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authorJason A. Donenfeld <Jason@zx2c4.com>2018-01-15 11:34:31 +0100
committerJason A. Donenfeld <Jason@zx2c4.com>2018-01-18 11:26:09 +0100
commit481a58e01943b873bcc361ed72299ef7d3a2655a (patch)
treecc664e9b1658f32a26bbf75ccd48ac102e47e6be
parent35180994b327c14bd5e668b6b9d9d4cc3cfbbb5a (diff)
curve25519: modularize implementation
Signed-off-by: Jason A. Donenfeld <Jason@zx2c4.com>
-rw-r--r--src/crypto/curve25519-arm.h14
-rw-r--r--src/crypto/curve25519-generic.h1038
-rw-r--r--src/crypto/curve25519-u128.h408
-rw-r--r--src/crypto/curve25519-x86_64.h175
-rw-r--r--src/crypto/curve25519.c1615
5 files changed, 1640 insertions, 1610 deletions
diff --git a/src/crypto/curve25519-arm.h b/src/crypto/curve25519-arm.h
new file mode 100644
index 0000000..4142e4e
--- /dev/null
+++ b/src/crypto/curve25519-arm.h
@@ -0,0 +1,14 @@
+/* SPDX-License-Identifier: GPL-2.0
+ *
+ * Copyright (C) 2015-2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
+ */
+
+#include <asm/hwcap.h>
+#include <asm/neon.h>
+#include <asm/simd.h>
+asmlinkage void curve25519_neon(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE]);
+static bool curve25519_use_neon __read_mostly;
+void __init curve25519_fpu_init(void)
+{
+ curve25519_use_neon = elf_hwcap & HWCAP_NEON;
+}
diff --git a/src/crypto/curve25519-generic.h b/src/crypto/curve25519-generic.h
new file mode 100644
index 0000000..185b62e
--- /dev/null
+++ b/src/crypto/curve25519-generic.h
@@ -0,0 +1,1038 @@
+/* SPDX-License-Identifier: GPL-2.0
+ *
+ * Copyright (C) 2008 Google Inc. All Rights Reserved.
+ * Copyright (C) 2015-2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
+ *
+ * Original author: Adam Langley <agl@imperialviolet.org>
+ */
+
+#define ARCH_HAS_SEPARATE_IRQ_STACK
+#if (defined(CONFIG_MIPS) && LINUX_VERSION_CODE < KERNEL_VERSION(4, 11, 0)) || defined(CONFIG_ARM)
+#undef ARCH_HAS_SEPARATE_IRQ_STACK
+#endif
+
+typedef s64 limb;
+
+/* Field element representation:
+ *
+ * Field elements are written as an array of signed, 64-bit limbs, least
+ * 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.
+ */
+
+/* Sum two numbers: output += in */
+static void fsum(limb *output, const limb *in)
+{
+ 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!).
+ */
+static void fdifference(limb *output, const limb *in)
+{
+ 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 int i;
+
+ for (i = 0; i < 10; ++i)
+ output[i] = in[i] * scalar;
+}
+
+/* Multiply two numbers: output = in2 * in
+ *
+ * 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.
+ */
+static void fproduct(limb *output, const limb *in2, const limb *in)
+{
+ output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]);
+ output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[0]);
+ output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[0]);
+ output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[0]);
+ output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) +
+ 2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[1])) +
+ ((limb) ((s32) in2[0])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[0]);
+ output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[0]);
+ output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[1])) +
+ ((limb) ((s32) in2[2])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[0]);
+ output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[0]);
+ output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) +
+ 2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[1])) +
+ ((limb) ((s32) in2[2])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[0]);
+ output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[0]);
+ output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[1])) +
+ ((limb) ((s32) in2[4])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[2]);
+ output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[2]);
+ output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) +
+ 2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[3])) +
+ ((limb) ((s32) in2[4])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[4]);
+ output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[4]);
+ output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[5])) +
+ ((limb) ((s32) in2[6])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[6]);
+ output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[6]);
+ output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) +
+ 2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[7]));
+ output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[8]);
+ output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]);
+}
+
+/* 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
+ */
+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.
+ */
+ output[8] += output[18] << 4;
+ output[8] += output[18] << 1;
+ output[8] += output[18];
+ output[7] += output[17] << 4;
+ output[7] += output[17] << 1;
+ output[7] += output[17];
+ output[6] += output[16] << 4;
+ output[6] += output[16] << 1;
+ output[6] += output[16];
+ output[5] += output[15] << 4;
+ output[5] += output[15] << 1;
+ output[5] += output[15];
+ output[4] += output[14] << 4;
+ output[4] += output[14] << 1;
+ output[4] += output[14];
+ output[3] += output[13] << 4;
+ output[3] += output[13] << 1;
+ output[3] += output[13];
+ output[2] += output[12] << 4;
+ output[2] += output[12] << 1;
+ output[2] += output[12];
+ output[1] += output[11] << 4;
+ output[1] += output[11] << 1;
+ output[1] += output[11];
+ output[0] += output[10] << 4;
+ output[0] += output[10] << 1;
+ output[0] += output[10];
+}
+
+#if (-1 & 3) != 3
+#error "This code only works on a two's complement system"
+#endif
+
+/* return v / 2^26, using only shifts and adds.
+ *
+ * On entry: v can take any value.
+ */
+static inline limb div_by_2_26(const limb v)
+{
+ /* High word of v; no shift needed. */
+ const u32 highword = (u32) (((u64) v) >> 32);
+ /* Set to all 1s if v was negative; else set to 0s. */
+ const s32 sign = ((s32) highword) >> 31;
+ /* Set to 0x3ffffff if v was negative; else set to 0. */
+ const s32 roundoff = ((u32) sign) >> 6;
+ /* Should return v / (1<<26) */
+ return (v + roundoff) >> 26;
+}
+
+/* return v / (2^25), using only shifts and adds.
+ *
+ * On entry: v can take any value.
+ */
+static inline limb div_by_2_25(const limb v)
+{
+ /* High word of v; no shift needed*/
+ const u32 highword = (u32) (((u64) v) >> 32);
+ /* Set to all 1s if v was negative; else set to 0s. */
+ const s32 sign = ((s32) highword) >> 31;
+ /* Set to 0x1ffffff if v was negative; else set to 0. */
+ const s32 roundoff = ((u32) sign) >> 7;
+ /* Should return v / (1<<25) */
+ return (v + roundoff) >> 25;
+}
+
+/* Reduce all coefficients of the short form input so that |x| < 2^26.
+ *
+ * On entry: |output[i]| < 280*2^54
+ */
+static void freduce_coefficients(limb *output)
+{
+ unsigned int i;
+
+ output[10] = 0;
+
+ for (i = 0; i < 10; i += 2) {
+ limb over = div_by_2_26(output[i]);
+ /* 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.
+ */
+ output[i] -= over << 26;
+ output[i+1] += over;
+
+ /* For the first iteration, |output[i+1]| < 281*2^54, thus |over| <
+ * 281*2^29. When this is added to the next limb, the resulting bound can
+ * be approximated as 281*2^54.
+ *
+ * For subsequent iterations of the loop, 281*2^54 remains a conservative
+ * bound and no overflow occurs.
+ */
+ over = div_by_2_25(output[i+1]);
+ output[i+1] -= over << 25;
+ output[i+2] += over;
+ }
+ /* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */
+ output[0] += output[10] << 4;
+ output[0] += output[10] << 1;
+ output[0] += output[10];
+
+ 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.
+ */
+ {
+ 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.
+ */
+}
+
+/* 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.
+ */
+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);
+ freduce_coefficients(t);
+ /* |t[i]| < 2^26 */
+ memcpy(output, t, sizeof(limb) * 10);
+}
+
+/* Square a number: output = in**2
+ *
+ * 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.
+ */
+static void fsquare_inner(limb *output, const limb *in)
+{
+ output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]);
+ output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]);
+ output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) +
+ ((limb) ((s32) in[0])) * ((s32) in[2]));
+ output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) +
+ ((limb) ((s32) in[0])) * ((s32) in[3]));
+ output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) +
+ 4 * ((limb) ((s32) in[1])) * ((s32) in[3]) +
+ 2 * ((limb) ((s32) in[0])) * ((s32) in[4]);
+ output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) +
+ ((limb) ((s32) in[1])) * ((s32) in[4]) +
+ ((limb) ((s32) in[0])) * ((s32) in[5]));
+ output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) +
+ ((limb) ((s32) in[2])) * ((s32) in[4]) +
+ ((limb) ((s32) in[0])) * ((s32) in[6]) +
+ 2 * ((limb) ((s32) in[1])) * ((s32) in[5]));
+ output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) +
+ ((limb) ((s32) in[2])) * ((s32) in[5]) +
+ ((limb) ((s32) in[1])) * ((s32) in[6]) +
+ ((limb) ((s32) in[0])) * ((s32) in[7]));
+ output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) +
+ 2 * (((limb) ((s32) in[2])) * ((s32) in[6]) +
+ ((limb) ((s32) in[0])) * ((s32) in[8]) +
+ 2 * (((limb) ((s32) in[1])) * ((s32) in[7]) +
+ ((limb) ((s32) in[3])) * ((s32) in[5])));
+ output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) +
+ ((limb) ((s32) in[3])) * ((s32) in[6]) +
+ ((limb) ((s32) in[2])) * ((s32) in[7]) +
+ ((limb) ((s32) in[1])) * ((s32) in[8]) +
+ ((limb) ((s32) in[0])) * ((s32) in[9]));
+ output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) +
+ ((limb) ((s32) in[4])) * ((s32) in[6]) +
+ ((limb) ((s32) in[2])) * ((s32) in[8]) +
+ 2 * (((limb) ((s32) in[3])) * ((s32) in[7]) +
+ ((limb) ((s32) in[1])) * ((s32) in[9])));
+ output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) +
+ ((limb) ((s32) in[4])) * ((s32) in[7]) +
+ ((limb) ((s32) in[3])) * ((s32) in[8]) +
+ ((limb) ((s32) in[2])) * ((s32) in[9]));
+ output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) +
+ 2 * (((limb) ((s32) in[4])) * ((s32) in[8]) +
+ 2 * (((limb) ((s32) in[5])) * ((s32) in[7]) +
+ ((limb) ((s32) in[3])) * ((s32) in[9])));
+ output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) +
+ ((limb) ((s32) in[5])) * ((s32) in[8]) +
+ ((limb) ((s32) in[4])) * ((s32) in[9]));
+ output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) +
+ ((limb) ((s32) in[6])) * ((s32) in[8]) +
+ 2 * ((limb) ((s32) in[5])) * ((s32) in[9]));
+ output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) +
+ ((limb) ((s32) in[6])) * ((s32) in[9]));
+ output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) +
+ 4 * ((limb) ((s32) in[7])) * ((s32) in[9]);
+ output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]);
+ output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]);
+}
+
+/* fsquare sets output = in^2.
+ *
+ * On entry: The |in| argument is in reduced coefficients form and |in[i]| <
+ * 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.
+ */
+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.
+ */
+ freduce_degree(t);
+ freduce_coefficients(t);
+ /* |t[i]| < 2^26 */
+ memcpy(output, t, sizeof(limb) * 10);
+}
+
+/* Take a little-endian, 32-byte number and expand it into polynomial form */
+static inline void fexpand(limb *output, const u8 *input)
+{
+#define F(n, start, shift, mask) \
+ output[n] = ((((limb) input[start + 0]) | \
+ ((limb) input[start + 1]) << 8 | \
+ ((limb) input[start + 2]) << 16 | \
+ ((limb) input[start + 3]) << 24) >> shift) & mask;
+ F(0, 0, 0, 0x3ffffff);
+ F(1, 3, 2, 0x1ffffff);
+ F(2, 6, 3, 0x3ffffff);
+ F(3, 9, 5, 0x1ffffff);
+ F(4, 12, 6, 0x3ffffff);
+ F(5, 16, 0, 0x1ffffff);
+ F(6, 19, 1, 0x3ffffff);
+ F(7, 22, 3, 0x1ffffff);
+ F(8, 25, 4, 0x3ffffff);
+ F(9, 28, 6, 0x1ffffff);
+#undef F
+}
+
+#if (-32 >> 1) != -16
+#error "This code only works when >> does sign-extension on negative numbers"
+#endif
+
+/* s32_eq returns 0xffffffff iff a == b and zero otherwise. */
+static s32 s32_eq(s32 a, s32 b)
+{
+ a = ~(a ^ b);
+ a &= a << 16;
+ a &= a << 8;
+ a &= a << 4;
+ a &= a << 2;
+ a &= a << 1;
+ return a >> 31;
+}
+
+/* s32_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are
+ * both non-negative.
+ */
+static s32 s32_gte(s32 a, s32 b)
+{
+ a -= b;
+ /* a >= 0 iff a >= b. */
+ return ~(a >> 31);
+}
+
+/* Take a fully reduced polynomial form number and contract it into a
+ * little-endian, 32-byte array.
+ *
+ * On entry: |input_limbs[i]| < 2^26
+ */
+static void fcontract(u8 *output, limb *input_limbs)
+{
+ int i;
+ int j;
+ s32 input[10];
+ s32 mask;
+
+ /* |input_limbs[i]| < 2^26, so it's valid to convert to an s32. */
+ for (i = 0; i < 10; i++) {
+ input[i] = input_limbs[i];
+ }
+
+ for (j = 0; j < 2; ++j) {
+ 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.
