Make Karatsuba multiply completely const time

3 files changed, 45 insertions, 19 deletions

diff --git a/src/lib/math/mp/mp_core.cpp b/src/lib/math/mp/mp_core.cpp
index b1add33a4..9f2999929 100644
--- a/src/lib/math/mp/mp_core.cpp
+++ b/src/lib/math/mp/mp_core.cpp
@@ -211,18 +211,35 @@ void bigint_sub2_rev(word x[],  const word y[], size_t y_size)
    BOTAN_ASSERT(!borrow, "y must be greater than x");
    }
 
-int32_t bigint_sub_abs(word z[], const word x[], const word y[], size_t sz)
+word bigint_sub_abs(word z[],
+                    const word x[], const word y[], size_t N,
+                    word ws[])
    {
-   word borrow = bigint_sub3(z, x, sz, y, sz);
+   // Subtract in both direction then conditional copy out the result
 
-   CT::unpoison(borrow);
-   if(borrow)
+   word* ws0 = ws;
+   word* ws1 = ws + N;
+
+   word borrow0 = 0;
+   word borrow1 = 0;
+
+   const size_t blocks = N - (N % 8);
+
+   for(size_t i = 0; i != blocks; i += 8)
       {
-      bigint_sub3(z, y, sz, x, sz);
-      return -1;
+      borrow0 = word8_sub3(ws0 + i, x + i, y + i, borrow0);
+      borrow1 = word8_sub3(ws1 + i, y + i, x + i, borrow1);
       }
 
-   return 1;
+   for(size_t i = blocks; i != N; ++i)
+      {
+      ws0[i] = word_sub(x[i], y[i], &borrow0);
+      ws1[i] = word_sub(y[i], x[i], &borrow1);
+      }
+
+   word mask = CT::conditional_copy_mem(borrow1, z, ws0, ws1, N);
+
+   return CT::select<word>(mask, 0, 1);
    }
 
 /*
diff --git a/src/lib/math/mp/mp_core.h b/src/lib/math/mp/mp_core.h
index 4ae28f7bb..9d8ad84db 100644
--- a/src/lib/math/mp/mp_core.h
+++ b/src/lib/math/mp/mp_core.h
@@ -100,9 +100,16 @@ word bigint_sub3(word z[],
 * Otherwise compute z = y - x
 * No borrow is possible since the result is always >= 0
 *
-* Returns 1 if x >= y or -1 if x < y
-*/
-int32_t bigint_sub_abs(word z[], const word x[], const word y[], size_t size);
+* Returns 1 if x >= y or 0 if x < y
+* @param z output array of at least N words
+* @param x input array of N words
+* @param y input array of N words
+* @param N length of x and y
+* @param ws array of at least 2*N words
+*/
+word bigint_sub_abs(word z[],
+                    const word x[], const word y[], size_t N,
+                    word ws[]);
 
 /*
 * Shift Operations
diff --git a/src/lib/math/mp/mp_karat.cpp b/src/lib/math/mp/mp_karat.cpp
index 03a37ed8d..27ae349ef 100644
--- a/src/lib/math/mp/mp_karat.cpp
+++ b/src/lib/math/mp/mp_karat.cpp
@@ -1,6 +1,6 @@
 /*
 * Multiplication and Squaring
-* (C) 1999-2010 Jack Lloyd
+* (C) 1999-2010,2018 Jack Lloyd
 *     2016 Matthias Gierlings
 *
 * Botan is released under the Simplified BSD License (see license.txt)
@@ -8,6 +8,7 @@
 
 #include <botan/internal/mp_core.h>
 #include <botan/internal/mp_asmi.h>
+#include <botan/internal/ct_utils.h>
 #include <botan/mem_ops.h>
 #include <botan/exceptn.h>
 
@@ -120,11 +121,10 @@ void karatsuba_mul(word z[], const word x[], const word y[], size_t N,
    */
 
    // First compute (X_lo - X_hi)*(Y_hi - Y_lo)
-   const int32_t cmp0 = bigint_sub_abs(z0, x0, x1, N2);
-   const int32_t cmp1 = bigint_sub_abs(z1, y1, y0, N2);
+   const word cmp0 = bigint_sub_abs(z0, x0, x1, N2, workspace);
+   const word cmp1 = bigint_sub_abs(z1, y1, y0, N2, workspace);
 
    karatsuba_mul(ws0, z0, z1, N2, ws1);
-   const bool is_negative = cmp0 != cmp1;
 
    // Compute X_lo * Y_lo
    karatsuba_mul(z0, x0, y0, N2, ws1);
@@ -138,10 +138,12 @@ void karatsuba_mul(word z[], const word x[], const word y[], size_t N,
    z_carry += bigint_add2_nc(z + N + N2, N2, &ws_carry, 1);
    bigint_add2_nc(z + N + N2, N2, &z_carry, 1);
 
-   if(is_negative)
-      bigint_sub2(z + N2, 2*N-N2, ws0, N);
-   else
-      bigint_add2_nc(z + N2, 2*N-N2, ws0, N);
+   clear_mem(workspace + N, N2);
+
+   const word is_negative = CT::expand_mask<word>(cmp0 != cmp1);
+
+   bigint_cnd_sub(is_negative,  z + N2, workspace, 2*N-N2);
+   bigint_cnd_add(~is_negative, z + N2, workspace, 2*N-N2);
    }
 
 /*
@@ -178,7 +180,7 @@ void karatsuba_sqr(word z[], const word x[], size_t N, word workspace[])
    clear_mem(workspace, 2*N);
 
    // See comment in karatsuba_mul
-   bigint_sub_abs(z0, x0, x1, N2);
+   bigint_sub_abs(z0, x0, x1, N2, workspace);
    karatsuba_sqr(ws0, z0, N2, ws1);
 
    karatsuba_sqr(z0, x0, N2, ws1);