static __always_inline void fmul(felem output, const felem in2, const felem in)
{
uint128_t t[5];
- limb r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
+ limb r0, r1, r2, r3, r4, s0, s1, s2, s3, s4, c;
r0 = in[0];
r1 = in[1];
static __always_inline void fsquare_times(felem output, const felem in, limb count)
{
uint128_t t[5];
- limb r0,r1,r2,r3,r4,c;
- limb d0,d1,d2,d4,d419;
+ limb r0, r1, r2, r3, r4, c;
+ limb d0, d1, d2, d4, d419;
r0 = in[0];
r1 = in[1];
r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL;
r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL;
r2 += c;
- } while(--count);
+ } while (--count);
output[0] = r0;
output[1] = r1;
limb *x3, limb *z3, /* output Q + Q' */
limb *x, limb *z, /* input Q */
limb *xprime, limb *zprime, /* input Q' */
+
const limb *qmqp /* input Q - Q' */)
{
limb origx[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5], zzprime[5], zzzprime[5];
*/
static void swap_conditional(limb a[static 5], limb b[static 5], limb iswap)
{
- unsigned i;
+ unsigned int i;
const limb swap = -iswap;
for (i = 0; i < 5; ++i) {
const limb x = swap & (a[i] ^ b[i]);
+
a[i] ^= x;
b[i] ^= x;
}
limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1};
limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
- unsigned i, j;
+ unsigned int i, j;
memcpy(nqpqx, q, sizeof(limb) * 5);
for (i = 0; i < 32; ++i) {
uint8_t byte = n[31 - i];
+
for (j = 0; j < 8; ++j) {
const limb bit = byte >> 7;
static void crecip(felem out, const felem z)
{
- felem a,t0,b,c;
+ felem a, t0, b, c;
/* 2 */ fsquare_times(a, z, 1); // a = 2
/* 8 */ fsquare_times(t0, a, 2);
* significant first. The value of the field element is:
* x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...
*
- * i.e. the limbs are 26, 25, 26, 25, ... bits wide. */
+ * i.e. the limbs are 26, 25, 26, 25, ... bits wide.
+ */
/* Sum two numbers: output += in */
static void fsum(limb *output, const limb *in)
{
- unsigned i;
+ unsigned int i;
+
for (i = 0; i < 10; i += 2) {
output[0 + i] = output[0 + i] + in[0 + i];
output[1 + i] = output[1 + i] + in[1 + i];
}
/* Find the difference of two numbers: output = in - output
- * (note the order of the arguments!). */
+ * (note the order of the arguments!).
+ */
static void fdifference(limb *output, const limb *in)
{
- unsigned i;
+ unsigned int i;
+
for (i = 0; i < 10; ++i) {
output[i] = in[i] - output[i];
}
/* Multiply a number by a scalar: output = in * scalar */
static void fscalar_product(limb *output, const limb *in, const limb scalar)
{
- unsigned i;
+ unsigned int i;
+
for (i = 0; i < 10; ++i) {
output[i] = in[i] * scalar;
}
* output must be distinct to both inputs. The inputs are reduced coefficient
* form, the output is not.
*
- * output[x] <= 14 * the largest product of the input limbs. */
+ * output[x] <= 14 * the largest product of the input limbs.
+ */
static void fproduct(limb *output, const limb *in2, const limb *in)
{
output[0] = ((limb) ((int32_t) in2[0])) * ((int32_t) in[0]);
/* Reduce a long form to a short form by taking the input mod 2^255 - 19.
*
* On entry: |output[i]| < 14*2^54
- * On exit: |output[0..8]| < 280*2^54 */
+ * On exit: |output[0..8]| < 280*2^54
+ */
static void freduce_degree(limb *output)
{
/* Each of these shifts and adds ends up multiplying the value by 19.
*
* For output[0..8], the absolute entry value is < 14*2^54 and we add, at
- * most, 19*14*2^54 thus, on exit, |output[0..8]| < 280*2^54. */
+ * most, 19*14*2^54 thus, on exit, |output[0..8]| < 280*2^54.
+ */
output[8] += output[18] << 4;
output[8] += output[18] << 1;
output[8] += output[18];
/* return v / 2^26, using only shifts and adds.