+ */
+ const s32 mask = input[i] >> 31;
+ const s32 carry = -((input[i] & mask) >> 25);
+
+ input[i] = input[i] + (carry << 25);
+ input[i+1] = input[i+1] - carry;
+ } else {
+ const s32 mask = input[i] >> 31;
+ const s32 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.
+ */
+ {
+ const s32 mask = input[9] >> 31;
+ const s32 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.
+ */
+ }
+
+ /* The first borrow-propagation pass above ended with every limb
+ except (possibly) input[0] non-negative.
+ If input[0] was negative after the first pass, then it was because of a
+ carry from input[9]. On entry, input[9] < 2^26 so the carry was, at most,
+ one, since (2**26-1) >> 25 = 1. Thus input[0] >= -19.
+ In the second pass, each limb is decreased by at most one. Thus the second
+ borrow-propagation pass could only have wrapped around to decrease
+ input[0] again if the first pass left input[0] negative *and* input[1]
+ through input[9] were all zero. In that case, input[1] is now 2^25 - 1,
+ and this last borrow-propagation step will leave input[1] non-negative. */
+ {
+ const s32 mask = input[0] >> 31;
+ const s32 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.
+ */
+ for (j = 0; j < 2; j++) {
+ for (i = 0; i < 9; i++) {
+ if ((i & 1) == 1) {
+ const s32 carry = input[i] >> 25;
+
+ input[i] &= 0x1ffffff;
+ input[i+1] += carry;
+ } else {
+ const s32 carry = input[i] >> 26;
+
+ input[i] &= 0x3ffffff;
+ input[i+1] += carry;
+ }
+ }
+
+ {
+ const s32 carry = input[9] >> 25;
+
+ input[9] &= 0x1ffffff;
+ input[0] += 19*carry;
+ }
+ }
+
+ /* If the first carry-chain pass, just above, ended up with a carry from
+ * input[9], and that caused input[0] to be out-of-bounds, then input[0] was
+ * < 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.
+ */
+
+ /* 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.
+ */
+ mask = s32_gte(input[0], 0x3ffffed);
+ for (i = 1; i < 10; i++) {
+ if ((i & 1) == 1) {
+ mask &= s32_eq(input[i], 0x1ffffff);
+ } else {
+ mask &= s32_eq(input[i], 0x3ffffff);
+ }
+ }
+
+ /* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus
+ * this conditionally subtracts 2^255-19.
+ */
+ input[0] -= mask & 0x3ffffed;
+
+ for (i = 1; i < 10; i++) {
+ if ((i & 1) == 1) {
+ input[i] -= mask & 0x1ffffff;
+ } else {
+ input[i] -= mask & 0x3ffffff;
+ }
+ }
+
+ input[1] <<= 2;
+ input[2] <<= 3;
+ input[3] <<= 5;
+ input[4] <<= 6;
+ input[6] <<= 1;
+ input[7] <<= 3;
+ input[8] <<= 4;
+ input[9] <<= 6;
+#define F(i, s) \
+ output[s+0] |= input[i] & 0xff; \
+ output[s+1] = (input[i] >> 8) & 0xff; \
+ output[s+2] = (input[i] >> 16) & 0xff; \
+ 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);
+#undef F
+}
+
+/* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave
+ * them unchanged if 'iswap' is 0. Runs in data-invariant time to avoid
+ * side-channel attacks.
+ *
+ * NOTE that this function requires that 'iswap' be 1 or 0; other values give
+ * 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.
+ */
+static void swap_conditional(limb a[19], limb b[19], limb iswap)
+{
+ unsigned int i;
+ const s32 swap = (s32) -iswap;
+
+ for (i = 0; i < 10; ++i) {
+ const s32 x = swap & (((s32)a[i]) ^ ((s32)b[i]));
+
+ a[i] = ((s32)a[i]) ^ x;
+ b[i] = ((s32)b[i]) ^ x;
+ }
+}
+
+static void crecip(limb *out, const limb *z)
+{
+ limb z2[10];
+ limb z9[10];
+ limb z11[10];
+ limb z2_5_0[10];
+ limb z2_10_0[10];
+ limb z2_20_0[10];
+ limb z2_50_0[10];
+ limb z2_100_0[10];
+ limb t0[10];
+ 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);
+}
+
+
+#ifdef ARCH_HAS_SEPARATE_IRQ_STACK
+/* Input: Q, Q', Q-Q'
+ * Output: 2Q, Q+Q'
+ *
+ * x2 z3: long form
+ * x3 z3: long form
+ * x z: short form, destroyed
+ * xprime zprime: short form, destroyed
+ * qmqp: short form, preserved
+ *
+ * On entry and exit, the absolute value of the limbs of all inputs and outputs
+ * 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],
+ zzprime[19], zzzprime[19], xxxprime[19];
+
+ memcpy(origx, x, 10 * sizeof(limb));
+ fsum(x, z);
+ /* |x[i]| < 2^27 */
+ fdifference(z, origx); /* does x - z */
+ /* |z[i]| < 2^27 */
+
+ memcpy(origxprime, xprime, sizeof(limb) * 10);
+ fsum(xprime, zprime);
+ /* |xprime[i]| < 2^27 */
+ fdifference(zprime, origxprime);
+ /* |zprime[i]| < 2^27 */
+ 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.)
+ */
+ fproduct(zzprime, x, zprime);
+ /* |zzprime[i]| < 14*2^54 */
+ freduce_degree(xxprime);
+ freduce_coefficients(xxprime);
+ /* |xxprime[i]| < 2^26 */
+ freduce_degree(zzprime);
+ freduce_coefficients(zzprime);
+ /* |zzprime[i]| < 2^26 */
+ memcpy(origxprime, xxprime, sizeof(limb) * 10);
+ fsum(xxprime, zzprime);
+ /* |xxprime[i]| < 2^27 */
+ fdifference(zzprime, origxprime);
+ /* |zzprime[i]| < 2^27 */
+ fsquare(xxxprime, xxprime);
+ /* |xxxprime[i]| < 2^26 */
+ fsquare(zzzprime, zzprime);
+ /* |zzzprime[i]| < 2^26 */
+ fproduct(zzprime, zzzprime, qmqp);
+ /* |zzprime[i]| < 14*2^52 */
+ freduce_degree(zzprime);
+ freduce_coefficients(zzprime);
+ /* |zzprime[i]| < 2^26 */
+ memcpy(x3, xxxprime, sizeof(limb) * 10);
+ memcpy(z3, zzprime, sizeof(limb) * 10);
+
+ fsquare(xx, x);
+ /* |xx[i]| < 2^26 */
+ fsquare(zz, z);
+ /* |zz[i]| < 2^26 */
+ fproduct(x2, xx, zz);
+ /* |x2[i]| < 14*2^52 */
+ freduce_degree(x2);
+ freduce_coefficients(x2);
+ /* |x2[i]| < 2^26 */
+ fdifference(zz, xx); // does zz = xx - zz
+ /* |zz[i]| < 2^27 */
+ memset(zzz + 10, 0, sizeof(limb) * 9);
+ fscalar_product(zzz, zz, 121665);
+ /* |zzz[i]| < 2^(27+17) */
+ /* No need to call freduce_degree here:
+ fscalar_product doesn't increase the degree of its input. */
+ freduce_coefficients(zzz);
+ /* |zzz[i]| < 2^26 */
+ fsum(zzz, xx);
+ /* |zzz[i]| < 2^27 */
+ fproduct(z2, zz, zzz);
+ /* |z2[i]| < 14*2^(26+27) */
+ freduce_degree(z2);
+ freduce_coefficients(z2);
+ /* |z2|i| < 2^26 */
+}
+
+/* Calculates nQ where Q is the x-coordinate of a point on the curve
+ *
+ * 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)
+ */
+static void cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q)
+{
+ limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};
+ limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
+ limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};
+ limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
+
+ unsigned int i, j;
+
+ memcpy(nqpqx, q, sizeof(limb) * 10);
+
+ for (i = 0; i < 32; ++i) {
+ u8 byte = n[31 - i];
+
+ for (j = 0; j < 8; ++j) {
+ const limb bit = byte >> 7;
+
+ swap_conditional(nqx, nqpqx, bit);
+ swap_conditional(nqz, nqpqz, bit);
+ fmonty(nqx2, nqz2,
+ nqpqx2, nqpqz2,
+ nqx, nqz,
+ nqpqx, nqpqz,
+ q);
+ swap_conditional(nqx2, nqpqx2, bit);
+ swap_conditional(nqz2, nqpqz2, bit);
+
+ t = nqx;
+ nqx = nqx2;
+ nqx2 = t;
+ t = nqz;
+ nqz = nqz2;
+ nqz2 = t;
+ t = nqpqx;
+ nqpqx = nqpqx2;
+ nqpqx2 = t;
+ t = nqpqz;
+ nqpqz = nqpqz2;
+ nqpqz2 = t;
+
+ byte <<= 1;
+ }
+ }
+
+ memcpy(resultx, nqx, sizeof(limb) * 10);
+ memcpy(resultz, nqz, sizeof(limb) * 10);
+}
+
+static bool curve25519_donna(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE])
+{
+ limb bp[10], x[10], z[11], zmone[10];
+ u8 e[32];
+
+ memcpy(e, secret, 32);
+ normalize_secret(e);
+
+ fexpand(bp, basepoint);
+ cmult(x, z, e, bp);
+ crecip(zmone, z);
+ fmul(z, x, zmone);
+ fcontract(mypublic, z);
+
+ memzero_explicit(e, sizeof(e));
+ memzero_explicit(bp, sizeof(bp));
+ memzero_explicit(x, sizeof(x));
+ memzero_explicit(z, sizeof(z));
+ memzero_explicit(zmone, sizeof(zmone));
+
+ return true;
+}
+#else
+struct other_stack {
+ limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19], zzprime[19], zzzprime[19], xxxprime[19];
+ limb a[19], b[19], c[19], d[19], e[19], f[19], g[19], h[19];
+ limb bp[10], x[10], z[11], zmone[10];
+ u8 ee[32];
+};
+
+/* Input: Q, Q', Q-Q'
+ * Output: 2Q, Q+Q'
+ *
+ * x2 z3: long form
+ * x3 z3: long form
+ * x z: short form, destroyed
+ * xprime zprime: short form, destroyed
+ * qmqp: short form, preserved
+ *
+ * On entry and exit, the absolute value of the limbs of all inputs and outputs
+ * are < 2^26.
+ */
+static void fmonty(struct other_stack *s,
+ 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' */)
+{
+ memcpy(s->origx, x, 10 * sizeof(limb));
+ fsum(x, z);
+ /* |x[i]| < 2^27 */
+ fdifference(z, s->origx); /* does x - z */
+ /* |z[i]| < 2^27 */
+
+ memcpy(s->origxprime, xprime, sizeof(limb) * 10);
+ fsum(xprime, zprime);
+ /* |xprime[i]| < 2^27 */
+ fdifference(zprime, s->origxprime);
+ /* |zprime[i]| < 2^27 */
+ fproduct(s->xxprime, xprime, z);
+ /* |s->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.)
