ec/curve25519.c: facilitate assembly implementations.

Currently it's limited to 64-bit platforms only as minimum radix
expected in assembly is 2^51.
Reviewed-by: NRich Salz <rsalz@openssl.org>
Reviewed-by: NPaul Dale <paul.dale@oracle.com>
(Merged from https://github.com/openssl/openssl/pull/5408)

crypto/ec/curve25519.c

@@ -11,16 +11,19 @@
 #include "ec_lcl.h"
 #include <openssl/sha.h>
 
-#if !defined(PEDANTIC) && \
-    !defined(__sparc__) && \
-    (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16)
+#if defined(X25519_ASM) \
+    || ( !defined(PEDANTIC) && \
+         !defined(__sparc__) && \
+         (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16) )
 /*
  * Base 2^51 implementation.
  */
 # define BASE_2_51_IMPLEMENTED
 
 typedef uint64_t fe51[5];
+# if !defined(X25519_ASM)
 typedef unsigned __int128 u128;
+# endif
 
 static const uint64_t MASK51 = 0x7ffffffffffff;
 
@@ -132,6 +135,250 @@ static void fe51_tobytes(uint8_t *s, const fe51 h)
     s[31] = h4 >> 44;
 }
 
+# ifdef X25519_ASM
+void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g);
+void x25519_fe51_sqr(fe51 h, const fe51 f);
+void x25519_fe51_mul121666(fe51 h, fe51 f);
+#  define fe51_mul x25519_fe51_mul
+#  define fe51_sq  x25519_fe51_sqr
+#  define fe51_mul121666 x25519_fe51_mul121666
+
+#  if defined(__x86_64) || defined(__x86_64__) || \
+      defined(_M_AMD64) || defined(_M_X64)
+
+#   define BASE_2_64_IMPLEMENTED
+
+typedef uint64_t fe64[4];
+
+int x25519_fe64_eligible();
+
+/*
+ * There are no reference C implementations for this radix.
+ */
+void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
+void x25519_fe64_sqr(fe64 h, const fe64 f);
+void x25519_fe64_mul121666(fe64 h, fe64 f);
+void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
+void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
+void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
+#   define fe64_mul x25519_fe64_mul
+#   define fe64_sqr x25519_fe64_sqr
+#   define fe64_mul121666 x25519_fe64_mul121666
+#   define fe64_add x25519_fe64_add
+#   define fe64_sub x25519_fe64_sub
+#   define fe64_tobytes x25519_fe64_tobytes
+
+static uint64_t load_8(const uint8_t *in)
+{
+    uint64_t result;
+
+    result = in[0];
+    result |= ((uint64_t)in[1]) << 8;
+    result |= ((uint64_t)in[2]) << 16;
+    result |= ((uint64_t)in[3]) << 24;
+    result |= ((uint64_t)in[4]) << 32;
+    result |= ((uint64_t)in[5]) << 40;
+    result |= ((uint64_t)in[6]) << 48;
+    result |= ((uint64_t)in[7]) << 56;
+
+    return result;
+}
+
+static void fe64_frombytes(fe64 h, const uint8_t *s)
+{
+    h[0] = load_8(s);
+    h[1] = load_8(s + 8);
+    h[2] = load_8(s + 16);
+    h[3] = load_8(s + 24) & 0x7fffffffffffffff;
+}
+
+static void fe64_0(fe64 h)
+{
+    h[0] = 0;
+    h[1] = 0;
+    h[2] = 0;
+    h[3] = 0;
+}
+
+static void fe64_1(fe64 h)
+{
+    h[0] = 1;
+    h[1] = 0;
+    h[2] = 0;
+    h[3] = 0;
+}
+
+static void fe64_copy(fe64 h, const fe64 f)
+{
+    h[0] = f[0];
+    h[1] = f[1];
+    h[2] = f[2];
+    h[3] = f[3];
+}
+
+static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
+{
+    int i;
+    uint64_t mask = 0 - (uint64_t)b;
+
+    for (i = 0; i < 4; i++) {
+        uint64_t x = f[i] ^ g[i];
+        x &= mask;
+        f[i] ^= x;
+        g[i] ^= x;
+    }
+}
+
+static void fe64_invert(fe64 out, const fe64 z)
+{
+    fe64 t0;
+    fe64 t1;
+    fe64 t2;
+    fe64 t3;
+    int i;
+
+    /*
+     * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
+     * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
