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-rw-r--r--src/CMakeLists.txt7
-rw-r--r--src/ec25519.c456
2 files changed, 463 insertions, 0 deletions
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
new file mode 100644
index 0000000..1bad208
--- /dev/null
+++ b/src/CMakeLists.txt
@@ -0,0 +1,7 @@
+include_directories(${LIBUECC_SOURCE_DIR}/include)
+
+add_library(uecc STATIC ec25519.c)
+
+install(TARGETS uecc
+ ARCHIVE DESTINATION lib
+)
diff --git a/src/ec25519.c b/src/ec25519.c
new file mode 100644
index 0000000..24c40f8
--- /dev/null
+++ b/src/ec25519.c
@@ -0,0 +1,456 @@
+/*
+ Copyright (c) 2012, Matthias Schiffer <mschiffer@universe-factory.net>
+ Partly based on public domain code by Matthew Dempsky and D. J. Bernstein.
+ All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions are met:
+
+ 1. Redistributions of source code must retain the above copyright notice,
+ this list of conditions and the following disclaimer.
+ 2. Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+ FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+ SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+ CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+ OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+
+/*
+ EC group operations for Twisted Edwards Curve ax^2 + y^2 + 1 + dx^2y^2 with
+ a = 486664
+ d = 486660
+ on prime field p = 2^255 - 19.
+
+ The curve is equivalent to the Montgomery Curve used in D. J. Bernstein's
+ Curve25519 Diffie-Hellman algorithm
+
+ See http://hyperelliptic.org/EFD/g1p/auto-twisted-inverted.html for add and
+ double operations
+*/
+
+#include <libuecc/ecc.h>
+
+
+static void add(unsigned int out[32], const unsigned int a[32], const unsigned int b[32]) {
+ unsigned int j;
+ unsigned int u;
+ u = 0;
+ for (j = 0;j < 31;++j) { u += a[j] + b[j]; out[j] = u & 255; u >>= 8; }
+ u += a[31] + b[31]; out[31] = u;
+}
+
+static void sub(unsigned int out[32], const unsigned int a[32], const unsigned int b[32]) {
+ unsigned int j;
+ unsigned int u;
+ u = 218;
+ for (j = 0;j < 31;++j) {
+ u += a[j] + 65280 - b[j];
+ out[j] = u & 255;
+ u >>= 8;
+ }
+ u += a[31] - b[31];
+ out[31] = u;
+}
+
+static void squeeze(unsigned int a[32]) {
+ unsigned int j;
+ unsigned int u;
+ u = 0;
+ for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
+ u += a[31]; a[31] = u & 127;
+ u = 19 * (u >> 7);
+ for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
+ u += a[31]; a[31] = u;
+}
+
+static const unsigned int minusp[32] = {
+ 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128
+} ;
+
+static void freeze(unsigned int a[32]) {