+ */
+ fproduct(s->zzprime, x, zprime);
+ /* |s->zzprime[i]| < 14*2^54 */
+ freduce_degree(s->xxprime);
+ freduce_coefficients(s->xxprime);
+ /* |s->xxprime[i]| < 2^26 */
+ freduce_degree(s->zzprime);
+ freduce_coefficients(s->zzprime);
+ /* |s->zzprime[i]| < 2^26 */
+ memcpy(s->origxprime, s->xxprime, sizeof(limb) * 10);
+ fsum(s->xxprime, s->zzprime);
+ /* |s->xxprime[i]| < 2^27 */
+ fdifference(s->zzprime, s->origxprime);
+ /* |s->zzprime[i]| < 2^27 */
+ fsquare(s->xxxprime, s->xxprime);
+ /* |s->xxxprime[i]| < 2^26 */
+ fsquare(s->zzzprime, s->zzprime);
+ /* |s->zzzprime[i]| < 2^26 */
+ fproduct(s->zzprime, s->zzzprime, qmqp);
+ /* |s->zzprime[i]| < 14*2^52 */
+ freduce_degree(s->zzprime);
+ freduce_coefficients(s->zzprime);
+ /* |s->zzprime[i]| < 2^26 */
+ memcpy(x3, s->xxxprime, sizeof(limb) * 10);
+ memcpy(z3, s->zzprime, sizeof(limb) * 10);
+
+ fsquare(s->xx, x);
+ /* |s->xx[i]| < 2^26 */
+ fsquare(s->zz, z);
+ /* |s->zz[i]| < 2^26 */
+ fproduct(x2, s->xx, s->zz);
+ /* |x2[i]| < 14*2^52 */
+ freduce_degree(x2);
+ freduce_coefficients(x2);
+ /* |x2[i]| < 2^26 */
+ fdifference(s->zz, s->xx); // does s->zz = s->xx - s->zz
+ /* |s->zz[i]| < 2^27 */
+ memset(s->zzz + 10, 0, sizeof(limb) * 9);
+ fscalar_product(s->zzz, s->zz, 121665);
+ /* |s->zzz[i]| < 2^(27+17) */
+ /* No need to call freduce_degree here:
+ fscalar_product doesn't increase the degree of its input. */
+ freduce_coefficients(s->zzz);
+ /* |s->zzz[i]| < 2^26 */
+ fsum(s->zzz, s->xx);
+ /* |s->zzz[i]| < 2^27 */
+ fproduct(z2, s->zz, s->zzz);
+ /* |z2[i]| < 14*2^(26+27) */
+ freduce_degree(z2);
+ freduce_coefficients(z2);
+ /* |z2|i| < 2^26 */
+}
+
+/* Calculates nQ where Q is the x-coordinate of a point on the curve
+ *
+ * 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)
+ */
+static void cmult(struct other_stack *s, limb *resultx, limb *resultz, const u8 *n, const limb *q)
+{
+ unsigned int i, j;
+ limb *nqpqx = s->a, *nqpqz = s->b, *nqx = s->c, *nqz = s->d, *t;
+ limb *nqpqx2 = s->e, *nqpqz2 = s->f, *nqx2 = s->g, *nqz2 = s->h;
+
+ *nqpqz = *nqx = *nqpqz2 = *nqz2 = 1;
+ memcpy(nqpqx, q, sizeof(limb) * 10);
+
+ for (i = 0; i < 32; ++i) {
+ u8 byte = n[31 - i];
+
+ for (j = 0; j < 8; ++j) {
+ const limb bit = byte >> 7;
+
+ swap_conditional(nqx, nqpqx, bit);
+ swap_conditional(nqz, nqpqz, bit);
+ fmonty(s,
+ nqx2, nqz2,
+ nqpqx2, nqpqz2,
+ nqx, nqz,
+ nqpqx, nqpqz,
+ q);
+ swap_conditional(nqx2, nqpqx2, bit);
+ swap_conditional(nqz2, nqpqz2, bit);
+
+ t = nqx;
+ nqx = nqx2;
+ nqx2 = t;
+ t = nqz;
+ nqz = nqz2;
+ nqz2 = t;
+ t = nqpqx;
+ nqpqx = nqpqx2;
+ nqpqx2 = t;
+ t = nqpqz;
+ nqpqz = nqpqz2;
+ nqpqz2 = t;
+
+ byte <<= 1;
+ }
+ }
+
+ memcpy(resultx, nqx, sizeof(limb) * 10);
+ memcpy(resultz, nqz, sizeof(limb) * 10);
+}
+
+static bool curve25519_donna(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE])
+{
+ struct other_stack *s = kzalloc(sizeof(struct other_stack), GFP_KERNEL);
+
+ if (unlikely(!s))
+ return false;
+
+ memcpy(s->ee, secret, 32);
+ normalize_secret(s->ee);
+
+ fexpand(s->bp, basepoint);
+ cmult(s, s->x, s->z, s->ee, s->bp);
+ crecip(s->zmone, s->z);
+ fmul(s->z, s->x, s->zmone);
+ fcontract(mypublic, s->z);
+
+ kzfree(s);
+ return true;
+}
+#endif
diff --git a/src/crypto/curve25519-u128.h b/src/crypto/curve25519-u128.h
new file mode 100644
index 0000000..9f9ab20
--- /dev/null
+++ b/src/crypto/curve25519-u128.h
@@ -0,0 +1,408 @@
+/* SPDX-License-Identifier: GPL-2.0
+ *
+ * Copyright (C) 2008 Google Inc. All Rights Reserved.
+ * Copyright (C) 2015-2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
+ *
+ * Original author: Adam Langley <agl@imperialviolet.org>
+ */
+
+typedef u64 limb;
+typedef limb felem[5];
+typedef __uint128_t u128;
+
+/* Sum two numbers: output += in */
+static __always_inline void fsum(limb *output, const limb *in)
+{
+ output[0] += in[0];
+ output[1] += in[1];
+ output[2] += in[2];
+ output[3] += in[3];
+ output[4] += in[4];
+}
+
+/* Find the difference of two numbers: output = in - output
+ * (note the order of the arguments!)
+ *
+ * Assumes that out[i] < 2**52
+ * On return, out[i] < 2**55
+ */
+static __always_inline void fdifference_backwards(felem out, const felem in)
+{
+ /* 152 is 19 << 3 */
+ static const limb two54m152 = (((limb)1) << 54) - 152;
+ static const limb two54m8 = (((limb)1) << 54) - 8;
+
+ out[0] = in[0] + two54m152 - out[0];
+ out[1] = in[1] + two54m8 - out[1];
+ out[2] = in[2] + two54m8 - out[2];
+ out[3] = in[3] + two54m8 - out[3];
+ out[4] = in[4] + two54m8 - out[4];
+}
+
+/* Multiply a number by a scalar: output = in * scalar */
+static __always_inline void fscalar_product(felem output, const felem in, const limb scalar)
+{
+ u128 a;
+
+ a = ((u128) in[0]) * scalar;
+ output[0] = ((limb)a) & 0x7ffffffffffffUL;
+
+ a = ((u128) in[1]) * scalar + ((limb) (a >> 51));
+ output[1] = ((limb)a) & 0x7ffffffffffffUL;
+
+ a = ((u128) in[2]) * scalar + ((limb) (a >> 51));
+ output[2] = ((limb)a) & 0x7ffffffffffffUL;
+
+ a = ((u128) in[3]) * scalar + ((limb) (a >> 51));
+ output[3] = ((limb)a) & 0x7ffffffffffffUL;
+
+ a = ((u128) in[4]) * scalar + ((limb) (a >> 51));
+ output[4] = ((limb)a) & 0x7ffffffffffffUL;
+
+ output[0] += (a >> 51) * 19;
+}
+
+/* Multiply two numbers: output = in2 * in
+ *
+ * output must be distinct to both inputs. The inputs are reduced coefficient
+ * form, the output is not.
+ *
+ * Assumes that in[i] < 2**55 and likewise for in2.
+ * On return, output[i] < 2**52
+ */
+static __always_inline void fmul(felem output, const felem in2, const felem in)
+{
+ u128 t[5];
+ limb r0, r1, r2, r3, r4, s0, s1, s2, s3, s4, c;
+
+ r0 = in[0];
+ r1 = in[1];
+ r2 = in[2];
+ r3 = in[3];
+ r4 = in[4];
+
+ s0 = in2[0];
+ s1 = in2[1];
+ s2 = in2[2];
+ s3 = in2[3];
+ s4 = in2[4];
+
+ t[0] = ((u128) r0) * s0;
+ t[1] = ((u128) r0) * s1 + ((u128) r1) * s0;
+ t[2] = ((u128) r0) * s2 + ((u128) r2) * s0 + ((u128) r1) * s1;
+ t[3] = ((u128) r0) * s3 + ((u128) r3) * s0 + ((u128) r1) * s2 + ((u128) r2) * s1;
+ t[4] = ((u128) r0) * s4 + ((u128) r4) * s0 + ((u128) r3) * s1 + ((u128) r1) * s3 + ((u128) r2) * s2;
+
+ r4 *= 19;
+ r1 *= 19;
+ r2 *= 19;
+ r3 *= 19;
+
+ t[0] += ((u128) r4) * s1 + ((u128) r1) * s4 + ((u128) r2) * s3 + ((u128) r3) * s2;
+ t[1] += ((u128) r4) * s2 + ((u128) r2) * s4 + ((u128) r3) * s3;
+ t[2] += ((u128) r4) * s3 + ((u128) r3) * s4;
+ t[3] += ((u128) r4) * s4;
+
+ r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51);
+ t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51);
+ t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51);
+ t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51);
+ t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51);
+ r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL;
+ r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL;
+ r2 += c;
+
+ output[0] = r0;
+ output[1] = r1;
+ output[2] = r2;
+ output[3] = r3;
+ output[4] = r4;
+}
+
+static __always_inline void fsquare_times(felem output, const felem in, limb count)
+{
+ u128 t[5];
+ limb r0, r1, r2, r3, r4, c;
+ limb d0, d1, d2, d4, d419;
+
+ r0 = in[0];
+ r1 = in[1];
+ r2 = in[2];
+ r3 = in[3];
+ r4 = in[4];
+
+ do {
+ d0 = r0 * 2;
+ d1 = r1 * 2;
+ d2 = r2 * 2 * 19;
+ d419 = r4 * 19;
+ d4 = d419 * 2;
+
+ t[0] = ((u128) r0) * r0 + ((u128) d4) * r1 + (((u128) d2) * (r3 ));
+ t[1] = ((u128) d0) * r1 + ((u128) d4) * r2 + (((u128) r3) * (r3 * 19));
+ t[2] = ((u128) d0) * r2 + ((u128) r1) * r1 + (((u128) d4) * (r3 ));
+ t[3] = ((u128) d0) * r3 + ((u128) d1) * r2 + (((u128) r4) * (d419 ));
+ t[4] = ((u128) d0) * r4 + ((u128) d1) * r3 + (((u128) r2) * (r2 ));
+
+ r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51);
+ t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51);
+ t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51);
+ t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51);
+ t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51);
+ r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL;
+ r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL;
+ r2 += c;
+ } while (--count);
+
+ output[0] = r0;
+ output[1] = r1;
+ output[2] = r2;
+ output[3] = r3;
+ output[4] = r4;
+}
+
+/* Load a little-endian 64-bit number */
+static inline limb load_limb(const u8 *in)
+{
+ return le64_to_cpu(*(__le64 *)in);
+}
+
+static inline void store_limb(u8 *out, limb in)
+{
+ *(__le64 *)out = cpu_to_le64(in);
+}
+
+/* Take a little-endian, 32-byte number and expand it into polynomial form */
+static inline void fexpand(limb *output, const u8 *in)
+{
+ output[0] = load_limb(in) & 0x7ffffffffffffUL;
+ output[1] = (load_limb(in + 6) >> 3) & 0x7ffffffffffffUL;
+ output[2] = (load_limb(in + 12) >> 6) & 0x7ffffffffffffUL;
+ output[3] = (load_limb(in + 19) >> 1) & 0x7ffffffffffffUL;
+ output[4] = (load_limb(in + 24) >> 12) & 0x7ffffffffffffUL;
+}
+
+/* Take a fully reduced polynomial form number and contract it into a
+ * little-endian, 32-byte array
+ */
+static void fcontract(u8 *output, const felem input)
+{
+ u128 t[5];
+
+ t[0] = input[0];
+ t[1] = input[1];
+ t[2] = input[2];
+ t[3] = input[3];
+ t[4] = input[4];
+
+ t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
+ t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
+ t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
+ t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
+ t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;
+
+ t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
+ t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
+ t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
+ t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
+ t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;
+
+ /* 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. */
+
+ t[0] += 19;
+
+ t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
+ t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
+ t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
+ t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
+ t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;
+
+ /* now between 19 and 2^255-1 in both cases, and offset by 19. */
+
+ t[0] += 0x8000000000000UL - 19;
+ t[1] += 0x8000000000000UL - 1;
+ t[2] += 0x8000000000000UL - 1;
+ t[3] += 0x8000000000000UL - 1;
+ t[4] += 0x8000000000000UL - 1;
+
+ /* now between 2^255 and 2^256-20, and offset by 2^255. */
+
+ t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
+ t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
+ t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
+ t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
+ t[4] &= 0x7ffffffffffffUL;
+
+ store_limb(output, t[0] | (t[1] << 51));
+ store_limb(output+8, (t[1] >> 13) | (t[2] << 38));
+ store_limb(output+16, (t[2] >> 26) | (t[3] << 25));
+ store_limb(output+24, (t[3] >> 39) | (t[4] << 12));
+}
+
+/* Input: Q, Q', Q-Q'
+ * Output: 2Q, Q+Q'
+ *
+ * x2 z3: long form
+ * x3 z3: long form
+ * x z: short form, destroyed
+ * xprime zprime: short form, destroyed
+ * qmqp: short form, preserved
+ */
+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[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5], zzprime[5], zzzprime[5];
+
+ memcpy(origx, x, 5 * sizeof(limb));
+ fsum(x, z);
+ fdifference_backwards(z, origx); // does x - z
+
+ memcpy(origxprime, xprime, sizeof(limb) * 5);
+ fsum(xprime, zprime);
+ fdifference_backwards(zprime, origxprime);
+ fmul(xxprime, xprime, z);
+ fmul(zzprime, x, zprime);
+ memcpy(origxprime, xxprime, sizeof(limb) * 5);
+ fsum(xxprime, zzprime);
+ fdifference_backwards(zzprime, origxprime);
+ fsquare_times(x3, xxprime, 1);
+ fsquare_times(zzzprime, zzprime, 1);
+ fmul(z3, zzzprime, qmqp);
+
+ fsquare_times(xx, x, 1);
+ fsquare_times(zz, z, 1);
+ fmul(x2, xx, zz);
+ fdifference_backwards(zz, xx); // does zz = xx - zz
+ fscalar_product(zzz, zz, 121665);
+ fsum(zzz, xx);
+ fmul(z2, zz, zzz);
+}
+
+/* Maybe swap the contents of two limb arrays (@a and @b), each @len elements
+ * long. Perform the swap iff @swap is non-zero.
+ *
+ * This function performs the swap without leaking any side-channel
+ * information.
