gmpsec: towards an mxladder implementation

1 files changed, 155 insertions, 49 deletions

diff --git a/gmpsec.c b/gmpsec.c
index 51e1fd3b9..3b536109a 100644
--- a/gmpsec.c
+++ b/gmpsec.c
@@ -4,17 +4,24 @@
 #include <gmp.h>
 
 // modulus, encoded as big-endian bytes
-static const unsigned char modulus[] = {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,0xff};
+static const unsigned char modulus[] = {0x7f,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,0xed};
+static const unsigned char a_minus_two_over_four[] = {0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0xdb,0x41};
 static const size_t modulus_bytes = sizeof(modulus);
-static const size_t modulus_limbs = (8*sizeof(modulus) + GMP_LIMB_BITS-1)/GMP_LIMB_BITS;
+#define modulus_limbs ((8*sizeof(modulus) + GMP_LIMB_BITS-1)/GMP_LIMB_BITS)
 
-static void print_limbs(mp_limb_t* fe) {
-	for (size_t i = 0; i<modulus_limbs; i++) { printf("0x%016lx ", fe[i]); } printf("\n");
+
+static void fe_print(mp_limb_t* fe) {
+	printf("0x");
+	for (size_t i = modulus_limbs-1; i > 0; --i) { printf("%016lx", fe[i]); }
+	printf("%016lx", fe[0]);
 }
 
-int main() {
+static void crypto_scalarmult(uint8_t *out, const uint8_t *point, const uint8_t *secret, size_t secretbits) {
+	// curve constants
 	mp_limb_t m[modulus_limbs+1];
+	mp_limb_t a24[modulus_limbs+1];
 	assert(mpn_set_str(m, modulus, modulus_bytes, 256) == (mp_size_t)modulus_limbs);
+	assert(mpn_set_str(a24, a_minus_two_over_four, sizeof(a_minus_two_over_four), 256) <= (mp_size_t)modulus_limbs);
 
 	// allocate scratch space for internal use by GMP.
 	// as GMP _itch are documented as functions, not macros, we use a
@@ -31,63 +38,162 @@ int main() {
 	          scratch_sz = (invscratch_sz > scratch_sz) ? invscratch_sz : scratch_sz;
 	mp_limb_t scratch[scratch_sz];
 
-	// allocate scratch space for use by the following macros.
+	// allocate scratch space for use by the field operation macros.
 	mp_limb_t _product_tmp[modulus_limbs+modulus_limbs];
 