+ unsigned int aorig[32];
+ unsigned int j;
+ unsigned int negative;
+
+ for (j = 0; j < 32; j++) aorig[j] = a[j];
+ add(a, a, minusp);
+ negative = -((a[31] >> 7) & 1);
+ for (j = 0; j < 32; j++) a[j] ^= negative & (aorig[j] ^ a[j]);
+}
+
+static void mult(unsigned int out[32], const unsigned int a[32], const unsigned int b[32]) {
+ unsigned int i;
+ unsigned int j;
+ unsigned int u;
+
+ for (i = 0; i < 32; ++i) {
+ u = 0;
+ for (j = 0;j <= i;++j) u += a[j] * b[i - j];
+ for (j = i + 1;j < 32;++j) u += 38 * a[j] * b[i + 32 - j];
+ out[i] = u;
+ }
+ squeeze(out);
+}
+
+static void mult_int(unsigned int out[32], const unsigned int n, const unsigned int a[32]) {
+ unsigned int j;
+ unsigned int u;
+
+ u = 0;
+ for (j = 0;j < 31;++j) { u += n * a[j]; out[j] = u & 255; u >>= 8; }
+ u += n * a[31]; out[31] = u & 127;
+ u = 19 * (u >> 7);
+ for (j = 0;j < 31;++j) { u += out[j]; out[j] = u & 255; u >>= 8; }
+ u += out[j]; out[j] = u;
+}
+
+static void square(unsigned int out[32], const unsigned int a[32]) {
+ unsigned int i;
+ unsigned int j;
+ unsigned int u;
+
+ for (i = 0; i < 32; ++i) {
+ u = 0;
+ for (j = 0;j < i - j;++j) u += a[j] * a[i - j];
+ for (j = i + 1;j < i + 32 - j;++j) u += 38 * a[j] * a[i + 32 - j];
+ u *= 2;
+ if ((i & 1) == 0) {
+ u += a[i / 2] * a[i / 2];
+ u += 38 * a[i / 2 + 16] * a[i / 2 + 16];
+ }
+ out[i] = u;
+ }
+ squeeze(out);
+}
+
+static int check_zero(const unsigned int x[32]) {
+ unsigned int differentbits = 0;
+ int i;
+
+ for (i = 0; i < 32; i++) {
+ differentbits |= (x[i] & 0xffff);
+ differentbits |= (x[i] >> 16);
+ }
+
+ return (1-(1 & ((differentbits - 1) >> 16)));
+}
+
+static int check_equal(const unsigned int x[32], const unsigned int y[32]) {
+ unsigned int differentbits = 0;
+ int i;
+
+ for (i = 0; i < 32; i++) {
+ differentbits |= ((x[i] ^ y[i]) & 0xffff);
+ differentbits |= ((x[i] ^ y[i]) >> 16);
+ }
+
+ return (1-(1 & ((differentbits - 1) >> 16)));
+}
+
+static void selectw(ec_25519_work *out, const ec_25519_work *r, const ec_25519_work *s, unsigned int b) {
+ unsigned int j;
+ unsigned int t;
+ unsigned int bminus1;
+
+ bminus1 = b - 1;
+ for (j = 0;j < 32;++j) {
+ t = bminus1 & (r->X[j] ^ s->X[j]);
+ out->X[j] = s->X[j] ^ t;
+
+ t = bminus1 & (r->Y[j] ^ s->Y[j]);
+ out->Y[j] = s->Y[j] ^ t;
+
+ t = bminus1 & (r->Z[j] ^ s->Z[j]);
+ out->Z[j] = s->Z[j] ^ t;
+ }
+}
+
+static void select(unsigned int out[32], const unsigned int r[32], const unsigned int s[32], unsigned int b) {
+ unsigned int j;
+ unsigned int t;
+ unsigned int bminus1;
+
+ bminus1 = b - 1;
+ for (j = 0;j < 32;++j) {
