Merge pull request #127

c35ff1e Convert lambda splitter to pure scalar code. (Pieter Wuille)
cc604e9 Avoid division when decomposing scalars (Peter Dettman)
ff8746d Add secp256k1_scalar_mul_shift_var (Pieter Wuille)

.travis.yml

@@ -19,6 +19,7 @@ env:
     - FIELD=32bit
     - FIELD=32bit     ENDOMORPHISM=yes
     - BIGNUM=none
+    - BIGNUM=none     ENDOMORPHISM=yes
     - BUILD=distcheck
     - EXTRAFLAGS=CFLAGS=-DDETERMINISTIC
 before_script: ./autogen.sh

configure.ac

@@ -270,10 +270,7 @@ if test x"$set_field" = x"gmp" || test x"$set_bignum" = x"gmp"; then
 fi
 
 if test x"$use_endomorphism" = x"yes"; then
-  if test x"$set_bignum" = x"none"; then
-    AC_MSG_ERROR([Cannot use endomorphism optimization without a bignum implementation])
-  fi
-  AC_DEFINE(USE_ENDOMORPHISM, 1, [Define this symbol to use endomorphism])
+  AC_DEFINE(USE_ENDOMORPHISM, 1, [Define this symbol to use endomorphism optimization])
 fi
 
 AC_MSG_NOTICE([Using field implementation: $set_field])

src/ecmult_impl.h

@@ -168,8 +168,10 @@ static void secp256k1_ecmult(secp256k1_gej_t *r, const secp256k1_gej_t *a, const
     secp256k1_scalar_split_lambda_var(&na_1, &na_lam, na);
 
     /* build wnaf representation for na_1 and na_lam. */
-    int wnaf_na_1[129];   int bits_na_1   = secp256k1_ecmult_wnaf(wnaf_na_1,   &na_1,   WINDOW_A);
-    int wnaf_na_lam[129]; int bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, &na_lam, WINDOW_A);
+    int wnaf_na_1[130];   int bits_na_1   = secp256k1_ecmult_wnaf(wnaf_na_1,   &na_1,   WINDOW_A);
+    int wnaf_na_lam[130]; int bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, &na_lam, WINDOW_A);
+    VERIFY_CHECK(bits_na_1 <= 130);
+    VERIFY_CHECK(bits_na_lam <= 130);
     int bits = bits_na_1;
     if (bits_na_lam > bits) bits = bits_na_lam;
 #else

src/num.h

@@ -47,15 +47,12 @@ static void secp256k1_num_sub(secp256k1_num_t *r, const secp256k1_num_t *a, cons
 /** Multiply two (signed) numbers. */
 static void secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
 
-/** Divide two (signed) numbers. */
-static void secp256k1_num_div(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
-
 /** Replace a number by its remainder modulo m. M's sign is ignored. The result is a number between 0 and m-1,
     even if r was negative. */
 static void secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *m);
 
-/** Right-shift the passed number by bits bits, and return those bits. */
-static int secp256k1_num_shift(secp256k1_num_t *r, int bits);
+/** Right-shift the passed number by bits bits. */
+static void secp256k1_num_shift(secp256k1_num_t *r, int bits);
 
 /** Check whether a number is zero. */
 static int secp256k1_num_is_zero(const secp256k1_num_t *a);

src/num_gmp_impl.h

@@ -206,31 +206,23 @@ static void secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, cons
     memset(tmp, 0, sizeof(tmp));
 }
 
-static void secp256k1_num_div(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
-    secp256k1_num_sanity(a);
-    secp256k1_num_sanity(b);
-    if (b->limbs > a->limbs) {
-        r->limbs = 1;
-        r->data[0] = 0;
-        r->neg = 0;
-        return;
+static void secp256k1_num_shift(secp256k1_num_t *r, int bits) {
+    if (bits % GMP_NUMB_BITS) {
+        // Shift within limbs.
+        mpn_rshift(r->data, r->data, r->limbs, bits % GMP_NUMB_BITS);
     }
-
-    mp_limb_t quo[2*NUM_LIMBS+1];
-    mp_limb_t rem[2*NUM_LIMBS+1];
-    mpn_tdiv_qr(quo, rem, 0, a->data, a->limbs, b->data, b->limbs);
-    mpn_copyi(r->data, quo, a->limbs - b->limbs + 1);
-    r->limbs = a->limbs - b->limbs + 1;
-    while (r->limbs > 1 && r->data[r->limbs - 1]==0) r->limbs--;
-    r->neg = a->neg ^ b->neg;
-}
-
-static int secp256k1_num_shift(secp256k1_num_t *r, int bits) {
-    VERIFY_CHECK(bits <= GMP_NUMB_BITS);
-    mp_limb_t ret = mpn_rshift(r->data, r->data, r->limbs, bits);
-    if (r->limbs>1 && r->data[r->limbs-1]==0) r->limbs--;
-    ret >>= (GMP_NUMB_BITS - bits);
-    return ret;
+    if (bits >= GMP_NUMB_BITS) {
+        // Shift full limbs.
+        for (int i = 0; i < r->limbs; i++) {
+            int index = i + (bits / GMP_NUMB_BITS);
+            if (index < r->limbs && index < 2*NUM_LIMBS) {
+                r->data[i] = r->data[index];
+            } else {
+                r->data[i] = 0;
+            }
+        }
+    }
+    while (r->limbs>1 && r->data[r->limbs-1]==0) r->limbs--;
 }
 
 static void secp256k1_num_negate(secp256k1_num_t *r) {

src/scalar.h

@@ -90,4 +90,7 @@ static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_
 static void secp256k1_scalar_split_lambda_var(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a);
 #endif
 