*
- * On entry: v can take any value. */
+ * On entry: v can take any value.
+ */
static inline limb div_by_2_26(const limb v)
{
/* High word of v; no shift needed. */
/* return v / (2^25), using only shifts and adds.
*
- * On entry: v can take any value. */
+ * On entry: v can take any value.
+ */
static inline limb div_by_2_25(const limb v)
{
/* High word of v; no shift needed*/
/* Reduce all coefficients of the short form input so that |x| < 2^26.
*
- * On entry: |output[i]| < 280*2^54 */
+ * On entry: |output[i]| < 280*2^54
+ */
static void freduce_coefficients(limb *output)
{
- unsigned i;
+ unsigned int i;
output[10] = 0;
/* The entry condition (that |output[i]| < 280*2^54) means that over is, at
* most, 280*2^28 in the first iteration of this loop. This is added to the
* next limb and we can approximate the resulting bound of that limb by
- * 281*2^54. */
+ * 281*2^54.
+ */
output[i] -= over << 26;
output[i+1] += over;
* be approximated as 281*2^54.
*
* For subsequent iterations of the loop, 281*2^54 remains a conservative
- * bound and no overflow occurs. */
+ * bound and no overflow occurs.
+ */
over = div_by_2_25(output[i+1]);
output[i+1] -= over << 25;
output[i+2] += over;
output[10] = 0;
/* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19*281*2^29
- * So |over| will be no more than 2^16. */
+ * So |over| will be no more than 2^16.
+ */
{
limb over = div_by_2_26(output[0]);
+
output[0] -= over << 26;
output[1] += over;
}
/* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 2^16 < 2^26. The
- * bound on |output[1]| is sufficient to meet our needs. */
+ * bound on |output[1]| is sufficient to meet our needs.
+ */
}
/* A helpful wrapper around fproduct: output = in * in2.
* On entry: |in[i]| < 2^27 and |in2[i]| < 2^27.
*
* output must be distinct to both inputs. The output is reduced degree
- * (indeed, one need only provide storage for 10 limbs) and |output[i]| < 2^26. */
+ * (indeed, one need only provide storage for 10 limbs) and |output[i]| < 2^26.
+ */
static void fmul(limb *output, const limb *in, const limb *in2)
{
limb t[19];
+
fproduct(t, in, in2);
/* |t[i]| < 14*2^54 */
freduce_degree(t);
* output must be distinct from the input. The inputs are reduced coefficient
* form, the output is not.
*
- * output[x] <= 14 * the largest product of the input limbs. */
+ * output[x] <= 14 * the largest product of the input limbs.
+ */
static void fsquare_inner(limb *output, const limb *in)
{
output[0] = ((limb) ((int32_t) in[0])) * ((int32_t) in[0]);
* 2^27.
*
* On exit: The |output| argument is in reduced coefficients form (indeed, one
- * need only provide storage for 10 limbs) and |out[i]| < 2^26. */
+ * need only provide storage for 10 limbs) and |out[i]| < 2^26.
+ */
static void fsquare(limb *output, const limb *in)
{
limb t[19];
+
fsquare_inner(t, in);
/* |t[i]| < 14*2^54 because the largest product of two limbs will be <
* 2^(27+27) and fsquare_inner adds together, at most, 14 of those
- * products. */
+ * products.
+ */
freduce_degree(t);
freduce_coefficients(t);
/* |t[i]| < 2^26 */
/* Take a little-endian, 32-byte number and expand it into polynomial form */
static void fexpand(limb *output, const uint8_t *input)
{
-#define F(n,start,shift,mask) \
+#define F(n, start, shift, mask) \
output[n] = ((((limb) input[start + 0]) | \
((limb) input[start + 1]) << 8 | \
((limb) input[start + 2]) << 16 | \
}
/* int32_t_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are
- * both non-negative. */
+ * both non-negative.
+ */
static int32_t int32_t_gte(int32_t a, int32_t b)
{
a -= b;
/* Take a fully reduced polynomial form number and contract it into a
* little-endian, 32-byte array.
