    f[9] <<= 6;
 
    #define F(i, s) \
        out[s+0] |= (unsigned char )(f[i] & 0xff); \
        out[s+1] = (unsigned char )((f[i] >> 8) & 0xff); \
        out[s+2] = (unsigned char )((f[i] >> 16) & 0xff); \
        out[s+3] = (unsigned char )((f[i] >> 24) & 0xff);
 
    out[0] = 0;
    out[16] = 0;
    F(0,0);
    F(1,3);
    F(2,6);
    F(3,9);
    F(4,12);
    F(5,16);
    F(6,19);
    F(7,22);
    F(8,25);
    F(9,28);
    #undef F
}
 
 
/* out = (flag) ? in : out */
DONNA_INLINE static void
curve25519_move_conditional_bytes(uint8_t out[96], const uint8_t in[96], uint32_t flag) {
    const uint32_t nb = flag - 1, b = ~nb;
    const uint32_t *inl = (const uint32_t *)in;
    uint32_t *outl = (uint32_t *)out;
    outl[0] = (outl[0] & nb) | (inl[0] & b);
    outl[1] = (outl[1] & nb) | (inl[1] & b);
    outl[2] = (outl[2] & nb) | (inl[2] & b);
    outl[3] = (outl[3] & nb) | (inl[3] & b);
    outl[4] = (outl[4] & nb) | (inl[4] & b);
    outl[5] = (outl[5] & nb) | (inl[5] & b);
    outl[6] = (outl[6] & nb) | (inl[6] & b);
    outl[7] = (outl[7] & nb) | (inl[7] & b);
    outl[8] = (outl[8] & nb) | (inl[8] & b);
    outl[9] = (outl[9] & nb) | (inl[9] & b);
    outl[10] = (outl[10] & nb) | (inl[10] & b);
    outl[11] = (outl[11] & nb) | (inl[11] & b);
    outl[12] = (outl[12] & nb) | (inl[12] & b);
    outl[13] = (outl[13] & nb) | (inl[13] & b);
    outl[14] = (outl[14] & nb) | (inl[14] & b);
    outl[15] = (outl[15] & nb) | (inl[15] & b);
    outl[16] = (outl[16] & nb) | (inl[16] & b);
    outl[17] = (outl[17] & nb) | (inl[17] & b);
    outl[18] = (outl[18] & nb) | (inl[18] & b);
    outl[19] = (outl[19] & nb) | (inl[19] & b);
    outl[20] = (outl[20] & nb) | (inl[20] & b);
    outl[21] = (outl[21] & nb) | (inl[21] & b);
    outl[22] = (outl[22] & nb) | (inl[22] & b);
    outl[23] = (outl[23] & nb) | (inl[23] & b);
 
}
 
/* if (iswap) swap(a, b) */
DONNA_INLINE static void
curve25519_swap_conditional(bignum25519 a, bignum25519 b, uint32_t iswap) {
    const uint32_t swap = (uint32_t)(-(int32_t)iswap);
    uint32_t x0,x1,x2,x3,x4,x5,x6,x7,x8,x9;
 
    x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0;
    x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1;
    x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2;
    x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3;
    x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4;
    x5 = swap & (a[5] ^ b[5]); a[5] ^= x5; b[5] ^= x5;
    x6 = swap & (a[6] ^ b[6]); a[6] ^= x6; b[6] ^= x6;
    x7 = swap & (a[7] ^ b[7]); a[7] ^= x7; b[7] ^= x7;
    x8 = swap & (a[8] ^ b[8]); a[8] ^= x8; b[8] ^= x8;
    x9 = swap & (a[9] ^ b[9]); a[9] ^= x9; b[9] ^= x9;
}