[EC] Use s2n-bignum's modular inversion for P-256/384/521 (#2057)

Use s2n-bignum's inversion modulo the field characteristic for curves P-256/384/521. This gives us the following performance improvements: ``` _____Apple M1____| before | after | speedup | P-256 ECDH | 22724 | 23419 | 1.03x | P-256 ECDSA sign | 60677 | 69731 | 1.15x | P-384 ECDH | 5863 | 6217 | 1.06x | P-384 ECDSA sign | 13232 | 15011 | 1.13x | P-521 ECDH | 4041 | 4163 | 1.03x | P-521 ECDSA sign | 7079 | 7584 | 1.07x | ______x86_64_____| before | after | speedup | P-256 ECDH | 19410 | 20408 | 1.05x | P-256 ECDSA sign | 54477 | 63617 | 1.17x | P-384 ECDH | 5309 | 5599 | 1.05x | P-384 ECDSA sign | 12087 | 13780 | 1.14x | P-521 ECDH | 3539 | 3677 | 1.04x | P-521 ECDSA sign | 6584 | 7068 | 1.07x | _______GV4_______| before | after | speedup | P-256 ECDH | 16642 | 17491 | 1.05x | P-256 ECDSA sign | 51527 | 61108 | 1.18x | P-384 ECDH | 4208 | 4453 | 1.06x | P-384 ECDSA sign | 9848 | 11308 | 1.15x | P-521 ECDH | 2668 | 2811 | 1.05x | P-521 ECDSA sign | 5092 | 5626 | 1.10x | ```
aws · Dec 17, 2024 · 51ae4b1 · 51ae4b1
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commit 51ae4b1
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diff --git a/crypto/fipsmodule/CMakeLists.txt b/crypto/fipsmodule/CMakeLists.txt
@@ -207,6 +207,7 @@ if((((ARCH STREQUAL "x86_64") AND NOT MY_ASSEMBLER_IS_TOO_OLD_FOR_512AVX) OR
 
     p256/p256_montjscalarmul.S
     p256/p256_montjscalarmul_alt.S
+    p256/bignum_montinv_p256.S
 
     p384/bignum_add_p384.S
     p384/bignum_sub_p384.S
@@ -223,6 +224,7 @@ if((((ARCH STREQUAL "x86_64") AND NOT MY_ASSEMBLER_IS_TOO_OLD_FOR_512AVX) OR
     p384/p384_montjdouble_alt.S
     p384/p384_montjscalarmul.S
     p384/p384_montjscalarmul_alt.S
+    p384/bignum_montinv_p384.S
 
     p521/bignum_add_p521.S
     p521/bignum_sub_p521.S
@@ -237,6 +239,7 @@ if((((ARCH STREQUAL "x86_64") AND NOT MY_ASSEMBLER_IS_TOO_OLD_FOR_512AVX) OR
     p521/p521_jdouble_alt.S
     p521/p521_jscalarmul.S
     p521/p521_jscalarmul_alt.S
+    p521/bignum_inv_p521.S
 
     curve25519/bignum_mod_n25519.S
     curve25519/bignum_neg_p25519.S

diff --git a/crypto/fipsmodule/ec/p256-nistz.c b/crypto/fipsmodule/ec/p256-nistz.c
@@ -126,6 +126,11 @@ static BN_ULONG is_not_zero(BN_ULONG in) {
 // the Montgomery domain.
 static void ecp_nistz256_mod_inverse_sqr_mont(BN_ULONG r[P256_LIMBS],
                                               const BN_ULONG in[P256_LIMBS]) {
+#if defined(EC_NISTP_USE_S2N_BIGNUM)
+  ec_nistp_felem_limb in_sqr[P256_LIMBS];
+  ecp_nistz256_sqr_mont(in_sqr, in);
+  bignum_montinv_p256(r, in_sqr);
+#else
   // This implements the addition chain described in
   // https://briansmith.org/ecc-inversion-addition-chains-01#p256_field_inversion
   BN_ULONG x2[P256_LIMBS], x3[P256_LIMBS], x6[P256_LIMBS], x12[P256_LIMBS],
@@ -188,6 +193,7 @@ static void ecp_nistz256_mod_inverse_sqr_mont(BN_ULONG r[P256_LIMBS],
 
   ecp_nistz256_sqr_mont(ret, ret);
   ecp_nistz256_sqr_mont(r, ret);  // 2^256 - 2^224 + 2^192 + 2^96 - 2^2
+#endif
 }
 