+/** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */
+static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b, unsigned int shift);
+
 #endif

src/scalar_4x64_impl.h

@@ -314,13 +314,11 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar_t *r, const uint64_t *l
     secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
 }
 
-static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
     /* 160 bit accumulator. */
     uint64_t c0 = 0, c1 = 0;
     uint32_t c2 = 0;
 
-    uint64_t l[8];
-
     /* l[0..7] = a[0..3] * b[0..3]. */
     muladd_fast(a->d[0], b->d[0]);
     extract_fast(l[0]);
@@ -347,17 +345,13 @@ static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t
     extract_fast(l[6]);
     VERIFY_CHECK(c1 <= 0);
     l[7] = c0;
-
-    secp256k1_scalar_reduce_512(r, l);
 }
 
-static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar_t *a) {
     /* 160 bit accumulator. */
     uint64_t c0 = 0, c1 = 0;
     uint32_t c2 = 0;
 
-    uint64_t l[8];
-
     /* l[0..7] = a[0..3] * b[0..3]. */
     muladd_fast(a->d[0], a->d[0]);
     extract_fast(l[0]);
@@ -378,8 +372,6 @@ static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t
     extract_fast(l[6]);
     VERIFY_CHECK(c1 == 0);
     l[7] = c0;
-
-    secp256k1_scalar_reduce_512(r, l);
 }
 
 #undef sumadd
@@ -390,6 +382,18 @@ static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t
 #undef extract
 #undef extract_fast
 
+static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+    uint64_t l[8];
+    secp256k1_scalar_mul_512(l, a, b);
+    secp256k1_scalar_reduce_512(r, l);
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
+    uint64_t l[8];
+    secp256k1_scalar_sqr_512(l, a);
+    secp256k1_scalar_reduce_512(r, l);
+}
+
 static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) {
     r1->d[0] = a->d[0];
     r1->d[1] = a->d[1];
@@ -405,4 +409,20 @@ SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar_t *a, con
     return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3])) == 0;
 }
 
+SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b, unsigned int shift) {
+    VERIFY_CHECK(shift >= 256);
+    uint64_t l[8];
+    secp256k1_scalar_mul_512(l, a, b);
+    unsigned int shiftlimbs = shift >> 6;
+    unsigned int shiftlow = shift & 0x3F;
+    unsigned int shifthigh = 64 - shiftlow;
+    r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[1] = shift < 448 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[2] = shift < 384 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[3] = shift < 320 ? (l[3 + shiftlimbs] >> shiftlow) : 0;
+    if ((l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1) {
+        secp256k1_scalar_add_bit(r, 0);
+    }
+}
+
 #endif

src/scalar_8x32_impl.h

@@ -451,12 +451,10 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar_t *r, const uint32_t *l
     secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
 }
 
-static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static void secp256k1_scalar_mul_512(uint32_t l[16], const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
     /* 96 bit accumulator. */
     uint32_t c0 = 0, c1 = 0, c2 = 0;
 
-    uint32_t l[16];
-
     /* l[0..15] = a[0..7] * b[0..7]. */
     muladd_fast(a->d[0], b->d[0]);
     extract_fast(l[0]);
@@ -539,16 +537,12 @@ static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t
     extract_fast(l[14]);
     VERIFY_CHECK(c1 == 0);
     l[15] = c0;
-
-    secp256k1_scalar_reduce_512(r, l);
 }
 
-static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_sqr_512(uint32_t l[16], const secp256k1_scalar_t *a) {
     /* 96 bit accumulator. */
     uint32_t c0 = 0, c1 = 0, c2 = 0;
 
-    uint32_t l[16];
-
     /* l[0..15] = a[0..7]^2. */
     muladd_fast(a->d[0], a->d[0]);
     extract_fast(l[0]);
@@ -603,8 +597,6 @@ static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t
     extract_fast(l[14]);
     VERIFY_CHECK(c1 == 0);
     l[15] = c0;
-
-    secp256k1_scalar_reduce_512(r, l);
 }
 
 #undef sumadd
@@ -615,6 +607,18 @@ static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t
 #undef extract
 #undef extract_fast
 
+static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+    uint32_t l[16];
+    secp256k1_scalar_mul_512(l, a, b);
+    secp256k1_scalar_reduce_512(r, l);
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
+    uint32_t l[16];
+    secp256k1_scalar_sqr_512(l, a);
+    secp256k1_scalar_reduce_512(r, l);
+}
+
 static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) {
     r1->d[0] = a->d[0];
     r1->d[1] = a->d[1];
@@ -638,4 +642,24 @@ SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar_t *a, con
     return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0;
 }
 
+SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b, unsigned int shift) {
+    VERIFY_CHECK(shift >= 256);
+    uint32_t l[16];
+    secp256k1_scalar_mul_512(l, a, b);
+    unsigned int shiftlimbs = shift >> 5;
+    unsigned int shiftlow = shift & 0x1F;
+    unsigned int shifthigh = 32 - shiftlow;
+    r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 480 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[1] = shift < 480 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[2] = shift < 448 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 416 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[3] = shift < 416 ? (l[3 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[4 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[4] = shift < 384 ? (l[4 + shiftlimbs] >> shiftlow | (shift < 352 && shiftlow ? (l[5 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow)  : 0;
+    if ((l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1) {
+        secp256k1_scalar_add_bit(r, 0);
+    }
+}
+
 #endif