+ */
+static void swap_conditional(limb a[5], limb b[5], limb iswap)
+{
+ 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;
+ }
+}
+
+/* Calculates nQ where Q is the x-coordinate of a point on the curve
+ *
+ * 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)
+ */
+static void cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q)
+{
+ limb a[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0};
+ limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
+ limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1};
+ limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
+
+ unsigned int i, j;
+
+ memcpy(nqpqx, q, sizeof(limb) * 5);
+
+ for (i = 0; i < 32; ++i) {
+ u8 byte = n[31 - i];
+
+ for (j = 0; j < 8; ++j) {
+ const limb bit = byte >> 7;
+
+ swap_conditional(nqx, nqpqx, bit);
+ swap_conditional(nqz, nqpqz, bit);
+ fmonty(nqx2, nqz2,
+ nqpqx2, nqpqz2,
+ nqx, nqz,
+ nqpqx, nqpqz,
+ q);
+ swap_conditional(nqx2, nqpqx2, bit);
+ swap_conditional(nqz2, nqpqz2, bit);
+
+ t = nqx;
+ nqx = nqx2;
+ nqx2 = t;
+ t = nqz;
+ nqz = nqz2;
+ nqz2 = t;
+ t = nqpqx;
+ nqpqx = nqpqx2;
+ nqpqx2 = t;
+ t = nqpqz;
+ nqpqz = nqpqz2;
+ nqpqz2 = t;
+
+ byte <<= 1;
+ }
+ }
+
+ memcpy(resultx, nqx, sizeof(limb) * 5);
+ memcpy(resultz, nqz, sizeof(limb) * 5);
+}
+
+static void crecip(felem out, const felem z)
+{
+ felem a, t0, b, c;
+
+ /* 2 */ fsquare_times(a, z, 1); // a = 2
+ /* 8 */ fsquare_times(t0, a, 2);
+ /* 9 */ fmul(b, t0, z); // b = 9
+ /* 11 */ fmul(a, b, a); // a = 11
+ /* 22 */ fsquare_times(t0, a, 1);
+ /* 2^5 - 2^0 = 31 */ fmul(b, t0, b);
+ /* 2^10 - 2^5 */ fsquare_times(t0, b, 5);
+ /* 2^10 - 2^0 */ fmul(b, t0, b);
+ /* 2^20 - 2^10 */ fsquare_times(t0, b, 10);
+ /* 2^20 - 2^0 */ fmul(c, t0, b);
+ /* 2^40 - 2^20 */ fsquare_times(t0, c, 20);
+ /* 2^40 - 2^0 */ fmul(t0, t0, c);
+ /* 2^50 - 2^10 */ fsquare_times(t0, t0, 10);
+ /* 2^50 - 2^0 */ fmul(b, t0, b);
+ /* 2^100 - 2^50 */ fsquare_times(t0, b, 50);
+ /* 2^100 - 2^0 */ fmul(c, t0, b);
+ /* 2^200 - 2^100 */ fsquare_times(t0, c, 100);
+ /* 2^200 - 2^0 */ fmul(t0, t0, c);
+ /* 2^250 - 2^50 */ fsquare_times(t0, t0, 50);
+ /* 2^250 - 2^0 */ fmul(t0, t0, b);
+ /* 2^255 - 2^5 */ fsquare_times(t0, t0, 5);
+ /* 2^255 - 21 */ fmul(out, t0, a);
+}
+
+static bool curve25519_donna(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE])
+{
+ limb bp[5], x[5], z[5], zmone[5];
+ u8 e[32];
+
+ memcpy(e, secret, 32);
+ normalize_secret(e);
+
+ fexpand(bp, basepoint);
+ cmult(x, z, e, bp);
+ crecip(zmone, z);
+ fmul(z, x, zmone);
+ fcontract(mypublic, z);
+
+ memzero_explicit(e, sizeof(e));
+ memzero_explicit(bp, sizeof(bp));
+ memzero_explicit(x, sizeof(x));
+ memzero_explicit(z, sizeof(z));
+ memzero_explicit(zmone, sizeof(zmone));
+
+ return true;
+}
diff --git a/src/crypto/curve25519-x86_64.h b/src/crypto/curve25519-x86_64.h
new file mode 100644
index 0000000..2d83d77
--- /dev/null
+++ b/src/crypto/curve25519-x86_64.h
@@ -0,0 +1,175 @@
+/* SPDX-License-Identifier: GPL-2.0
+ *
+ * Copyright (C) 2015-2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
+ *
+ * Based on algorithms from Tung Chou <blueprint@crypto.tw>
+ */
+
+#include <asm/cpufeature.h>
+#include <asm/processor.h>
+#include <asm/fpu/api.h>
+#include <asm/simd.h>
+static bool curve25519_use_avx __read_mostly;
+void __init curve25519_fpu_init(void)
+{
+#ifndef CONFIG_UML
+ curve25519_use_avx = boot_cpu_has(X86_FEATURE_AVX) && cpu_has_xfeatures(XFEATURE_MASK_SSE | XFEATURE_MASK_YMM, NULL);
+#endif
+}
+
+typedef u64 fe[10];
+typedef u64 fe51[5];
+asmlinkage void curve25519_sandy2x_ladder(fe *, const u8 *);
+asmlinkage void curve25519_sandy2x_ladder_base(fe *, const u8 *);
+asmlinkage void curve25519_sandy2x_fe51_pack(u8 *, const fe51 *);
+asmlinkage void curve25519_sandy2x_fe51_mul(fe51 *, const fe51 *, const fe51 *);
+asmlinkage void curve25519_sandy2x_fe51_nsquare(fe51 *, const fe51 *, int);
+
+static inline u32 le24_to_cpupv(const u8 *in)
+{
+ return le16_to_cpup((__le16 *)in) | ((u32)in[2]) << 16;
+}
+
+static inline void fe_frombytes(fe h, const u8 *s)
+{
+ u64 h0 = le32_to_cpup((__le32 *)s);
+ u64 h1 = le24_to_cpupv(s + 4) << 6;
+ u64 h2 = le24_to_cpupv(s + 7) << 5;
+ u64 h3 = le24_to_cpupv(s + 10) << 3;
+ u64 h4 = le24_to_cpupv(s + 13) << 2;
+ u64 h5 = le32_to_cpup((__le32 *)(s + 16));
+ u64 h6 = le24_to_cpupv(s + 20) << 7;
+ u64 h7 = le24_to_cpupv(s + 23) << 5;
+ u64 h8 = le24_to_cpupv(s + 26) << 4;
+ u64 h9 = (le24_to_cpupv(s + 29) & 8388607) << 2;
+ u64 carry0, carry1, carry2, carry3, carry4, carry5, carry6, carry7, carry8, carry9;
+
+ carry9 = h9 >> 25; h0 += carry9 * 19; h9 &= 0x1FFFFFF;
+ carry1 = h1 >> 25; h2 += carry1; h1 &= 0x1FFFFFF;
+ carry3 = h3 >> 25; h4 += carry3; h3 &= 0x1FFFFFF;
+ carry5 = h5 >> 25; h6 += carry5; h5 &= 0x1FFFFFF;
+ carry7 = h7 >> 25; h8 += carry7; h7 &= 0x1FFFFFF;
+
+ carry0 = h0 >> 26; h1 += carry0; h0 &= 0x3FFFFFF;
+ carry2 = h2 >> 26; h3 += carry2; h2 &= 0x3FFFFFF;
+ carry4 = h4 >> 26; h5 += carry4; h4 &= 0x3FFFFFF;
+ carry6 = h6 >> 26; h7 += carry6; h6 &= 0x3FFFFFF;
+ carry8 = h8 >> 26; h9 += carry8; h8 &= 0x3FFFFFF;
+
+ h[0] = h0;
+ h[1] = h1;
+ h[2] = h2;
+ h[3] = h3;
+ h[4] = h4;
+ h[5] = h5;
+ h[6] = h6;
+ h[7] = h7;
+ h[8] = h8;
+ h[9] = h9;
+}
+
+static inline void fe51_invert(fe51 *r, const fe51 *x)
+{
+ fe51 z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t;
+
+ /* 2 */ curve25519_sandy2x_fe51_nsquare(&z2, x, 1);
+ /* 4 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2, 1);
+ /* 8 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 1);
+ /* 9 */ curve25519_sandy2x_fe51_mul(&z9, (const fe51 *)&t, x);
+ /* 11 */ curve25519_sandy2x_fe51_mul(&z11, (const fe51 *)&z9, (const fe51 *)&z2);
+ /* 22 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z11, 1);
+ /* 2^5 - 2^0 = 31 */ curve25519_sandy2x_fe51_mul(&z2_5_0, (const fe51 *)&t, (const fe51 *)&z9);
+
+ /* 2^10 - 2^5 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_5_0, 5);
+ /* 2^10 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_10_0, (const fe51 *)&t, (const fe51 *)&z2_5_0);
+
+ /* 2^20 - 2^10 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_10_0, 10);
+ /* 2^20 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_20_0, (const fe51 *)&t, (const fe51 *)&z2_10_0);
+
+ /* 2^40 - 2^20 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_20_0, 20);
+ /* 2^40 - 2^0 */ curve25519_sandy2x_fe51_mul(&t, (const fe51 *)&t, (const fe51 *)&z2_20_0);
+
+ /* 2^50 - 2^10 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 10);
+ /* 2^50 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_50_0, (const fe51 *)&t, (const fe51 *)&z2_10_0);
+
+ /* 2^100 - 2^50 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_50_0, 50);
+ /* 2^100 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_100_0, (const fe51 *)&t, (const fe51 *)&z2_50_0);
+
+ /* 2^200 - 2^100 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_100_0, 100);
+ /* 2^200 - 2^0 */ curve25519_sandy2x_fe51_mul(&t, (const fe51 *)&t, (const fe51 *)&z2_100_0);
+
+ /* 2^250 - 2^50 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 50);
+ /* 2^250 - 2^0 */ curve25519_sandy2x_fe51_mul(&t, (const fe51 *)&t, (const fe51 *)&z2_50_0);
+
+ /* 2^255 - 2^5 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 5);
+ /* 2^255 - 21 */ curve25519_sandy2x_fe51_mul(r, (const fe51 *)t, (const fe51 *)&z11);
+}
+
+static void curve25519_sandy2x(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE])
+{
+ u8 e[32];
+ fe var[3];
+ fe51 x_51, z_51;
+
+ memcpy(e, secret, 32);
+ normalize_secret(e);
+#define x1 var[0]
+#define x2 var[1]
+#define z2 var[2]
+ fe_frombytes(x1, basepoint);
+ curve25519_sandy2x_ladder(var, e);
+ z_51[0] = (z2[1] << 26) + z2[0];
+ z_51[1] = (z2[3] << 26) + z2[2];
+ z_51[2] = (z2[5] << 26) + z2[4];
+ z_51[3] = (z2[7] << 26) + z2[6];
+ z_51[4] = (z2[9] << 26) + z2[8];
+ x_51[0] = (x2[1] << 26) + x2[0];
+ x_51[1] = (x2[3] << 26) + x2[2];
+ x_51[2] = (x2[5] << 26) + x2[4];
+ x_51[3] = (x2[7] << 26) + x2[6];
+ x_51[4] = (x2[9] << 26) + x2[8];
+#undef x1
+#undef x2
+#undef z2
+ fe51_invert(&z_51, (const fe51 *)&z_51);
+ curve25519_sandy2x_fe51_mul(&x_51, (const fe51 *)&x_51, (const fe51 *)&z_51);
+ curve25519_sandy2x_fe51_pack(mypublic, (const fe51 *)&x_51);
+
+ memzero_explicit(e, sizeof(e));
+ memzero_explicit(var, sizeof(var));
+ memzero_explicit(x_51, sizeof(x_51));
+ memzero_explicit(z_51, sizeof(z_51));
+}
+
+static void curve25519_sandy2x_base(u8 pub[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE])
+{
+ u8 e[32];
+ fe var[3];
+ fe51 x_51, z_51;
+
+ memcpy(e, secret, 32);
+ normalize_secret(e);
+ curve25519_sandy2x_ladder_base(var, e);
+#define x2 var[0]
+#define z2 var[1]
+ z_51[0] = (z2[1] << 26) + z2[0];
+ z_51[1] = (z2[3] << 26) + z2[2];
+ z_51[2] = (z2[5] << 26) + z2[4];
+ z_51[3] = (z2[7] << 26) + z2[6];
+ z_51[4] = (z2[9] << 26) + z2[8];
+ x_51[0] = (x2[1] << 26) + x2[0];
+ x_51[1] = (x2[3] << 26) + x2[2];
+ x_51[2] = (x2[5] << 26) + x2[4];
+ x_51[3] = (x2[7] << 26) + x2[6];
+ x_51[4] = (x2[9] << 26) + x2[8];
+#undef x2
+#undef z2
+ fe51_invert(&z_51, (const fe51 *)&z_51);
+ curve25519_sandy2x_fe51_mul(&x_51, (const fe51 *)&x_51, (const fe51 *)&z_51);
+ curve25519_sandy2x_fe51_pack(pub, (const fe51 *)&x_51);
+
+ memzero_explicit(e, sizeof(e));
+ memzero_explicit(var, sizeof(var));
+ memzero_explicit(x_51, sizeof(x_51));
+ memzero_explicit(z_51, sizeof(z_51));
+}
diff --git a/src/crypto/curve25519.c b/src/crypto/curve25519.c
index e343c85..dd7f4bd 100644
--- a/src/crypto/curve25519.c
+++ b/src/crypto/curve25519.c
@@ -1,9 +1,6 @@
/* SPDX-License-Identifier: GPL-2.0
*
- * Copyright (C) 2008 Google Inc. All Rights Reserved.