 // r = p * p_scalar

diff --git a/crypto/fipsmodule/ec/p384.c b/crypto/fipsmodule/ec/p384.c
@@ -131,6 +131,11 @@ static void p384_from_scalar(p384_felem out, const EC_SCALAR *in) {
 //       ffffffff 00000000 00000000 fffffffc
 static void p384_inv_square(p384_felem out,
                             const p384_felem in) {
+#if defined(EC_NISTP_USE_S2N_BIGNUM)
+  ec_nistp_felem_limb in_sqr[P384_NLIMBS];
+  p384_felem_sqr(in_sqr, in);
+  bignum_montinv_p384(out, in_sqr);
+#else
   // This implements the addition chain described in
   // https://briansmith.org/ecc-inversion-addition-chains-01#p384_field_inversion
   // The side comments show the value of the exponent:
@@ -222,6 +227,7 @@ static void p384_inv_square(p384_felem out,
 
   p384_felem_sqr(ret, ret);
   p384_felem_sqr(out, ret);      // 2^384 - 2^128 - 2^96 + 2^32 - 2^2 = p - 3
+#endif
 }
 
 static void p384_point_double(p384_felem x_out,

diff --git a/crypto/fipsmodule/ec/p521.c b/crypto/fipsmodule/ec/p521.c
@@ -183,6 +183,9 @@ static void p521_to_generic(EC_FELEM *out, const p521_felem in) {
 // The code is autogenerated by the ECCKiila project:
 //   https://arxiv.org/abs/2007.11481
 static void p521_felem_inv(p521_felem output, const p521_felem t1) {
+#if defined(EC_NISTP_USE_S2N_BIGNUM)
+    bignum_inv_p521(output, t1);
+#else
     /* temporary variables */
     p521_felem acc, t2, t4, t8, t16, t32, t64;
     p521_felem t128, t256, t512, t516, t518, t519;
@@ -240,6 +243,7 @@ static void p521_felem_inv(p521_felem output, const p521_felem t1) {
     p521_felem_sqr(acc, t519);
     p521_felem_sqr(acc, acc);
     p521_felem_mul(output, acc, t1);
+#endif
 }
 
 static void p521_point_double(p521_felem x_out,

diff --git a/third_party/s2n-bignum/arm/curve25519/bignum_mod_n25519.S b/third_party/s2n-bignum/arm/curve25519/bignum_mod_n25519.S
@@ -110,7 +110,7 @@ S2N_BN_SYMBOL(bignum_mod_n25519):
 
         cbz     k, writeback
 
-loop:
+bignum_mod_n25519_loop:
 
 // Assume that the new 5-digit x is 2^64 * previous_x + next_digit.
 // Get the quotient estimate q = max (floor(x/2^252)) (2^64 - 1)
@@ -154,7 +154,7 @@ loop:
         adcs    m2, t2, xzr
         adc     m3, t3, m3
 
-        cbnz    k, loop
+        cbnz    k, bignum_mod_n25519_loop
 
 // Finally write back [m3;m2;m1;m0] and return
 

diff --git a/third_party/s2n-bignum/arm/p521/bignum_inv_p521.S b/third_party/s2n-bignum/arm/p521/bignum_inv_p521.S
@@ -789,9 +789,9 @@ S2N_BN_SYMBOL(bignum_inv_p521):
 
         mov     i, #21
         mov     d, #1
-        b       midloop
+        b       bignum_inv_p521_midloop
 
-loop:
+bignum_inv_p521_loop:
 
 // Separate the matrix elements into sign-magnitude pairs
 
@@ -1424,7 +1424,7 @@ loop:
         adc     x2, x2, x6
         str     x2, [v+64]
 
-midloop:
+bignum_inv_p521_midloop:
 
         mov     x1, d
         ldr     x2, [f]
@@ -1435,7 +1435,7 @@ midloop:
 // Next iteration
 
         subs    i, i, #1
-        bne     loop
+        bne     bignum_inv_p521_loop
 
 // The 21st and last iteration does not need anything except the
 // u value and the sign of f; the latter can be obtained from the

diff --git a/third_party/s2n-bignum/include/s2n-bignum_aws-lc.h b/third_party/s2n-bignum/include/s2n-bignum_aws-lc.h
@@ -63,6 +63,11 @@ static inline void p256_montjscalarmul_selector(uint64_t res[S2N_BIGNUM_STATIC 1
   else { p256_montjscalarmul(res, scalar, point); }
 }
 