-	#define fe_mul(out, x, y) do { \
-		mpn_sec_mul(_product_tmp, x, modulus_limbs, y, modulus_limbs, scratch); \
-		mpn_sec_div_r(_product_tmp, modulus_limbs+modulus_limbs, m, modulus_limbs, scratch); \
-		for (size_t i = 0; i<modulus_limbs; i++) { out[i] = _product_tmp[i]; } \
-	} while (0)
+  mp_limb_t a[modulus_limbs] = {0}; mp_limb_t *nqpqx = a;
+	mp_limb_t b[modulus_limbs] = {1}; mp_limb_t *nqpqz = b;
+	mp_limb_t c[modulus_limbs] ={1}; mp_limb_t *nqx = c;
+	mp_limb_t d[modulus_limbs] = {0}; mp_limb_t *nqz = d;
+  mp_limb_t e[modulus_limbs] = {0}; mp_limb_t *nqpqx2 = e;
+	mp_limb_t f[modulus_limbs] = {1}; mp_limb_t *nqpqz2 = f;
+	mp_limb_t g[modulus_limbs] = {0}; mp_limb_t *nqx2 = g;
+	mp_limb_t h[modulus_limbs] = {1}; mp_limb_t *nqz2 = h;
+	mp_limb_t *t;
+
+	uint8_t revpoint[modulus_bytes];
+	for (size_t i = 0; i<secretbits/8; i++) { revpoint[i] = point[secretbits/8-1-i]; }
+	for (size_t i = 0; i<modulus_limbs; i++) { nqpqx[i] = 0; }
+	assert(mpn_set_str(nqpqx, revpoint, modulus_bytes, 256) <= (mp_size_t)modulus_limbs);
+
+	mp_limb_t qmqp[modulus_limbs];
+	for (size_t i = 0; i<modulus_limbs; i++) { qmqp[i] = nqpqx[i]; }
+
+	for (size_t i = secretbits-1; i < secretbits; --i) {
+		mp_limb_t bit = (secret[i/8] >> (i%8))&1;
+
+		mpn_cnd_swap(bit, nqx, nqpqx, modulus_limbs);
+		mpn_cnd_swap(bit, nqz, nqpqz, modulus_limbs);
+
+		mp_limb_t *x2 = nqx2;
+	 	mp_limb_t *z2 = nqz2;
+		mp_limb_t *x3 = nqpqx2;
+		mp_limb_t *z3 = nqpqz2;
+		mp_limb_t *x = nqx;
+		mp_limb_t *z = nqz;
+		mp_limb_t *xprime = nqpqx;
+	 	mp_limb_t *zprime = nqpqz;
+		// fmonty(mp_limb_t *x2, mp_limb_t 0*z2, /* output 2Q */
+		//        mp_limb_t *x3, mp_limb_t *z3, /* output Q + Q' */
+		//        mp_limb_t *x, mp_limb_t *z,   /* input Q */
+		//        mp_limb_t *xprime, mp_limb_t *zprime, /* input Q' */
+		//        const mp_limb_t *qmqp /* input Q - Q' */) {
+	
+		#define fe_mul(out, x, y) do { \
+			mpn_sec_mul(_product_tmp, x, modulus_limbs, y, modulus_limbs, scratch); \
+			mpn_sec_div_r(_product_tmp, modulus_limbs+modulus_limbs, m, modulus_limbs, scratch); \
+			for (size_t i = 0; i<modulus_limbs; i++) { out[i] = _product_tmp[i]; } \
+		} while (0)
+		
+		#define fe_sqr(out, x) do { \
+			mpn_sec_sqr(_product_tmp, x, modulus_limbs, scratch); \
+			mpn_sec_div_r(_product_tmp, modulus_limbs+modulus_limbs, m, modulus_limbs, scratch); \
+			for (size_t i = 0; i<modulus_limbs; i++) { out[i] = _product_tmp[i]; } \
+		} while (0)
+		
+		#define fe_add(out, x, y) do { \
+			mpn_cnd_sub_n(mpn_add_n(out, x, y, modulus_limbs), out, out, m, modulus_limbs); \
+		} while (0)
+		
+		#define fe_sub(out, x, y) do { \
+			mpn_cnd_add_n(mpn_sub_n(out, x, y, modulus_limbs), out, out, m, modulus_limbs); \
+		} while (0)
+		
+		#define fe_inv(out, x) do { \
+			for (size_t i = 0; i<modulus_limbs; i++) { _product_tmp[i] = x[i]; } \
+			mp_size_t invertible = mpn_sec_invert(out, _product_tmp, m, modulus_limbs, 2*modulus_limbs*GMP_NUMB_BITS, scratch); \
+			mpn_cnd_sub_n(1-invertible, out, out, out, modulus_limbs); \
+		} while (0)
 	
-	#define fe_sqr(out, x) do { \
-		mpn_sec_sqr(_product_tmp, x, modulus_limbs, scratch); \
-		mpn_sec_div_r(_product_tmp, modulus_limbs+modulus_limbs, m, modulus_limbs, scratch); \
-		for (size_t i = 0; i<modulus_limbs; i++) { out[i] = _product_tmp[i]; } \
-	} while (0)
+	  mp_limb_t origx[modulus_limbs], origxprime[modulus_limbs], zzz[modulus_limbs], xx[modulus_limbs], zz[modulus_limbs], xxprime[modulus_limbs], zzprime[modulus_limbs], zzzprime[modulus_limbs];
 	
-	#define fe_add(out, x, y) do { \
-		mpn_cnd_sub_n(mpn_add_n(out, x, y, modulus_limbs), out, out, m, modulus_limbs); \
-	} while (0)
+		for (size_t i = 0; i<modulus_limbs; i++) { origx[i] = x[i]; }
+	  fe_add(x, x, z);
+		fe_sub(z, origx, z);
 	
-	#define fe_sub(out, x, y) do { \
-		mpn_cnd_add_n(mpn_sub_n(out, x, y, modulus_limbs), out, out, m, modulus_limbs); \
-	} while (0)
+		for (size_t i = 0; i<modulus_limbs; i++) { origxprime[i] = xprime[i]; }
+		fe_add(xprime, xprime, zprime);
+		fe_sub(zprime, origxprime, zprime);
+	  fe_mul(xxprime, xprime, z);
+	  fe_mul(zzprime, x, zprime);
+		for (size_t i = 0; i<modulus_limbs; i++) { origxprime[i] = xxprime[i]; }
+		fe_add(xxprime, xxprime, zzprime);
+		fe_sub(zzprime, origxprime, zzprime);
+		fe_sqr(x3, xxprime);
+		fe_sqr(zzzprime, zzprime);
+	  fe_mul(z3, zzzprime, qmqp);
 	