* Copyright (C) 2015-2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
- *
- * Original author: Adam Langley <agl@imperialviolet.org>
*/
#include "curve25519.h"
@@ -13,11 +10,6 @@
#include <linux/random.h>
#include <crypto/algapi.h>
-#define ARCH_HAS_SEPARATE_IRQ_STACK
-#if (defined(CONFIG_MIPS) && LINUX_VERSION_CODE < KERNEL_VERSION(4, 11, 0)) || defined(CONFIG_ARM)
-#undef ARCH_HAS_SEPARATE_IRQ_STACK
-#endif
-
static __always_inline void normalize_secret(u8 secret[CURVE25519_POINT_SIZE])
{
secret[0] &= 248;
@@ -26,1615 +18,17 @@ static __always_inline void normalize_secret(u8 secret[CURVE25519_POINT_SIZE])
}
#if defined(CONFIG_X86_64) && defined(CONFIG_AS_AVX)
-#include <asm/cpufeature.h>
-#include <asm/processor.h>
-#include <asm/fpu/api.h>
-#include <asm/simd.h>
-static bool curve25519_use_avx __read_mostly;
-void __init curve25519_fpu_init(void)
-{
-#ifndef CONFIG_UML
- curve25519_use_avx = boot_cpu_has(X86_FEATURE_AVX) && cpu_has_xfeatures(XFEATURE_MASK_SSE | XFEATURE_MASK_YMM, NULL);
-#endif
-}
-
-typedef u64 fe[10];
-typedef u64 fe51[5];
-asmlinkage void curve25519_sandy2x_ladder(fe *, const u8 *);
-asmlinkage void curve25519_sandy2x_ladder_base(fe *, const u8 *);
-asmlinkage void curve25519_sandy2x_fe51_pack(u8 *, const fe51 *);
-asmlinkage void curve25519_sandy2x_fe51_mul(fe51 *, const fe51 *, const fe51 *);
-asmlinkage void curve25519_sandy2x_fe51_nsquare(fe51 *, const fe51 *, int);
-
-static inline u32 le24_to_cpupv(const u8 *in)
-{
- return le16_to_cpup((__le16 *)in) | ((u32)in[2]) << 16;
-}
-
-static inline void fe_frombytes(fe h, const u8 *s)
-{
- u64 h0 = le32_to_cpup((__le32 *)s);
- u64 h1 = le24_to_cpupv(s + 4) << 6;
- u64 h2 = le24_to_cpupv(s + 7) << 5;
- u64 h3 = le24_to_cpupv(s + 10) << 3;
- u64 h4 = le24_to_cpupv(s + 13) << 2;
- u64 h5 = le32_to_cpup((__le32 *)(s + 16));
- u64 h6 = le24_to_cpupv(s + 20) << 7;
- u64 h7 = le24_to_cpupv(s + 23) << 5;
- u64 h8 = le24_to_cpupv(s + 26) << 4;
- u64 h9 = (le24_to_cpupv(s + 29) & 8388607) << 2;
- u64 carry0, carry1, carry2, carry3, carry4, carry5, carry6, carry7, carry8, carry9;
-
- carry9 = h9 >> 25; h0 += carry9 * 19; h9 &= 0x1FFFFFF;
- carry1 = h1 >> 25; h2 += carry1; h1 &= 0x1FFFFFF;
- carry3 = h3 >> 25; h4 += carry3; h3 &= 0x1FFFFFF;
- carry5 = h5 >> 25; h6 += carry5; h5 &= 0x1FFFFFF;
- carry7 = h7 >> 25; h8 += carry7; h7 &= 0x1FFFFFF;
-
- carry0 = h0 >> 26; h1 += carry0; h0 &= 0x3FFFFFF;
- carry2 = h2 >> 26; h3 += carry2; h2 &= 0x3FFFFFF;
- carry4 = h4 >> 26; h5 += carry4; h4 &= 0x3FFFFFF;
- carry6 = h6 >> 26; h7 += carry6; h6 &= 0x3FFFFFF;
- carry8 = h8 >> 26; h9 += carry8; h8 &= 0x3FFFFFF;
-
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
-}
-
-static inline void fe51_invert(fe51 *r, const fe51 *x)
-{
- fe51 z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t;
-
- /* 2 */ curve25519_sandy2x_fe51_nsquare(&z2, x, 1);
- /* 4 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2, 1);
- /* 8 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 1);
- /* 9 */ curve25519_sandy2x_fe51_mul(&z9, (const fe51 *)&t, x);
- /* 11 */ curve25519_sandy2x_fe51_mul(&z11, (const fe51 *)&z9, (const fe51 *)&z2);
- /* 22 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z11, 1);
- /* 2^5 - 2^0 = 31 */ curve25519_sandy2x_fe51_mul(&z2_5_0, (const fe51 *)&t, (const fe51 *)&z9);
-
- /* 2^10 - 2^5 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_5_0, 5);
- /* 2^10 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_10_0, (const fe51 *)&t, (const fe51 *)&z2_5_0);
-
- /* 2^20 - 2^10 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_10_0, 10);
- /* 2^20 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_20_0, (const fe51 *)&t, (const fe51 *)&z2_10_0);
-
- /* 2^40 - 2^20 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_20_0, 20);
- /* 2^40 - 2^0 */ curve25519_sandy2x_fe51_mul(&t, (const fe51 *)&t, (const fe51 *)&z2_20_0);
-
- /* 2^50 - 2^10 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 10);
- /* 2^50 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_50_0, (const fe51 *)&t, (const fe51 *)&z2_10_0);
-
- /* 2^100 - 2^50 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_50_0, 50);
- /* 2^100 - 2^0 */ curve25519_sandy2x_fe51_mul(&z2_100_0, (const fe51 *)&t, (const fe51 *)&z2_50_0);
-
- /* 2^200 - 2^100 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&z2_100_0, 100);
- /* 2^200 - 2^0 */ curve25519_sandy2x_fe51_mul(&t, (const fe51 *)&t, (const fe51 *)&z2_100_0);
-
- /* 2^250 - 2^50 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 50);
- /* 2^250 - 2^0 */ curve25519_sandy2x_fe51_mul(&t, (const fe51 *)&t, (const fe51 *)&z2_50_0);
-
- /* 2^255 - 2^5 */ curve25519_sandy2x_fe51_nsquare(&t, (const fe51 *)&t, 5);
- /* 2^255 - 21 */ curve25519_sandy2x_fe51_mul(r, (const fe51 *)t, (const fe51 *)&z11);
-}
-
-static void curve25519_sandy2x(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE])
-{
- u8 e[32];
- fe var[3];
- fe51 x_51, z_51;
-
- memcpy(e, secret, 32);
- normalize_secret(e);
-#define x1 var[0]
-#define x2 var[1]
-#define z2 var[2]
- fe_frombytes(x1, basepoint);
- curve25519_sandy2x_ladder(var, e);
- z_51[0] = (z2[1] << 26) + z2[0];
- z_51[1] = (z2[3] << 26) + z2[2];
- z_51[2] = (z2[5] << 26) + z2[4];
- z_51[3] = (z2[7] << 26) + z2[6];
- z_51[4] = (z2[9] << 26) + z2[8];
- x_51[0] = (x2[1] << 26) + x2[0];
- x_51[1] = (x2[3] << 26) + x2[2];
- x_51[2] = (x2[5] << 26) + x2[4];
- x_51[3] = (x2[7] << 26) + x2[6];
- x_51[4] = (x2[9] << 26) + x2[8];
-#undef x1
-#undef x2
-#undef z2
- fe51_invert(&z_51, (const fe51 *)&z_51);
- curve25519_sandy2x_fe51_mul(&x_51, (const fe51 *)&x_51, (const fe51 *)&z_51);
- curve25519_sandy2x_fe51_pack(mypublic, (const fe51 *)&x_51);
-
- memzero_explicit(e, sizeof(e));
- memzero_explicit(var, sizeof(var));
- memzero_explicit(x_51, sizeof(x_51));
- memzero_explicit(z_51, sizeof(z_51));
-}
-
-static void curve25519_sandy2x_base(u8 pub[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE])
-{
- u8 e[32];
- fe var[3];
- fe51 x_51, z_51;
-
- memcpy(e, secret, 32);
- normalize_secret(e);
- curve25519_sandy2x_ladder_base(var, e);
-#define x2 var[0]
-#define z2 var[1]
- z_51[0] = (z2[1] << 26) + z2[0];
- z_51[1] = (z2[3] << 26) + z2[2];
- z_51[2] = (z2[5] << 26) + z2[4];
- z_51[3] = (z2[7] << 26) + z2[6];
- z_51[4] = (z2[9] << 26) + z2[8];
- x_51[0] = (x2[1] << 26) + x2[0];
- x_51[1] = (x2[3] << 26) + x2[2];
- x_51[2] = (x2[5] << 26) + x2[4];
- x_51[3] = (x2[7] << 26) + x2[6];
- x_51[4] = (x2[9] << 26) + x2[8];
-#undef x2
-#undef z2
- fe51_invert(&z_51, (const fe51 *)&z_51);
- curve25519_sandy2x_fe51_mul(&x_51, (const fe51 *)&x_51, (const fe51 *)&z_51);
- curve25519_sandy2x_fe51_pack(pub, (const fe51 *)&x_51);
-
- memzero_explicit(e, sizeof(e));
- memzero_explicit(var, sizeof(var));
- memzero_explicit(x_51, sizeof(x_51));
- memzero_explicit(z_51, sizeof(z_51));
-}
+#include "curve25519-x86_64.h"
#elif IS_ENABLED(CONFIG_KERNEL_MODE_NEON) && defined(CONFIG_ARM)
-#include <asm/hwcap.h>
-#include <asm/neon.h>
-#include <asm/simd.h>
-asmlinkage void curve25519_neon(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE]);
-static bool curve25519_use_neon __read_mostly;
-void __init curve25519_fpu_init(void)
-{
- curve25519_use_neon = elf_hwcap & HWCAP_NEON;
-}
+#include "curve25519-arm.h"
#else
void __init curve25519_fpu_init(void) { }
#endif
#if defined(CONFIG_ARCH_SUPPORTS_INT128) && defined(__SIZEOF_INT128__)
-typedef u64 limb;
-typedef limb felem[5];
-typedef __uint128_t u128;
-
-/* Sum two numbers: output += in */
-static __always_inline void fsum(limb *output, const limb *in)
-{
- output[0] += in[0];
- output[1] += in[1];
- output[2] += in[2];
- output[3] += in[3];
- output[4] += in[4];
-}
-
-/* Find the difference of two numbers: output = in - output
- * (note the order of the arguments!)
- *
- * Assumes that out[i] < 2**52
- * On return, out[i] < 2**55
- */
-static __always_inline void fdifference_backwards(felem out, const felem in)
-{
- /* 152 is 19 << 3 */
- static const limb two54m152 = (((limb)1) << 54) - 152;
- static const limb two54m8 = (((limb)1) << 54) - 8;
-
- out[0] = in[0] + two54m152 - out[0];
- out[1] = in[1] + two54m8 - out[1];
- out[2] = in[2] + two54m8 - out[2];
- out[3] = in[3] + two54m8 - out[3];
- out[4] = in[4] + two54m8 - out[4];
-}
-
-/* Multiply a number by a scalar: output = in * scalar */
-static __always_inline void fscalar_product(felem output, const felem in, const limb scalar)
-{
- u128 a;
-
- a = ((u128) in[0]) * scalar;
- output[0] = ((limb)a) & 0x7ffffffffffffUL;
-
- a = ((u128) in[1]) * scalar + ((limb) (a >> 51));
- output[1] = ((limb)a) & 0x7ffffffffffffUL;
-
- a = ((u128) in[2]) * scalar + ((limb) (a >> 51));
- output[2] = ((limb)a) & 0x7ffffffffffffUL;
-
- a = ((u128) in[3]) * scalar + ((limb) (a >> 51));
- output[3] = ((limb)a) & 0x7ffffffffffffUL;
-
- a = ((u128) in[4]) * scalar + ((limb) (a >> 51));
- output[4] = ((limb)a) & 0x7ffffffffffffUL;
-
- output[0] += (a >> 51) * 19;
-}
-
-/* Multiply two numbers: output = in2 * in
- *
- * output must be distinct to both inputs. The inputs are reduced coefficient
- * form, the output is not.
- *
- * Assumes that in[i] < 2**55 and likewise for in2.