+ t = bminus1 & (r[j] ^ s[j]);
+ out[j] = s[j] ^ t;
+ }
+}
+
+static const unsigned int rho_s[32] = {
+ 0xb0, 0xa0, 0x0e, 0x4a, 0x27, 0x1b, 0xee, 0xc4,
+ 0x78, 0xe4, 0x2f, 0xad, 0x06, 0x18, 0x43, 0x2f,
+ 0xa7, 0xd7, 0xfb, 0x3d, 0x99, 0x00, 0x4d, 0x2b,
+ 0x0b, 0xdf, 0xc1, 0x4f, 0x80, 0x24, 0x83, 0x2b
+};
+
+static const unsigned int zero[32] = {0};
+static const unsigned int minus1[32] = {
+ 0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f
+};
+
+static void square_root(unsigned int out[32], const unsigned int z[32]) {
+ /* raise z to the (2^252-2)th power */
+
+ unsigned int z2[32];
+ unsigned int z9[32];
+ unsigned int z11[32];
+ unsigned int z2_5_0[32];
+ unsigned int z2_10_0[32];
+ unsigned int z2_20_0[32];
+ unsigned int z2_50_0[32];
+ unsigned int z2_100_0[32];
+ unsigned int t0[32];
+ unsigned int t1[32];
+ unsigned int rt_sq[32];
+ int i;
+
+ /* 2 */ square(z2, z);
+ /* 4 */ square(t1, z2);
+ /* 8 */ square(t0, t1);
+ /* 9 */ mult(z9, t0, z);
+ /* 11 */ mult(z11, z9, z2);
+ /* 22 */ square(t0, z11);
+ /* 2^5 - 2^0 = 31 */ mult(z2_5_0, t0, z9);
+
+ /* 2^6 - 2^1 */ square(t0, z2_5_0);
+ /* 2^7 - 2^2 */ square(t1, t0);
+ /* 2^8 - 2^3 */ square(t0, t1);
+ /* 2^9 - 2^4 */ square(t1, t0);
+ /* 2^10 - 2^5 */ square(t0, t1);
+ /* 2^10 - 2^0 */ mult(z2_10_0, t0, z2_5_0);
+
+ /* 2^11 - 2^1 */ square(t0, z2_10_0);
+ /* 2^12 - 2^2 */ square(t1, t0);
+ /* 2^20 - 2^10 */ for (i = 2; i < 10; i += 2) { square(t0, t1); square(t1, t0); }
+ /* 2^20 - 2^0 */ mult(z2_20_0, t1, z2_10_0);
+
+ /* 2^21 - 2^1 */ square(t0, z2_20_0);
+ /* 2^22 - 2^2 */ square(t1, t0);
+ /* 2^40 - 2^20 */ for (i = 2; i < 20; i += 2) { square(t0, t1); square(t1, t0); }
+ /* 2^40 - 2^0 */ mult(t0, t1, z2_20_0);
+
+ /* 2^41 - 2^1 */ square(t1, t0);
+ /* 2^42 - 2^2 */ square(t0, t1);
+ /* 2^50 - 2^10 */ for (i = 2; i < 10; i += 2) { square(t1, t0); square(t0, t1); }
+ /* 2^50 - 2^0 */ mult(z2_50_0, t0, z2_10_0);
+
+ /* 2^51 - 2^1 */ square(t0, z2_50_0);
+ /* 2^52 - 2^2 */ square(t1, t0);
+ /* 2^100 - 2^50 */ for (i = 2; i < 50; i += 2) { square(t0, t1); square(t1, t0); }
+ /* 2^100 - 2^0 */ mult(z2_100_0, t1, z2_50_0);
+
+ /* 2^101 - 2^1 */ square(t1, z2_100_0);
+ /* 2^102 - 2^2 */ square(t0, t1);
+ /* 2^200 - 2^100 */ for (i = 2; i < 100; i += 2) { square(t1, t0); square(t0, t1); }
+ /* 2^200 - 2^0 */ mult(t1, t0, z2_100_0);
+
+ /* 2^201 - 2^1 */ square(t0, t1);
+ /* 2^202 - 2^2 */ square(t1, t0);
+ /* 2^250 - 2^50 */ for (i = 2; i < 50; i += 2) { square(t0, t1); square(t1, t0); }
+ /* 2^250 - 2^0 */ mult(t0, t1, z2_50_0);
+
+ /* 2^251 - 2^1 */ square(t1, t0);