+     */
+
+    /* t0 = z ** 2 */
+    fe64_sqr(t0, z);
+
+    /* t1 = t0 ** (2 ** 2) = z ** 8 */
+    fe64_sqr(t1, t0);
+    fe64_sqr(t1, t1);
+
+    /* t1 = z * t1 = z ** 9 */
+    fe64_mul(t1, z, t1);
+    /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
+    fe64_mul(t0, t0, t1);
+
+    /* t2 = t0 ** 2 = z ** 22 */
+    fe64_sqr(t2, t0);
+
+    /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
+    fe64_mul(t1, t1, t2);
+
+    /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
+    fe64_sqr(t2, t1);
+    for (i = 1; i < 5; ++i)
+        fe64_sqr(t2, t2);
+
+    /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
+    fe64_mul(t1, t2, t1);
+
+    /* Continuing similarly... */
+
+    /* t2 = z ** (2 ** 20 - 1) */
+    fe64_sqr(t2, t1);
+    for (i = 1; i < 10; ++i)
+        fe64_sqr(t2, t2);
+
+    fe64_mul(t2, t2, t1);
+
+    /* t2 = z ** (2 ** 40 - 1) */
+    fe64_sqr(t3, t2);
+    for (i = 1; i < 20; ++i)
+        fe64_sqr(t3, t3);
+
+    fe64_mul(t2, t3, t2);
+
+    /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
+    for (i = 0; i < 10; ++i)
+        fe64_sqr(t2, t2);
+
+    /* t1 = z ** (2 ** 50 - 1) */
+    fe64_mul(t1, t2, t1);
+
+    /* t2 = z ** (2 ** 100 - 1) */
+    fe64_sqr(t2, t1);
+    for (i = 1; i < 50; ++i)
+        fe64_sqr(t2, t2);
+
+    fe64_mul(t2, t2, t1);
+
+    /* t2 = z ** (2 ** 200 - 1) */
+    fe64_sqr(t3, t2);
+    for (i = 1; i < 100; ++i)
+        fe64_sqr(t3, t3);
+
+    fe64_mul(t2, t3, t2);
+
+    /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
+    for (i = 0; i < 50; ++i)
+        fe64_sqr(t2, t2);
+
+    /* t1 = z ** (2 ** 250 - 1) */
+    fe64_mul(t1, t2, t1);
+
+    /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
+    for (i = 0; i < 5; ++i)
+        fe64_sqr(t1, t1);
+
+    /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
+    fe64_mul(out, t1, t0);
+}
+
+/*
+ * Duplicate of original x25519_scalar_mult_generic, but using
+ * fe64_* subroutines.
+ */
+static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
+                               const uint8_t point[32])
+{
+    fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
+    uint8_t e[32];
+    unsigned swap = 0;
+    int pos;
+
+    memcpy(e, scalar, 32);
+    e[0]  &= 0xf8;
+    e[31] &= 0x7f;
+    e[31] |= 0x40;
+    fe64_frombytes(x1, point);
+    fe64_1(x2);
+    fe64_0(z2);
+    fe64_copy(x3, x1);
+    fe64_1(z3);
+
+    for (pos = 254; pos >= 0; --pos) {
+        unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
+
+        swap ^= b;
+        fe64_cswap(x2, x3, swap);
+        fe64_cswap(z2, z3, swap);
+        swap = b;
+        fe64_sub(tmp0, x3, z3);
+        fe64_sub(tmp1, x2, z2);
+        fe64_add(x2, x2, z2);
+        fe64_add(z2, x3, z3);
+        fe64_mul(z3, x2, tmp0);
+        fe64_mul(z2, z2, tmp1);
+        fe64_sqr(tmp0, tmp1);
+        fe64_sqr(tmp1, x2);
+        fe64_add(x3, z3, z2);
+        fe64_sub(z2, z3, z2);
+        fe64_mul(x2, tmp1, tmp0);
+        fe64_sub(tmp1, tmp1, tmp0);
+        fe64_sqr(z2, z2);
+        fe64_mul121666(z3, tmp1);
+        fe64_sqr(x3, x3);
+        fe64_add(tmp0, tmp0, z3);
+        fe64_mul(z3, x1, z2);
+        fe64_mul(z2, tmp1, tmp0);
+    }
+
+    fe64_invert(z2, z2);
+    fe64_mul(x2, x2, z2);
+    fe64_tobytes(out, x2);
+
+    OPENSSL_cleanse(e, sizeof(e));
+}
+#  endif
+
+# else
+
 static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
 {
     u128 h0, h1, h2, h3, h4;
@@ -192,9 +439,9 @@ static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
 