- * On return, output[i] < 2**52
- */
-static __always_inline void fmul(felem output, const felem in2, const felem in)
-{
- u128 t[5];
- limb r0, r1, r2, r3, r4, s0, s1, s2, s3, s4, c;
-
- r0 = in[0];
- r1 = in[1];
- r2 = in[2];
- r3 = in[3];
- r4 = in[4];
-
- s0 = in2[0];
- s1 = in2[1];
- s2 = in2[2];
- s3 = in2[3];
- s4 = in2[4];
-
- t[0] = ((u128) r0) * s0;
- t[1] = ((u128) r0) * s1 + ((u128) r1) * s0;
- t[2] = ((u128) r0) * s2 + ((u128) r2) * s0 + ((u128) r1) * s1;
- t[3] = ((u128) r0) * s3 + ((u128) r3) * s0 + ((u128) r1) * s2 + ((u128) r2) * s1;
- t[4] = ((u128) r0) * s4 + ((u128) r4) * s0 + ((u128) r3) * s1 + ((u128) r1) * s3 + ((u128) r2) * s2;
-
- r4 *= 19;
- r1 *= 19;
- r2 *= 19;
- r3 *= 19;
-
- t[0] += ((u128) r4) * s1 + ((u128) r1) * s4 + ((u128) r2) * s3 + ((u128) r3) * s2;
- t[1] += ((u128) r4) * s2 + ((u128) r2) * s4 + ((u128) r3) * s3;
- t[2] += ((u128) r4) * s3 + ((u128) r3) * s4;
- t[3] += ((u128) r4) * s4;
-
- r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51);
- t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51);
- t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51);
- t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51);
- t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51);
- r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL;
- r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL;
- r2 += c;
-
- output[0] = r0;
- output[1] = r1;
- output[2] = r2;
- output[3] = r3;
- output[4] = r4;
-}
-
-static __always_inline void fsquare_times(felem output, const felem in, limb count)
-{
- u128 t[5];
- limb r0, r1, r2, r3, r4, c;
- limb d0, d1, d2, d4, d419;
-
- r0 = in[0];
- r1 = in[1];
- r2 = in[2];
- r3 = in[3];
- r4 = in[4];
-
- do {
- d0 = r0 * 2;
- d1 = r1 * 2;
- d2 = r2 * 2 * 19;
- d419 = r4 * 19;
- d4 = d419 * 2;
-
- t[0] = ((u128) r0) * r0 + ((u128) d4) * r1 + (((u128) d2) * (r3 ));
- t[1] = ((u128) d0) * r1 + ((u128) d4) * r2 + (((u128) r3) * (r3 * 19));
- t[2] = ((u128) d0) * r2 + ((u128) r1) * r1 + (((u128) d4) * (r3 ));
- t[3] = ((u128) d0) * r3 + ((u128) d1) * r2 + (((u128) r4) * (d419 ));
- t[4] = ((u128) d0) * r4 + ((u128) d1) * r3 + (((u128) r2) * (r2 ));
-
- r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51);
- t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51);
- t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51);
- t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51);
- t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51);
- r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL;
- r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL;
- r2 += c;
- } while (--count);
-
- output[0] = r0;
- output[1] = r1;
- output[2] = r2;
- output[3] = r3;
- output[4] = r4;
-}
-
-/* Load a little-endian 64-bit number */
-static inline limb load_limb(const u8 *in)
-{
- return le64_to_cpu(*(__le64 *)in);
-}
-
-static inline void store_limb(u8 *out, limb in)
-{
- *(__le64 *)out = cpu_to_le64(in);
-}
-
-/* Take a little-endian, 32-byte number and expand it into polynomial form */
-static inline void fexpand(limb *output, const u8 *in)
-{
- output[0] = load_limb(in) & 0x7ffffffffffffUL;
- output[1] = (load_limb(in + 6) >> 3) & 0x7ffffffffffffUL;
- output[2] = (load_limb(in + 12) >> 6) & 0x7ffffffffffffUL;
- output[3] = (load_limb(in + 19) >> 1) & 0x7ffffffffffffUL;
- output[4] = (load_limb(in + 24) >> 12) & 0x7ffffffffffffUL;
-}
-
-/* Take a fully reduced polynomial form number and contract it into a
- * little-endian, 32-byte array
- */
-static void fcontract(u8 *output, const felem input)
-{
- u128 t[5];
-
- t[0] = input[0];
- t[1] = input[1];
- t[2] = input[2];
- t[3] = input[3];
- t[4] = input[4];
-
- t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
- t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
- t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
- t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
- t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;
-
- t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
- t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
- t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
- t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
- t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;
-
- /* 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. */
-
- t[0] += 19;
-
- t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
- t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
- t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
- t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
- t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;
-
- /* now between 19 and 2^255-1 in both cases, and offset by 19. */
-
- t[0] += 0x8000000000000UL - 19;
- t[1] += 0x8000000000000UL - 1;
- t[2] += 0x8000000000000UL - 1;
- t[3] += 0x8000000000000UL - 1;
- t[4] += 0x8000000000000UL - 1;
-
- /* now between 2^255 and 2^256-20, and offset by 2^255. */
-
- t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
- t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
- t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
- t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
- t[4] &= 0x7ffffffffffffUL;
-
- store_limb(output, t[0] | (t[1] << 51));
- store_limb(output+8, (t[1] >> 13) | (t[2] << 38));
- store_limb(output+16, (t[2] >> 26) | (t[3] << 25));
- store_limb(output+24, (t[3] >> 39) | (t[4] << 12));
-}
-
-/* Input: Q, Q', Q-Q'
- * Output: 2Q, Q+Q'
- *
- * x2 z3: long form
- * x3 z3: long form
- * x z: short form, destroyed
- * xprime zprime: short form, destroyed
- * qmqp: short form, preserved
- */
-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[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5], zzprime[5], zzzprime[5];
-
- memcpy(origx, x, 5 * sizeof(limb));
- fsum(x, z);
- fdifference_backwards(z, origx); // does x - z
-
- memcpy(origxprime, xprime, sizeof(limb) * 5);
- fsum(xprime, zprime);
- fdifference_backwards(zprime, origxprime);
- fmul(xxprime, xprime, z);
- fmul(zzprime, x, zprime);
- memcpy(origxprime, xxprime, sizeof(limb) * 5);
- fsum(xxprime, zzprime);
- fdifference_backwards(zzprime, origxprime);
- fsquare_times(x3, xxprime, 1);
- fsquare_times(zzzprime, zzprime, 1);
- fmul(z3, zzzprime, qmqp);
-
- fsquare_times(xx, x, 1);
- fsquare_times(zz, z, 1);
- fmul(x2, xx, zz);
- fdifference_backwards(zz, xx); // does zz = xx - zz
- fscalar_product(zzz, zz, 121665);
- fsum(zzz, xx);
- fmul(z2, zz, zzz);
-}
-
-/* Maybe swap the contents of two limb arrays (@a and @b), each @len elements
- * long. Perform the swap iff @swap is non-zero.
- *
- * This function performs the swap without leaking any side-channel
- * information.
- */
-static void swap_conditional(limb a[5], limb b[5], limb iswap)
-{
- 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;
- }
-}
-
-/* Calculates nQ where Q is the x-coordinate of a point on the curve
- *
- * 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)
- */
-static void cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q)
-{
- limb a[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0};
- limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
- limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1};
- limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
-
- unsigned int i, j;
-
- memcpy(nqpqx, q, sizeof(limb) * 5);
-
- for (i = 0; i < 32; ++i) {
- u8 byte = n[31 - i];
-
- for (j = 0; j < 8; ++j) {
- const limb bit = byte >> 7;
-
- swap_conditional(nqx, nqpqx, bit);
- swap_conditional(nqz, nqpqz, bit);
- fmonty(nqx2, nqz2,
- nqpqx2, nqpqz2,
- nqx, nqz,
- nqpqx, nqpqz,
- q);
- swap_conditional(nqx2, nqpqx2, bit);
- swap_conditional(nqz2, nqpqz2, bit);
-
- t = nqx;
- nqx = nqx2;
- nqx2 = t;
- t = nqz;
- nqz = nqz2;
- nqz2 = t;
- t = nqpqx;
- nqpqx = nqpqx2;
- nqpqx2 = t;
- t = nqpqz;
- nqpqz = nqpqz2;
- nqpqz2 = t;
-
- byte <<= 1;
- }
- }
-
- memcpy(resultx, nqx, sizeof(limb) * 5);
- memcpy(resultz, nqz, sizeof(limb) * 5);
-}
-
-static void crecip(felem out, const felem z)
-{
- felem a, t0, b, c;
-
- /* 2 */ fsquare_times(a, z, 1); // a = 2
- /* 8 */ fsquare_times(t0, a, 2);
- /* 9 */ fmul(b, t0, z); // b = 9
- /* 11 */ fmul(a, b, a); // a = 11
- /* 22 */ fsquare_times(t0, a, 1);
- /* 2^5 - 2^0 = 31 */ fmul(b, t0, b);
- /* 2^10 - 2^5 */ fsquare_times(t0, b, 5);
- /* 2^10 - 2^0 */ fmul(b, t0, b);
- /* 2^20 - 2^10 */ fsquare_times(t0, b, 10);
- /* 2^20 - 2^0 */ fmul(c, t0, b);
- /* 2^40 - 2^20 */ fsquare_times(t0, c, 20);
- /* 2^40 - 2^0 */ fmul(t0, t0, c);
- /* 2^50 - 2^10 */ fsquare_times(t0, t0, 10);
- /* 2^50 - 2^0 */ fmul(b, t0, b);
- /* 2^100 - 2^50 */ fsquare_times(t0, b, 50);
- /* 2^100 - 2^0 */ fmul(c, t0, b);
- /* 2^200 - 2^100 */ fsquare_times(t0, c, 100);
- /* 2^200 - 2^0 */ fmul(t0, t0, c);
- /* 2^250 - 2^50 */ fsquare_times(t0, t0, 50);
- /* 2^250 - 2^0 */ fmul(t0, t0, b);
- /* 2^255 - 2^5 */ fsquare_times(t0, t0, 5);
- /* 2^255 - 21 */ fmul(out, t0, a);
-}
-
-static bool curve25519_donna(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE])
-{
- limb bp[5], x[5], z[5], zmone[5];
- u8 e[32];
-
- memcpy(e, secret, 32);
- normalize_secret(e);
-
- fexpand(bp, basepoint);
- cmult(x, z, e, bp);
- crecip(zmone, z);
- fmul(z, x, zmone);
- fcontract(mypublic, z);
-
- memzero_explicit(e, sizeof(e));
- memzero_explicit(bp, sizeof(bp));
- memzero_explicit(x, sizeof(x));
- memzero_explicit(z, sizeof(z));
- memzero_explicit(zmone, sizeof(zmone));
-
- return true;
-}
+#include "curve25519-u128.h"
#else
-typedef s64 limb;
-
-/* Field element representation:
- *
- * Field elements are written as an array of signed, 64-bit limbs, least
- * 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.
- */
-
-/* Sum two numbers: output += in */
-static void fsum(limb *output, const limb *in)
-{
- 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!).
- */
-static void fdifference(limb *output, const limb *in)
-{
- 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 int i;
-
- for (i = 0; i < 10; ++i)
- output[i] = in[i] * scalar;
-}
-
-/* Multiply two numbers: output = in2 * in
- *
- * 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.
- */
-static void fproduct(limb *output, const limb *in2, const limb *in)
-{
- output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]);
- output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) +
- ((limb) ((s32) in2[1])) * ((s32) in[0]);
- output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) +
- ((limb) ((s32) in2[0])) * ((s32) in[2]) +
- ((limb) ((s32) in2[2])) * ((s32) in[0]);
- output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) +
- ((limb) ((s32) in2[2])) * ((s32) in[1]) +
- ((limb) ((s32) in2[0])) * ((s32) in[3]) +
- ((limb) ((s32) in2[3])) * ((s32) in[0]);
- output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) +
- 2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) +
- ((limb) ((s32) in2[3])) * ((s32) in[1])) +
- ((limb) ((s32) in2[0])) * ((s32) in[4]) +
- ((limb) ((s32) in2[4])) * ((s32) in[0]);
- output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) +
- ((limb) ((s32) in2[3])) * ((s32) in[2]) +
- ((limb) ((s32) in2[1])) * ((s32) in[4]) +
- ((limb) ((s32) in2[4])) * ((s32) in[1]) +
- ((limb) ((s32) in2[0])) * ((s32) in[5]) +
- ((limb) ((s32) in2[5])) * ((s32) in[0]);
- output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) +
- ((limb) ((s32) in2[1])) * ((s32) in[5]) +
- ((limb) ((s32) in2[5])) * ((s32) in[1])) +
- ((limb) ((s32) in2[2])) * ((s32) in[4]) +
- ((limb) ((s32) in2[4])) * ((s32) in[2]) +
- ((limb) ((s32) in2[0])) * ((s32) in[6]) +
- ((limb) ((s32) in2[6])) * ((s32) in[0]);
- output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) +
- ((limb) ((s32) in2[4])) * ((s32) in[3]) +
- ((limb) ((s32) in2[2])) * ((s32) in[5]) +
- ((limb) ((s32) in2[5])) * ((s32) in[2]) +
- ((limb) ((s32) in2[1])) * ((s32) in[6]) +
- ((limb) ((s32) in2[6])) * ((s32) in[1]) +
- ((limb) ((s32) in2[0])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[0]);
- output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) +
- 2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) +
- ((limb) ((s32) in2[5])) * ((s32) in[3]) +
- ((limb) ((s32) in2[1])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[1])) +
- ((limb) ((s32) in2[2])) * ((s32) in[6]) +
- ((limb) ((s32) in2[6])) * ((s32) in[2]) +
- ((limb) ((s32) in2[0])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[0]);
- output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) +
- ((limb) ((s32) in2[5])) * ((s32) in[4]) +
- ((limb) ((s32) in2[3])) * ((s32) in[6]) +
- ((limb) ((s32) in2[6])) * ((s32) in[3]) +
- ((limb) ((s32) in2[2])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[2]) +
- ((limb) ((s32) in2[1])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[1]) +
- ((limb) ((s32) in2[0])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[0]);
- output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) +
- ((limb) ((s32) in2[3])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[3]) +
- ((limb) ((s32) in2[1])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[1])) +
- ((limb) ((s32) in2[4])) * ((s32) in[6]) +
- ((limb) ((s32) in2[6])) * ((s32) in[4]) +
- ((limb) ((s32) in2[2])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[2]);
- output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) +
- ((limb) ((s32) in2[6])) * ((s32) in[5]) +
- ((limb) ((s32) in2[4])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[4]) +
- ((limb) ((s32) in2[3])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[3]) +
- ((limb) ((s32) in2[2])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[2]);
- output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) +
- 2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[5]) +
- ((limb) ((s32) in2[3])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[3])) +
- ((limb) ((s32) in2[4])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[4]);
- output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) +
- ((limb) ((s32) in2[7])) * ((s32) in[6]) +
- ((limb) ((s32) in2[5])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[5]) +
- ((limb) ((s32) in2[4])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[4]);
- output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) +
- ((limb) ((s32) in2[5])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[5])) +
- ((limb) ((s32) in2[6])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[6]);
- output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) +
- ((limb) ((s32) in2[8])) * ((s32) in[7]) +
- ((limb) ((s32) in2[6])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[6]);
- output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) +
- 2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[7]));
- output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) +
- ((limb) ((s32) in2[9])) * ((s32) in[8]);
- output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]);
-}
-
-/* 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
- */
-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.