*
- * On entry: |input_limbs[i]| < 2^26 */
+ * On entry: |input_limbs[i]| < 2^26
+ */
static void fcontract(uint8_t *output, limb *input_limbs)
{
int i;
for (i = 0; i < 9; ++i) {
if ((i & 1) == 1) {
/* This calculation is a time-invariant way to make input[i]
- * non-negative by borrowing from the next-larger limb. */
+ * non-negative by borrowing from the next-larger limb.
+ */
const int32_t mask = input[i] >> 31;
const int32_t carry = -((input[i] & mask) >> 25);
+
input[i] = input[i] + (carry << 25);
input[i+1] = input[i+1] - carry;
} else {
const int32_t mask = input[i] >> 31;
const int32_t carry = -((input[i] & mask) >> 26);
+
input[i] = input[i] + (carry << 26);
input[i+1] = input[i+1] - carry;
}
}
/* There's no greater limb for input[9] to borrow from, but we can multiply
- * by 19 and borrow from input[0], which is valid mod 2^255-19. */
+ * by 19 and borrow from input[0], which is valid mod 2^255-19.
+ */
{
const int32_t mask = input[9] >> 31;
const int32_t carry = -((input[9] & mask) >> 25);
+
input[9] = input[9] + (carry << 25);
input[0] = input[0] - (carry * 19);
}
/* After the first iteration, input[1..9] are non-negative and fit within
* 25 or 26 bits, depending on position. However, input[0] may be
- * negative. */
+ * negative.
+ */
}
/* The first borrow-propagation pass above ended with every limb
{
const int32_t mask = input[0] >> 31;
const int32_t carry = -((input[0] & mask) >> 26);
+
input[0] = input[0] + (carry << 26);
input[1] = input[1] - carry;
}
/* All input[i] are now non-negative. However, there might be values between
- * 2^25 and 2^26 in a limb which is, nominally, 25 bits wide. */
+ * 2^25 and 2^26 in a limb which is, nominally, 25 bits wide.
+ */
for (j = 0; j < 2; j++) {
for (i = 0; i < 9; i++) {
if ((i & 1) == 1) {
const int32_t carry = input[i] >> 25;
+
input[i] &= 0x1ffffff;
input[i+1] += carry;
} else {
const int32_t carry = input[i] >> 26;
+
input[i] &= 0x3ffffff;
input[i+1] += carry;
}
{
const int32_t carry = input[9] >> 25;
+
input[9] &= 0x1ffffff;
input[0] += 19*carry;
}
* < 2^26 + 2*19, because the carry was, at most, two.
*
* If the second pass carried from input[9] again then input[0] is < 2*19 and
- * the input[9] -> input[0] carry didn't push input[0] out of bounds. */
+ * the input[9] -> input[0] carry didn't push input[0] out of bounds.
+ */
/* It still remains the case that input might be between 2^255-19 and 2^255.
* In this case, input[1..9] must take their maximum value and input[0] must
- * be >= (2^255-19) & 0x3ffffff, which is 0x3ffffed. */
+ * be >= (2^255-19) & 0x3ffffff, which is 0x3ffffed.
+ */
mask = int32_t_gte(input[0], 0x3ffffed);
for (i = 1; i < 10; i++) {
if ((i & 1) == 1) {
}
/* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus
- * this conditionally subtracts 2^255-19. */
+ * this conditionally subtracts 2^255-19.
+ */
input[0] -= mask & 0x3ffffed;
for (i = 1; i < 10; i++) {
output[s+3] = (input[i] >> 24) & 0xff;
output[0] = 0;
output[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);
+ 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
}
* qmqp: short form, preserved
*
* On entry and exit, the absolute value of the limbs of all inputs and outputs
- * are < 2^26. */
+ * are < 2^26.
+ */
static void fmonty(limb *x2, limb *z2, /* output 2Q */
limb *x3, limb *z3, /* output Q + Q' */
limb *x, limb *z, /* input Q */
limb *xprime, limb *zprime, /* input Q' */
+
const limb *qmqp /* input Q - Q' */)
{
limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19],
fproduct(xxprime, xprime, z);
/* |xxprime[i]| < 14*2^54: the largest product of two limbs will be <
* 2^(27+27) and fproduct adds together, at most, 14 of those products.
- * (Approximating that to 2^58 doesn't work out.) */
+ * (Approximating that to 2^58 doesn't work out.)