-	#define fe_inv(out, x) do { \
-		for (size_t i = 0; i<modulus_limbs; i++) { _product_tmp[i] = x[i]; } \
-		mp_size_t invertible = mpn_sec_invert(out, _product_tmp, m, modulus_limbs, 2*modulus_limbs*GMP_NUMB_BITS, scratch); \
-		mpn_cnd_sub_n(1-invertible, out, out, out, modulus_limbs); \
-	} while (0)
+	  fe_sqr(xx, x);
+	  fe_sqr(zz, z);
+	  fe_mul(x2, xx, zz);
+	  fe_sub(zz, xx, zz);
+	  fe_mul(zzz, zz, a24);
+	  fe_add(zzz, zzz, xx);
+	  fe_mul(z2, zz, zzz);
 
-	mp_limb_t x[modulus_limbs]; mpn_zero(x, modulus_limbs);
-	x[3] = 7;
-	print_limbs(x);
-	mp_limb_t y[modulus_limbs]; mpn_zero(y, modulus_limbs);
-	y[3] = 5;
-	print_limbs(y);
+		// } fmonty
 
-	mp_limb_t xy[modulus_limbs];
+		mpn_cnd_swap(bit, nqx2, nqpqx2, modulus_limbs);
+		mpn_cnd_swap(bit, nqz2, nqpqz2, modulus_limbs);
 
-	fe_mul(xy, x,y);
-	print_limbs(xy);
+		t = nqx;
+		nqx = nqx2;
+		nqx2 = t;
+		t = nqz;
+		nqz = nqz2;
+		nqz2 = t;
+		t = nqpqx;
+		nqpqx = nqpqx2;
+		nqpqx2 = t;
+		t = nqpqz;
+		nqpqz = nqpqz2;
+		nqpqz2 = t;
 
-	fe_sqr(xy, xy);
-	print_limbs(xy);
+		// { mp_limb_t pr[modulus_limbs]; fe_inv(pr, nqz); fe_mul(pr, pr, nqx); fe_print(pr); }
+		// printf(" "); 
+		// { mp_limb_t pr[modulus_limbs]; fe_inv(pr, nqpqz); fe_mul(pr, pr, nqpqx); fe_print(pr); }
+		// printf("\n");
+
+	}
+
+	fe_inv(nqz, nqz);
+	fe_mul(nqx, nqx, nqz);
+
+	for (size_t i = 0; i < 8*sizeof(modulus); i++) {
+		mp_limb_t bit = (nqx[i/GMP_LIMB_BITS] >> (i%GMP_LIMB_BITS))&1;
+		out [i/8] |= bit<<(i%8);
+	}
+}
+
+
+int main() {
+	// {
+	// 	uint8_t out[sizeof(modulus)] = {0};
+	// 	uint8_t point[sizeof(modulus)] = {9};
+	// 	uint8_t secret[sizeof(modulus)] = {1};
+	// 	crypto_scalarmult(out, point, secret, 256);
+	// 	printf("0x"); for (int i = 31; i>=0; --i) { printf("%02x", out[i]); }; printf("\n");
+	// }
 
-	fe_add(xy, xy, xy);
-	print_limbs(xy);
+	{
+		const uint8_t expected[32] = {0x89, 0x16, 0x1f, 0xde, 0x88, 0x7b, 0x2b, 0x53, 0xde, 0x54, 0x9a, 0xf4, 0x83, 0x94, 0x01, 0x06, 0xec, 0xc1, 0x14, 0xd6, 0x98, 0x2d, 0xaa, 0x98, 0x25, 0x6d, 0xe2, 0x3b, 0xdf, 0x77, 0x66, 0x1a};
+		const uint8_t basepoint[32] = {9, 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, 0};
 
-	fe_sub(xy, xy, m);
-	print_limbs(xy);
 
-	print_limbs(y);
-	fe_inv(x, y);
-	print_limbs(x);
+		uint8_t a[32] = {0}, b[32] = {0};
+		uint8_t* in = a;
+		uint8_t* out = b;
+		a[0] = 1;
 
-	fe_mul(xy, x, y);
-	print_limbs(xy);
+		for (int i = 0; i < 200; i++) {
+			printf("0x"); for (int i = 31; i>=0; --i) { printf("%02x", in[i]); }; printf("\n");
+			crypto_scalarmult(out, basepoint, in, 254);
+			uint8_t* t = out;
+			out = in;
+			in = t;
+		}
 
-	fe_inv(x, m);
-	print_limbs(x);
+		printf("0x"); for (int i = 31; i>=0; --i) { printf("%02x", out[i]); }; printf("\n");
+		printf("0x"); for (int i = 31; i>=0; --i) { printf("%02x", expected[i]); }; printf("\n");
+	}
 }