+ /* 2^252 - 2^2 */ square(t0, t1);
+
+ /* 2^252 - 2 */ mult(t1, t0, z2);
+
+ mult(t0, t1, rho_s);
+
+ square(rt_sq, t1);
+
+ select(out, t0, t1, check_equal(rt_sq, minus1));
+}
+
+static void recip(unsigned int out[32], const unsigned int z[32]) {
+ unsigned int z2[32];
+ unsigned int z9[32];
+ unsigned int z11[32];
+ unsigned int z2_5_0[32];
+ unsigned int z2_10_0[32];
+ unsigned int z2_20_0[32];
+ unsigned int z2_50_0[32];
+ unsigned int z2_100_0[32];
+ unsigned int t0[32];
+ unsigned int t1[32];
+ int i;
+
+ /* 2 */ square(z2, z);
+ /* 4 */ square(t1, z2);
+ /* 8 */ square(t0, t1);
+ /* 9 */ mult(z9, t0, z);
+ /* 11 */ mult(z11, z9, z2);
+ /* 22 */ square(t0, z11);
+ /* 2^5 - 2^0 = 31 */ mult(z2_5_0, t0, z9);
+
+ /* 2^6 - 2^1 */ square(t0, z2_5_0);
+ /* 2^7 - 2^2 */ square(t1, t0);
+ /* 2^8 - 2^3 */ square(t0, t1);
+ /* 2^9 - 2^4 */ square(t1, t0);
+ /* 2^10 - 2^5 */ square(t0, t1);
+ /* 2^10 - 2^0 */ mult(z2_10_0, t0, z2_5_0);
+
+ /* 2^11 - 2^1 */ square(t0, z2_10_0);
+ /* 2^12 - 2^2 */ square(t1, t0);
+ /* 2^20 - 2^10 */ for (i = 2; i < 10; i += 2) { square(t0, t1); square(t1, t0); }
+ /* 2^20 - 2^0 */ mult(z2_20_0, t1, z2_10_0);
+
+ /* 2^21 - 2^1 */ square(t0, z2_20_0);
+ /* 2^22 - 2^2 */ square(t1, t0);
+ /* 2^40 - 2^20 */ for (i = 2; i < 20; i += 2) { square(t0, t1); square(t1, t0); }
+ /* 2^40 - 2^0 */ mult(t0, t1, z2_20_0);
+
+ /* 2^41 - 2^1 */ square(t1, t0);
+ /* 2^42 - 2^2 */ square(t0, t1);
+ /* 2^50 - 2^10 */ for (i = 2; i < 10; i += 2) { square(t1, t0); square(t0, t1); }
+ /* 2^50 - 2^0 */ mult(z2_50_0, t0, z2_10_0);
+
+ /* 2^51 - 2^1 */ square(t0, z2_50_0);
+ /* 2^52 - 2^2 */ square(t1, t0);
+ /* 2^100 - 2^50 */ for (i = 2; i < 50; i += 2) { square(t0, t1); square(t1, t0); }
+ /* 2^100 - 2^0 */ mult(z2_100_0, t1, z2_50_0);
+
+ /* 2^101 - 2^1 */ square(t1, z2_100_0);
+ /* 2^102 - 2^2 */ square(t0, t1);
+ /* 2^200 - 2^100 */ for (i = 2; i < 100; i += 2) { square(t1, t0); square(t0, t1); }
+ /* 2^200 - 2^0 */ mult(t1, t0, z2_100_0);
+
+ /* 2^201 - 2^1 */ square(t0, t1);
+ /* 2^202 - 2^2 */ square(t1, t0);
+ /* 2^250 - 2^50 */ for (i = 2; i < 50; i += 2) { square(t0, t1); square(t1, t0); }
+ /* 2^250 - 2^0 */ mult(t0, t1, z2_50_0);
+
+ /* 2^251 - 2^1 */ square(t1, t0);
+ /* 2^252 - 2^2 */ square(t0, t1);
+ /* 2^253 - 2^3 */ square(t1, t0);
+ /* 2^254 - 2^4 */ square(t0, t1);
+ /* 2^255 - 2^5 */ square(t1, t0);
+ /* 2^255 - 21 */ mult(out, t1, z11);
+}
+
+void inflate(ec_25519_work *out, const ec_public_key_256 *in) {
+ int i;
+ unsigned int X2[32], d_X2[32] = {0x04, 0x6d, 0x07} /* 486660 */, a_X2[32] = {0x08, 0x6d, 0x07} /* 486664 */, _1_a_X2[32], d_X2_a_X2[32], Y[32], Yt[32];