+ */
fproduct(zzprime, x, zprime);
/* |zzprime[i]| < 14*2^54 */
freduce_degree(xxprime);
* wrong results. Also, the two limb arrays must be in reduced-coefficient,
* reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped,
* and all all values in a[0..9],b[0..9] must have magnitude less than
- * INT32_MAX. */
+ * INT32_MAX.
+ */
static void swap_conditional(limb a[static 19], limb b[static 19], limb iswap)
{
- unsigned i;
+ unsigned int i;
const int32_t swap = (int32_t) -iswap;
for (i = 0; i < 10; ++i) {
- const int32_t x = swap & ( ((int32_t)a[i]) ^ ((int32_t)b[i]) );
+ const int32_t x = swap & (((int32_t)a[i]) ^ ((int32_t)b[i]));
+
a[i] = ((int32_t)a[i]) ^ x;
b[i] = ((int32_t)b[i]) ^ x;
}
*
* resultx/resultz: the x coordinate of the resulting curve point (short form)
* n: a little endian, 32-byte number
- * q: a point of the curve (short form) */
+ * q: a point of the curve (short form)
+ */
static void cmult(limb *resultx, limb *resultz, const uint8_t *n, const limb *q)
{
limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};
limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};
limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
- unsigned i, j;
+ unsigned int i, j;
memcpy(nqpqx, q, sizeof(limb) * 10);
for (i = 0; i < 32; ++i) {
uint8_t byte = n[31 - i];
+
for (j = 0; j < 8; ++j) {
const limb bit = byte >> 7;
limb t1[10];
int i;
- /* 2 */ fsquare(z2,z);
- /* 4 */ fsquare(t1,z2);
- /* 8 */ fsquare(t0,t1);
- /* 9 */ fmul(z9,t0,z);
- /* 11 */ fmul(z11,z9,z2);
- /* 22 */ fsquare(t0,z11);
- /* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9);
-
- /* 2^6 - 2^1 */ fsquare(t0,z2_5_0);
- /* 2^7 - 2^2 */ fsquare(t1,t0);
- /* 2^8 - 2^3 */ fsquare(t0,t1);
- /* 2^9 - 2^4 */ fsquare(t1,t0);
- /* 2^10 - 2^5 */ fsquare(t0,t1);
- /* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0);
-
- /* 2^11 - 2^1 */ fsquare(t0,z2_10_0);
- /* 2^12 - 2^2 */ fsquare(t1,t0);
- /* 2^20 - 2^10 */ for (i = 2; i < 10; i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
- /* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0);
-
- /* 2^21 - 2^1 */ fsquare(t0,z2_20_0);
- /* 2^22 - 2^2 */ fsquare(t1,t0);
- /* 2^40 - 2^20 */ for (i = 2; i < 20; i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
- /* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0);
-
- /* 2^41 - 2^1 */ fsquare(t1,t0);
- /* 2^42 - 2^2 */ fsquare(t0,t1);
- /* 2^50 - 2^10 */ for (i = 2; i < 10; i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
- /* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0);
-
- /* 2^51 - 2^1 */ fsquare(t0,z2_50_0);
- /* 2^52 - 2^2 */ fsquare(t1,t0);
- /* 2^100 - 2^50 */ for (i = 2; i < 50; i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
- /* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0);
-
- /* 2^101 - 2^1 */ fsquare(t1,z2_100_0);
- /* 2^102 - 2^2 */ fsquare(t0,t1);
- /* 2^200 - 2^100 */ for (i = 2; i < 100; i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