- */
- output[8] += output[18] << 4;
- output[8] += output[18] << 1;
- output[8] += output[18];
- output[7] += output[17] << 4;
- output[7] += output[17] << 1;
- output[7] += output[17];
- output[6] += output[16] << 4;
- output[6] += output[16] << 1;
- output[6] += output[16];
- output[5] += output[15] << 4;
- output[5] += output[15] << 1;
- output[5] += output[15];
- output[4] += output[14] << 4;
- output[4] += output[14] << 1;
- output[4] += output[14];
- output[3] += output[13] << 4;
- output[3] += output[13] << 1;
- output[3] += output[13];
- output[2] += output[12] << 4;
- output[2] += output[12] << 1;
- output[2] += output[12];
- output[1] += output[11] << 4;
- output[1] += output[11] << 1;
- output[1] += output[11];
- output[0] += output[10] << 4;
- output[0] += output[10] << 1;
- output[0] += output[10];
-}
-
-#if (-1 & 3) != 3
-#error "This code only works on a two's complement system"
-#endif
-
-/* return v / 2^26, using only shifts and adds.
- *
- * On entry: v can take any value.
- */
-static inline limb div_by_2_26(const limb v)
-{
- /* High word of v; no shift needed. */
- const u32 highword = (u32) (((u64) v) >> 32);
- /* Set to all 1s if v was negative; else set to 0s. */
- const s32 sign = ((s32) highword) >> 31;
- /* Set to 0x3ffffff if v was negative; else set to 0. */
- const s32 roundoff = ((u32) sign) >> 6;
- /* Should return v / (1<<26) */
- return (v + roundoff) >> 26;
-}
-
-/* return v / (2^25), using only shifts and adds.
- *
- * On entry: v can take any value.
- */
-static inline limb div_by_2_25(const limb v)
-{
- /* High word of v; no shift needed*/
- const u32 highword = (u32) (((u64) v) >> 32);
- /* Set to all 1s if v was negative; else set to 0s. */
- const s32 sign = ((s32) highword) >> 31;
- /* Set to 0x1ffffff if v was negative; else set to 0. */
- const s32 roundoff = ((u32) sign) >> 7;
- /* Should return v / (1<<25) */
- return (v + roundoff) >> 25;
-}
-
-/* Reduce all coefficients of the short form input so that |x| < 2^26.
- *
- * On entry: |output[i]| < 280*2^54
- */
-static void freduce_coefficients(limb *output)
-{
- unsigned int i;
-
- output[10] = 0;
-
- for (i = 0; i < 10; i += 2) {
- limb over = div_by_2_26(output[i]);
- /* 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.
- */
- output[i] -= over << 26;
- output[i+1] += over;
-
- /* For the first iteration, |output[i+1]| < 281*2^54, thus |over| <
- * 281*2^29. When this is added to the next limb, the resulting bound can
- * be approximated as 281*2^54.
- *
- * For subsequent iterations of the loop, 281*2^54 remains a conservative
- * bound and no overflow occurs.
- */
- over = div_by_2_25(output[i+1]);
- output[i+1] -= over << 25;
- output[i+2] += over;
- }
- /* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */
- output[0] += output[10] << 4;
- output[0] += output[10] << 1;
- output[0] += output[10];
-
- 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.
- */
- {
- 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.
- */
-}
-
-/* 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.
- */
-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);
- freduce_coefficients(t);
- /* |t[i]| < 2^26 */
- memcpy(output, t, sizeof(limb) * 10);
-}
-
-/* Square a number: output = in**2
- *
- * 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.
- */
-static void fsquare_inner(limb *output, const limb *in)
-{
- output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]);
- output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]);
- output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) +
- ((limb) ((s32) in[0])) * ((s32) in[2]));
- output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) +
- ((limb) ((s32) in[0])) * ((s32) in[3]));
- output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) +
- 4 * ((limb) ((s32) in[1])) * ((s32) in[3]) +
- 2 * ((limb) ((s32) in[0])) * ((s32) in[4]);
- output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) +
- ((limb) ((s32) in[1])) * ((s32) in[4]) +
- ((limb) ((s32) in[0])) * ((s32) in[5]));
- output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) +
- ((limb) ((s32) in[2])) * ((s32) in[4]) +
- ((limb) ((s32) in[0])) * ((s32) in[6]) +
- 2 * ((limb) ((s32) in[1])) * ((s32) in[5]));
- output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) +
- ((limb) ((s32) in[2])) * ((s32) in[5]) +
- ((limb) ((s32) in[1])) * ((s32) in[6]) +
- ((limb) ((s32) in[0])) * ((s32) in[7]));
- output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) +
- 2 * (((limb) ((s32) in[2])) * ((s32) in[6]) +
- ((limb) ((s32) in[0])) * ((s32) in[8]) +
- 2 * (((limb) ((s32) in[1])) * ((s32) in[7]) +
- ((limb) ((s32) in[3])) * ((s32) in[5])));
- output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) +
- ((limb) ((s32) in[3])) * ((s32) in[6]) +
- ((limb) ((s32) in[2])) * ((s32) in[7]) +
- ((limb) ((s32) in[1])) * ((s32) in[8]) +
- ((limb) ((s32) in[0])) * ((s32) in[9]));
- output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) +
- ((limb) ((s32) in[4])) * ((s32) in[6]) +
- ((limb) ((s32) in[2])) * ((s32) in[8]) +
- 2 * (((limb) ((s32) in[3])) * ((s32) in[7]) +
- ((limb) ((s32) in[1])) * ((s32) in[9])));
- output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) +
- ((limb) ((s32) in[4])) * ((s32) in[7]) +
- ((limb) ((s32) in[3])) * ((s32) in[8]) +
- ((limb) ((s32) in[2])) * ((s32) in[9]));
- output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) +
- 2 * (((limb) ((s32) in[4])) * ((s32) in[8]) +
- 2 * (((limb) ((s32) in[5])) * ((s32) in[7]) +
- ((limb) ((s32) in[3])) * ((s32) in[9])));
- output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) +
- ((limb) ((s32) in[5])) * ((s32) in[8]) +
- ((limb) ((s32) in[4])) * ((s32) in[9]));
- output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) +
- ((limb) ((s32) in[6])) * ((s32) in[8]) +
- 2 * ((limb) ((s32) in[5])) * ((s32) in[9]));
- output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) +
- ((limb) ((s32) in[6])) * ((s32) in[9]));
- output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) +
- 4 * ((limb) ((s32) in[7])) * ((s32) in[9]);
- output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]);
- output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]);
-}
-
-/* fsquare sets output = in^2.
- *
- * On entry: The |in| argument is in reduced coefficients form and |in[i]| <
- * 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.
- */
-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.
- */
- freduce_degree(t);
- freduce_coefficients(t);
- /* |t[i]| < 2^26 */
- memcpy(output, t, sizeof(limb) * 10);
-}
-
-/* Take a little-endian, 32-byte number and expand it into polynomial form */
-static inline void fexpand(limb *output, const u8 *input)
-{
-#define F(n, start, shift, mask) \
- output[n] = ((((limb) input[start + 0]) | \
- ((limb) input[start + 1]) << 8 | \
- ((limb) input[start + 2]) << 16 | \
- ((limb) input[start + 3]) << 24) >> shift) & mask;
- F(0, 0, 0, 0x3ffffff);
- F(1, 3, 2, 0x1ffffff);
- F(2, 6, 3, 0x3ffffff);
- F(3, 9, 5, 0x1ffffff);
- F(4, 12, 6, 0x3ffffff);
- F(5, 16, 0, 0x1ffffff);
- F(6, 19, 1, 0x3ffffff);
- F(7, 22, 3, 0x1ffffff);
- F(8, 25, 4, 0x3ffffff);
- F(9, 28, 6, 0x1ffffff);
-#undef F
-}
-
-#if (-32 >> 1) != -16
-#error "This code only works when >> does sign-extension on negative numbers"
-#endif
-
-/* s32_eq returns 0xffffffff iff a == b and zero otherwise. */
-static s32 s32_eq(s32 a, s32 b)
-{
- a = ~(a ^ b);
- a &= a << 16;
- a &= a << 8;
- a &= a << 4;
- a &= a << 2;
- a &= a << 1;
- return a >> 31;
-}
-
-/* s32_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are
- * both non-negative.
- */
-static s32 s32_gte(s32 a, s32 b)
-{
- a -= b;
- /* a >= 0 iff a >= b. */
- return ~(a >> 31);
-}
-
-/* Take a fully reduced polynomial form number and contract it into a
- * little-endian, 32-byte array.
- *
- * On entry: |input_limbs[i]| < 2^26
- */
-static void fcontract(u8 *output, limb *input_limbs)
-{
- int i;
- int j;
- s32 input[10];
- s32 mask;
-
- /* |input_limbs[i]| < 2^26, so it's valid to convert to an s32. */
- for (i = 0; i < 10; i++) {
- input[i] = input_limbs[i];
- }
-
- for (j = 0; j < 2; ++j) {
- 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.
- */
- const s32 mask = input[i] >> 31;
- const s32 carry = -((input[i] & mask) >> 25);
-
- input[i] = input[i] + (carry << 25);
- input[i+1] = input[i+1] - carry;
- } else {
- const s32 mask = input[i] >> 31;
- const s32 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.
- */
- {
- const s32 mask = input[9] >> 31;
- const s32 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.
- */
- }
-
- /* The first borrow-propagation pass above ended with every limb
- except (possibly) input[0] non-negative.
- If input[0] was negative after the first pass, then it was because of a
- carry from input[9]. On entry, input[9] < 2^26 so the carry was, at most,
- one, since (2**26-1) >> 25 = 1. Thus input[0] >= -19.
- In the second pass, each limb is decreased by at most one. Thus the second
- borrow-propagation pass could only have wrapped around to decrease
- input[0] again if the first pass left input[0] negative *and* input[1]
- through input[9] were all zero. In that case, input[1] is now 2^25 - 1,
- and this last borrow-propagation step will leave input[1] non-negative. */
- {
- const s32 mask = input[0] >> 31;
- const s32 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.
- */
- for (j = 0; j < 2; j++) {
- for (i = 0; i < 9; i++) {
- if ((i & 1) == 1) {
- const s32 carry = input[i] >> 25;
-
- input[i] &= 0x1ffffff;
- input[i+1] += carry;
- } else {
- const s32 carry = input[i] >> 26;
-
- input[i] &= 0x3ffffff;
- input[i+1] += carry;
- }
- }
-
- {
- const s32 carry = input[9] >> 25;
-
- input[9] &= 0x1ffffff;
- input[0] += 19*carry;
- }
- }
-
- /* If the first carry-chain pass, just above, ended up with a carry from
- * input[9], and that caused input[0] to be out-of-bounds, then input[0] was
- * < 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.
- */
-
- /* 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.
- */
- mask = s32_gte(input[0], 0x3ffffed);
- for (i = 1; i < 10; i++) {
- if ((i & 1) == 1) {
- mask &= s32_eq(input[i], 0x1ffffff);
- } else {
- mask &= s32_eq(input[i], 0x3ffffff);
- }
- }
-
- /* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus
- * this conditionally subtracts 2^255-19.