+
+ for (i = 0; i < 32; i++) {
+ out->X[i] = in->p[i];
+ out->Z[i] = (i == 0);
+ }
+
+ out->X[31] &= 0x7f;
+
+ square(X2, out->X);
+ sub(d_X2, d_X2, X2);
+ sub(a_X2, a_X2, X2);
+ recip(_1_a_X2, a_X2);
+ mult(d_X2_a_X2, d_X2, _1_a_X2);
+ square_root(Y, d_X2_a_X2);
+ sub(Yt, zero, Y);
+
+ select(out->Y, Y, Yt, in->p[31] >> 7);
+}
+
+void deflate(ec_public_key_256 *out, ec_25519_work *in) {
+ unsigned int x[32], y[32], z[32];
+ int i;
+
+ recip(z, in->Z);
+
+ mult(x, z, in->X);
+ mult(y, z, in->Y);
+
+ freeze(x);
+ freeze(y);
+
+ for (i = 0; i < 32; i++)
+ out->p[i] = x[i];
+
+ out->p[31] |= (y[0] << 7);
+}
+
+static const ec_25519_work infty = {{0}, {0}, {1}};
+
+void ec25519_double(ec_25519_work *out, const ec_25519_work *in) {
+ unsigned int A[32], B[32], C[32], D[32], E[32], U[32], t0[32], t1[32], t2[32], t3[32], t4[32], t5[32];
+
+ square(A, in->X);
+ square(B, in->Y);
+ mult_int(U, 486664, B);
+ add(C, A, U);
+ sub(D, A, U);
+ add(t0, in->X, in->Y);
+ square(t1, t0);
+ sub(t2, t1, A);
+ sub(E, t2, B);
+ mult(out->X, C, D);
+ square(t3, in->Z);
+ mult_int(t4, 973320, t3);
+ sub(t5, C, t4);
+ mult(out->Y, E, t5);
+ mult(out->Z, D, E);
+ selectw(out, &infty, out, check_zero(out->X)*check_zero(out->Y));
+}
+
+void ec25519_add(ec_25519_work *out, const ec_25519_work *in1, const ec_25519_work *in2) {
+ unsigned int A[32], B[32], C[32], D[32], E[32], H[32], I[32], t0[32], t1[32], t2[32], t3[32], t4[32], t5[32], t6[32], t7[32], t8[32];
+
+ mult(A, in1->Z, in2->Z);
+ square(t0, A);
+ mult_int(B, 486660, t0);
+ mult(C, in1->X, in2->X);
+ mult(D, in1->Y, in2->Y);
+ mult(E, C, D);
+ mult_int(t1, 486664, D);
+ sub(H, C, t1);
+ add(t2, in1->X, in1->Y);
+ add(t3, in2->X, in2->Y);
+ mult(t4, t2, t3);
+ sub(t5, t4, C);
+ sub(I, t5, D);
+ add(t6, E, B);
+ mult(out->X, t6, H);
+ sub(t7, E, B);
+ mult(out->Y, t7, I);
+ mult(t8, H, I);
+ mult(out->Z, A, t8);
+ selectw(out, in1, out, check_zero(t3));
+ selectw(out, in2, out, check_zero(t2));
+}
+
+void ec25519_scalarmult(ec_25519_work *out, const ec_secret_key_256 *n, const ec_25519_work *base) {
+ ec_25519_work Q2, Q2p, cur;
+ int i, b, pos;
+
+ for (i = 0; i < 32; i++) {
+ cur.X[i] = 0;
+ cur.Y[i] = 0;
+ cur.Z[i] = (i == 0);
+ }
+
+ for (pos = 254;pos >= 0;--pos) {
+ b = n->s[pos / 8] >> (pos & 7);
+ b &= 1;
+
+ ec25519_double(&Q2, &cur);
+ ec25519_add(&Q2p, &Q2, base);
+ selectw(&cur, &Q2, &Q2p, b);
+ }
+
+ for (i = 0; i < 32; i++) {
+ out->X[i] = cur.X[i];
+ out->Y[i] = cur.Y[i];
+ out->Z[i] = cur.Z[i];
+ }
+}
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