 static void fe51_sq(fe51 h, const fe51 f)
 {
-# if defined(OPENSSL_SMALL_FOOTPRINT)
+#  if defined(OPENSSL_SMALL_FOOTPRINT)
     fe51_mul(h, f, f);
-# else
+#  else
     /* dedicated squaring gives 16-25% overall improvement */
     uint64_t g0 = f[0];
     uint64_t g1 = f[1];
@@ -241,9 +488,36 @@ static void fe51_sq(fe51 h, const fe51 f)
     h[2] = g2;
     h[3] = g3;
     h[4] = g4;
-# endif
+#  endif
 }
 
+static void fe51_mul121666(fe51 h, fe51 f)
+{
+    u128 h0 = f[0] * (u128)121666;
+    u128 h1 = f[1] * (u128)121666;
+    u128 h2 = f[2] * (u128)121666;
+    u128 h3 = f[3] * (u128)121666;
+    u128 h4 = f[4] * (u128)121666;
+    uint64_t g0, g1, g2, g3, g4;
+
+    h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
+    h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
+
+    h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
+    g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
+
+    g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
+    g3 += g2 >> 51; g2 &= MASK51;
+    g1 += g0 >> 51; g0 &= MASK51;
+
+    h[0] = g0;
+    h[1] = g1;
+    h[2] = g2;
+    h[3] = g3;
+    h[4] = g4;
+}
+# endif
+
 static void fe51_add(fe51 h, const fe51 f, const fe51 g)
 {
     h[0] = f[0] + g[0];
@@ -397,32 +671,6 @@ static void fe51_invert(fe51 out, const fe51 z)
     fe51_mul(out, t1, t0);
 }
 
-static void fe51_mul121666(fe51 h, fe51 f)
-{
-    u128 h0 = f[0] * (u128)121666;
-    u128 h1 = f[1] * (u128)121666;
-    u128 h2 = f[2] * (u128)121666;
-    u128 h3 = f[3] * (u128)121666;
-    u128 h4 = f[4] * (u128)121666;
-    uint64_t g0, g1, g2, g3, g4;
-
-    h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
-    h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
-
-    h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
-    g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
-
-    g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
-    g3 += g2 >> 51; g2 &= MASK51;
-    g1 += g0 >> 51; g0 &= MASK51;
-
-    h[0] = g0;
-    h[1] = g1;
-    h[2] = g2;
-    h[3] = g3;
-    h[4] = g4;
-}
-
 /*
  * Duplicate of original x25519_scalar_mult_generic, but using
  * fe51_* subroutines.
@@ -435,6 +683,13 @@ static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
     unsigned swap = 0;
     int pos;
 
+# ifdef BASE_2_64_IMPLEMENTED
+    if (x25519_fe64_eligible()) {
+        x25519_scalar_mulx(out, scalar, point);
+        return;
+    }
+# endif
+
     memcpy(e, scalar, 32);
     e[0]  &= 0xf8;
     e[31] &= 0x7f;