- */
- input[0] -= mask & 0x3ffffed;
-
- for (i = 1; i < 10; i++) {
- if ((i & 1) == 1) {
- input[i] -= mask & 0x1ffffff;
- } else {
- input[i] -= mask & 0x3ffffff;
- }
- }
-
- input[1] <<= 2;
- input[2] <<= 3;
- input[3] <<= 5;
- input[4] <<= 6;
- input[6] <<= 1;
- input[7] <<= 3;
- input[8] <<= 4;
- input[9] <<= 6;
-#define F(i, s) \
- output[s+0] |= input[i] & 0xff; \
- output[s+1] = (input[i] >> 8) & 0xff; \
- output[s+2] = (input[i] >> 16) & 0xff; \
- 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);
-#undef F
-}
-
-/* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave
- * them unchanged if 'iswap' is 0. Runs in data-invariant time to avoid
- * side-channel attacks.
- *
- * NOTE that this function requires that 'iswap' be 1 or 0; other values give
- * 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.
- */
-static void swap_conditional(limb a[19], limb b[19], limb iswap)
-{
- unsigned int i;
- const s32 swap = (s32) -iswap;
-
- for (i = 0; i < 10; ++i) {
- const s32 x = swap & (((s32)a[i]) ^ ((s32)b[i]));
-
- a[i] = ((s32)a[i]) ^ x;
- b[i] = ((s32)b[i]) ^ x;
- }
-}
-
-static void crecip(limb *out, const limb *z)
-{
- limb z2[10];
- limb z9[10];
- limb z11[10];
- limb z2_5_0[10];
- limb z2_10_0[10];
- limb z2_20_0[10];
- limb z2_50_0[10];
- limb z2_100_0[10];
- limb t0[10];
- 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);
-}
-
-
-#ifdef ARCH_HAS_SEPARATE_IRQ_STACK
-/* Input: Q, Q', Q-Q'
- * Output: 2Q, Q+Q'
- *
- * x2 z3: long form
- * x3 z3: long form
- * x z: short form, destroyed
- * xprime zprime: short form, destroyed
- * qmqp: short form, preserved
- *
- * On entry and exit, the absolute value of the limbs of all inputs and outputs
- * 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],
- zzprime[19], zzzprime[19], xxxprime[19];
-
- memcpy(origx, x, 10 * sizeof(limb));
- fsum(x, z);
- /* |x[i]| < 2^27 */
- fdifference(z, origx); /* does x - z */
- /* |z[i]| < 2^27 */
-
- memcpy(origxprime, xprime, sizeof(limb) * 10);
- fsum(xprime, zprime);
- /* |xprime[i]| < 2^27 */
- fdifference(zprime, origxprime);
- /* |zprime[i]| < 2^27 */
- 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.)
- */
- fproduct(zzprime, x, zprime);
- /* |zzprime[i]| < 14*2^54 */
- freduce_degree(xxprime);
- freduce_coefficients(xxprime);
- /* |xxprime[i]| < 2^26 */
- freduce_degree(zzprime);
- freduce_coefficients(zzprime);
- /* |zzprime[i]| < 2^26 */
- memcpy(origxprime, xxprime, sizeof(limb) * 10);
- fsum(xxprime, zzprime);
- /* |xxprime[i]| < 2^27 */
- fdifference(zzprime, origxprime);
- /* |zzprime[i]| < 2^27 */
- fsquare(xxxprime, xxprime);
- /* |xxxprime[i]| < 2^26 */
- fsquare(zzzprime, zzprime);
- /* |zzzprime[i]| < 2^26 */
- fproduct(zzprime, zzzprime, qmqp);
- /* |zzprime[i]| < 14*2^52 */
- freduce_degree(zzprime);
- freduce_coefficients(zzprime);
- /* |zzprime[i]| < 2^26 */
- memcpy(x3, xxxprime, sizeof(limb) * 10);
- memcpy(z3, zzprime, sizeof(limb) * 10);
-
- fsquare(xx, x);
- /* |xx[i]| < 2^26 */
- fsquare(zz, z);
- /* |zz[i]| < 2^26 */
- fproduct(x2, xx, zz);
- /* |x2[i]| < 14*2^52 */
- freduce_degree(x2);
- freduce_coefficients(x2);
- /* |x2[i]| < 2^26 */
- fdifference(zz, xx); // does zz = xx - zz
- /* |zz[i]| < 2^27 */
- memset(zzz + 10, 0, sizeof(limb) * 9);
- fscalar_product(zzz, zz, 121665);
- /* |zzz[i]| < 2^(27+17) */
- /* No need to call freduce_degree here:
- fscalar_product doesn't increase the degree of its input. */
- freduce_coefficients(zzz);
- /* |zzz[i]| < 2^26 */
- fsum(zzz, xx);
- /* |zzz[i]| < 2^27 */
- fproduct(z2, zz, zzz);
- /* |z2[i]| < 14*2^(26+27) */
- freduce_degree(z2);
- freduce_coefficients(z2);
- /* |z2|i| < 2^26 */
-}
-
-/* Calculates nQ where Q is the x-coordinate of a point on the curve
- *
- * 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)
- */
-static void cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q)
-{
- limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};
- limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
- limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};
- limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
-
- unsigned int i, j;
-
- memcpy(nqpqx, q, sizeof(limb) * 10);
-
- for (i = 0; i < 32; ++i) {
- u8 byte = n[31 - i];
-
- for (j = 0; j < 8; ++j) {
- const limb bit = byte >> 7;
-
- swap_conditional(nqx, nqpqx, bit);
- swap_conditional(nqz, nqpqz, bit);
- fmonty(nqx2, nqz2,
- nqpqx2, nqpqz2,
- nqx, nqz,
- nqpqx, nqpqz,
- q);
- swap_conditional(nqx2, nqpqx2, bit);
- swap_conditional(nqz2, nqpqz2, bit);
-
- t = nqx;
- nqx = nqx2;
- nqx2 = t;
- t = nqz;
- nqz = nqz2;
- nqz2 = t;
- t = nqpqx;
- nqpqx = nqpqx2;
- nqpqx2 = t;
- t = nqpqz;
- nqpqz = nqpqz2;
- nqpqz2 = t;
-
- byte <<= 1;
- }
- }
-
- memcpy(resultx, nqx, sizeof(limb) * 10);
- memcpy(resultz, nqz, sizeof(limb) * 10);
-}
-
-static bool curve25519_donna(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE])
-{
- limb bp[10], x[10], z[11], zmone[10];
- u8 e[32];
-
- memcpy(e, secret, 32);
- normalize_secret(e);
-
- fexpand(bp, basepoint);
- cmult(x, z, e, bp);
- crecip(zmone, z);
- fmul(z, x, zmone);
- fcontract(mypublic, z);
-
- memzero_explicit(e, sizeof(e));
- memzero_explicit(bp, sizeof(bp));
- memzero_explicit(x, sizeof(x));
- memzero_explicit(z, sizeof(z));
- memzero_explicit(zmone, sizeof(zmone));
-
- return true;
-}
-#else
-struct other_stack {
- limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19], zzprime[19], zzzprime[19], xxxprime[19];
- limb a[19], b[19], c[19], d[19], e[19], f[19], g[19], h[19];
- limb bp[10], x[10], z[11], zmone[10];
- u8 ee[32];
-};
-
-/* Input: Q, Q', Q-Q'
- * Output: 2Q, Q+Q'
- *
- * x2 z3: long form
- * x3 z3: long form
- * x z: short form, destroyed
- * xprime zprime: short form, destroyed
- * qmqp: short form, preserved
- *
- * On entry and exit, the absolute value of the limbs of all inputs and outputs
- * are < 2^26.
- */
-static void fmonty(struct other_stack *s,
- 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' */)
-{
- memcpy(s->origx, x, 10 * sizeof(limb));
- fsum(x, z);
- /* |x[i]| < 2^27 */
- fdifference(z, s->origx); /* does x - z */
- /* |z[i]| < 2^27 */
-
- memcpy(s->origxprime, xprime, sizeof(limb) * 10);
- fsum(xprime, zprime);
- /* |xprime[i]| < 2^27 */
- fdifference(zprime, s->origxprime);
- /* |zprime[i]| < 2^27 */
- fproduct(s->xxprime, xprime, z);
- /* |s->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.)
- */
- fproduct(s->zzprime, x, zprime);
- /* |s->zzprime[i]| < 14*2^54 */
- freduce_degree(s->xxprime);
- freduce_coefficients(s->xxprime);
- /* |s->xxprime[i]| < 2^26 */
- freduce_degree(s->zzprime);
- freduce_coefficients(s->zzprime);
- /* |s->zzprime[i]| < 2^26 */
- memcpy(s->origxprime, s->xxprime, sizeof(limb) * 10);
- fsum(s->xxprime, s->zzprime);
- /* |s->xxprime[i]| < 2^27 */
- fdifference(s->zzprime, s->origxprime);
- /* |s->zzprime[i]| < 2^27 */
- fsquare(s->xxxprime, s->xxprime);
- /* |s->xxxprime[i]| < 2^26 */
- fsquare(s->zzzprime, s->zzprime);
- /* |s->zzzprime[i]| < 2^26 */
- fproduct(s->zzprime, s->zzzprime, qmqp);
- /* |s->zzprime[i]| < 14*2^52 */
- freduce_degree(s->zzprime);
- freduce_coefficients(s->zzprime);
- /* |s->zzprime[i]| < 2^26 */
- memcpy(x3, s->xxxprime, sizeof(limb) * 10);
- memcpy(z3, s->zzprime, sizeof(limb) * 10);
-
- fsquare(s->xx, x);
- /* |s->xx[i]| < 2^26 */
- fsquare(s->zz, z);
- /* |s->zz[i]| < 2^26 */
- fproduct(x2, s->xx, s->zz);
- /* |x2[i]| < 14*2^52 */
- freduce_degree(x2);
- freduce_coefficients(x2);
- /* |x2[i]| < 2^26 */
- fdifference(s->zz, s->xx); // does s->zz = s->xx - s->zz
- /* |s->zz[i]| < 2^27 */
- memset(s->zzz + 10, 0, sizeof(limb) * 9);
- fscalar_product(s->zzz, s->zz, 121665);
- /* |s->zzz[i]| < 2^(27+17) */
- /* No need to call freduce_degree here:
- fscalar_product doesn't increase the degree of its input. */
- freduce_coefficients(s->zzz);
- /* |s->zzz[i]| < 2^26 */
- fsum(s->zzz, s->xx);
- /* |s->zzz[i]| < 2^27 */
- fproduct(z2, s->zz, s->zzz);
- /* |z2[i]| < 14*2^(26+27) */
- freduce_degree(z2);
- freduce_coefficients(z2);
- /* |z2|i| < 2^26 */
-}
-
-/* Calculates nQ where Q is the x-coordinate of a point on the curve
- *
- * 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)
- */
-static void cmult(struct other_stack *s, limb *resultx, limb *resultz, const u8 *n, const limb *q)
-{
- unsigned int i, j;
- limb *nqpqx = s->a, *nqpqz = s->b, *nqx = s->c, *nqz = s->d, *t;
- limb *nqpqx2 = s->e, *nqpqz2 = s->f, *nqx2 = s->g, *nqz2 = s->h;
-
- *nqpqz = *nqx = *nqpqz2 = *nqz2 = 1;
- memcpy(nqpqx, q, sizeof(limb) * 10);
-
- for (i = 0; i < 32; ++i) {
- u8 byte = n[31 - i];
-
- for (j = 0; j < 8; ++j) {
- const limb bit = byte >> 7;
-
- swap_conditional(nqx, nqpqx, bit);
- swap_conditional(nqz, nqpqz, bit);
- fmonty(s,
- nqx2, nqz2,
- nqpqx2, nqpqz2,
- nqx, nqz,
- nqpqx, nqpqz,
- q);
- swap_conditional(nqx2, nqpqx2, bit);
- swap_conditional(nqz2, nqpqz2, bit);
-
- t = nqx;
- nqx = nqx2;
- nqx2 = t;
- t = nqz;
- nqz = nqz2;
- nqz2 = t;
- t = nqpqx;
- nqpqx = nqpqx2;
- nqpqx2 = t;
- t = nqpqz;
- nqpqz = nqpqz2;
- nqpqz2 = t;
-
- byte <<= 1;
- }
- }
-
- memcpy(resultx, nqx, sizeof(limb) * 10);
- memcpy(resultz, nqz, sizeof(limb) * 10);
-}
-
-static bool curve25519_donna(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE])
-{
- struct other_stack *s = kzalloc(sizeof(struct other_stack), GFP_KERNEL);
-
- if (unlikely(!s))
- return false;
-
- memcpy(s->ee, secret, 32);
- normalize_secret(s->ee);
-
- fexpand(s->bp, basepoint);
- cmult(s, s->x, s->z, s->ee, s->bp);
- crecip(s->zmone, s->z);
- fmul(s->z, s->x, s->zmone);
- fcontract(mypublic, s->z);
-
- kzfree(s);
- return true;
-}
-#endif
+#include "curve25519-generic.h"
#endif
static const u8 null_point[CURVE25519_POINT_SIZE] = { 0 };
@@ -1642,6 +36,7 @@ static const u8 null_point[CURVE25519_POINT_SIZE] = { 0 };
bool curve25519(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE])
{
bool ret = true;
+
#if defined(CONFIG_X86_64) && defined(CONFIG_AS_AVX)
if (curve25519_use_avx && irq_fpu_usable()) {
kernel_fpu_begin();