- /* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0);
-
- /* 2^201 - 2^1 */ fsquare(t0,t1);
- /* 2^202 - 2^2 */ fsquare(t1,t0);
- /* 2^250 - 2^50 */ for (i = 2; i < 50; i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
- /* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0);
-
- /* 2^251 - 2^1 */ fsquare(t1,t0);
- /* 2^252 - 2^2 */ fsquare(t0,t1);
- /* 2^253 - 2^3 */ fsquare(t1,t0);
- /* 2^254 - 2^4 */ fsquare(t0,t1);
- /* 2^255 - 2^5 */ fsquare(t1,t0);
- /* 2^255 - 21 */ fmul(out,t1,z11);
+ /* 2 */ fsquare(z2, z);
+ /* 4 */ fsquare(t1, z2);
+ /* 8 */ fsquare(t0, t1);
+ /* 9 */ fmul(z9, t0, z);
+ /* 11 */ fmul(z11, z9, z2);
+ /* 22 */ fsquare(t0, z11);
+ /* 2^5 - 2^0 = 31 */ fmul(z2_5_0, t0, z9);
+
+ /* 2^6 - 2^1 */ fsquare(t0, z2_5_0);
+ /* 2^7 - 2^2 */ fsquare(t1, t0);
+ /* 2^8 - 2^3 */ fsquare(t0, t1);
+ /* 2^9 - 2^4 */ fsquare(t1, t0);
+ /* 2^10 - 2^5 */ fsquare(t0, t1);
+ /* 2^10 - 2^0 */ fmul(z2_10_0, t0, z2_5_0);
+
+ /* 2^11 - 2^1 */ fsquare(t0, z2_10_0);
+ /* 2^12 - 2^2 */ fsquare(t1, t0);
+ /* 2^20 - 2^10 */ for (i = 2; i < 10; i += 2) { fsquare(t0, t1); fsquare(t1, t0); }
+ /* 2^20 - 2^0 */ fmul(z2_20_0, t1, z2_10_0);
+
+ /* 2^21 - 2^1 */ fsquare(t0, z2_20_0);
+ /* 2^22 - 2^2 */ fsquare(t1, t0);
+ /* 2^40 - 2^20 */ for (i = 2; i < 20; i += 2) { fsquare(t0, t1); fsquare(t1, t0); }
+ /* 2^40 - 2^0 */ fmul(t0, t1, z2_20_0);
+
+ /* 2^41 - 2^1 */ fsquare(t1, t0);
+ /* 2^42 - 2^2 */ fsquare(t0, t1);
+ /* 2^50 - 2^10 */ for (i = 2; i < 10; i += 2) { fsquare(t1, t0); fsquare(t0, t1); }
+ /* 2^50 - 2^0 */ fmul(z2_50_0, t0, z2_10_0);
+
+ /* 2^51 - 2^1 */ fsquare(t0, z2_50_0);
+ /* 2^52 - 2^2 */ fsquare(t1, t0);
+ /* 2^100 - 2^50 */ for (i = 2; i < 50; i += 2) { fsquare(t0, t1); fsquare(t1, t0); }
+ /* 2^100 - 2^0 */ fmul(z2_100_0, t1, z2_50_0);
+
+ /* 2^101 - 2^1 */ fsquare(t1, z2_100_0);
+ /* 2^102 - 2^2 */ fsquare(t0, t1);
+ /* 2^200 - 2^100 */ for (i = 2; i < 100; i += 2) { fsquare(t1, t0); fsquare(t0, t1); }
+ /* 2^200 - 2^0 */ fmul(t1, t0, z2_100_0);
+
+ /* 2^201 - 2^1 */ fsquare(t0, t1);
+ /* 2^202 - 2^2 */ fsquare(t1, t0);
+ /* 2^250 - 2^50 */ for (i = 2; i < 50; i += 2) { fsquare(t0, t1); fsquare(t1, t0); }
+ /* 2^250 - 2^0 */ fmul(t0, t1, z2_50_0);
+
+ /* 2^251 - 2^1 */ fsquare(t1, t0);
+ /* 2^252 - 2^2 */ fsquare(t0, t1);
+ /* 2^253 - 2^3 */ fsquare(t1, t0);
+ /* 2^254 - 2^4 */ fsquare(t0, t1);
+ /* 2^255 - 2^5 */ fsquare(t1, t0);
+ /* 2^255 - 21 */ fmul(out, t1, z11);
}
void curve25519(uint8_t mypublic[static CURVE25519_POINT_SIZE], const uint8_t secret[static CURVE25519_POINT_SIZE], const uint8_t basepoint[static CURVE25519_POINT_SIZE])
void curve25519_generate_public(uint8_t pub[static CURVE25519_POINT_SIZE], const uint8_t secret[static CURVE25519_POINT_SIZE])
{
static const uint8_t basepoint[CURVE25519_POINT_SIZE] = { 9 };
+
curve25519(pub, secret, basepoint);
}
projects / thirdparty / wireguard-tools.git / commitdiff