+// Montgomery inverse modulo p_256 = 2^256 - 2^224 + 2^192 + 2^96 - 1
+//   z = x^-1 mod p_256.
+// The function is constant-time.
+extern void bignum_montinv_p256(uint64_t z[S2N_BIGNUM_STATIC 4], const uint64_t x[S2N_BIGNUM_STATIC 4]);
+
 // Add modulo p_384, z := (x + y) mod p_384, assuming x and y reduced
 // Inputs x[6], y[6]; output z[6]
 extern void bignum_add_p384(uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6], const uint64_t y[S2N_BIGNUM_STATIC 6]);
@@ -124,6 +129,11 @@ static inline void p384_montjscalarmul_selector(uint64_t res[S2N_BIGNUM_STATIC 1
   else { p384_montjscalarmul(res, scalar, point); }
 }
 
+// Montgomery inverse modulo p_384 = 2^384 - 2^128 - 2^96 + 2^32 - 1
+//   z = x^-1 mod p_384.
+// The function is constant-time.
+extern void bignum_montinv_p384(uint64_t z[S2N_BIGNUM_STATIC 6], const uint64_t x[S2N_BIGNUM_STATIC 6]);
+
 // Convert 6-digit (384-bit) bignum from little-endian form
 // Input x[6]; output z[6]
 extern void bignum_fromlebytes_6(uint64_t z[S2N_BIGNUM_STATIC 6], const uint8_t x[S2N_BIGNUM_STATIC 48]);
@@ -185,6 +195,11 @@ static inline void p521_jscalarmul_selector(uint64_t res[S2N_BIGNUM_STATIC 27],
     else { p521_jscalarmul(res, scalar, point); }
 }
 
+// Modular inverse modulo p_521 =  2^521 - 1
+//   z = x^-1 mod p_521.
+// The function is constant-time.
+extern void bignum_inv_p521(uint64_t z[S2N_BIGNUM_STATIC 9], const uint64_t x[S2N_BIGNUM_STATIC 9]);
+
 // curve25519_x25519_byte and curve25519_x25519_byte_alt computes the x25519
 // function specified in https://www.rfc-editor.org/rfc/rfc7748. |scalar| is the
 // scalar, |point| is the u-coordinate of the elliptic curve

diff --git a/third_party/s2n-bignum/x86_att/curve25519/bignum_mod_n25519.S b/third_party/s2n-bignum/x86_att/curve25519/bignum_mod_n25519.S
@@ -121,7 +121,7 @@ S2N_BN_SYMBOL(bignum_mod_n25519):
         testq   k, k
         jz      writeback
 
-loop:
+bignum_mod_n25519_loop:
 
 // Assume that the new 5-digit x is 2^64 * previous_x + next_digit.
 // Get the quotient estimate q = max (floor(x/2^252)) (2^64 - 1)
@@ -183,7 +183,7 @@ loop:
         movq    d, m0
 
         decq    k
-        jnz     loop
+        jnz     bignum_mod_n25519_loop
 
 // Write back
 

diff --git a/third_party/s2n-bignum/x86_att/p521/bignum_inv_p521.S b/third_party/s2n-bignum/x86_att/p521/bignum_inv_p521.S
@@ -1095,9 +1095,9 @@ S2N_BN_SYMBOL(bignum_inv_p521):
 
         movq    $21, i
         movq    $1, d
-        jmp     midloop
+        jmp     bignum_inv_p521_midloop
 
-loop:
+bignum_inv_p521_loop:
 
 // Separate out the matrix into sign-magnitude pairs
 
@@ -1775,15 +1775,15 @@ loop:
         adcq    %rax, %rbp
         movq    %rbp, V+8*N(%rsp)
 
-midloop:
+bignum_inv_p521_midloop:
 
         divstep59(d,ff,gg)
         movq    %rsi, d
 
 // Next iteration
 
         decq    i
-        jnz     loop
+        jnz     bignum_inv_p521_loop
 
 // The 21st and last iteration does not need anything except the
 // u value and the sign of f; the latter can be obtained from the