Merge pull request #278 from ARMmbed/dev/yanesca/iotcrypt-767-ecdsa-timing-side-channel

ECDSA timing side channel due to non-constant-time integer comparison

Author: gilles-peskine-arm

include/mbedtls/bignum.h

@@ -185,7 +185,7 @@ extern "C" {
  */
 typedef struct mbedtls_mpi
 {
-    int s;              /*!<  integer sign      */
+    int s;              /*!<  Sign: -1 if the mpi is negative, 1 otherwise */
     size_t n;           /*!<  total # of limbs  */
     mbedtls_mpi_uint *p;          /*!<  pointer to limbs  */
 }
@@ -594,6 +594,24 @@ int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
  */
 int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
 
+/**
+ * \brief          Check if an MPI is less than the other in constant time.
+ *
+ * \param X        The left-hand MPI. This must point to an initialized MPI
+ *                 with the same allocated length as Y.
+ * \param Y        The right-hand MPI. This must point to an initialized MPI
+ *                 with the same allocated length as X.
+ * \param ret      The result of the comparison:
+ *                 \c 1 if \p X is less than \p Y.
+ *                 \c 0 if \p X is greater than or equal to \p Y.
+ *
+ * \return         0 on success.
+ * \return         MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the allocated length of
+ *                 the two input MPIs is not the same.
+ */
+int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y,
+        unsigned *ret );
+
 /**
  * \brief          Compare an MPI with an integer.
  *

library/bignum.c

@@ -1148,6 +1148,107 @@ int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y )
     return( 0 );
 }
 
+/** Decide if an integer is less than the other, without branches.
+ *
+ * \param x         First integer.
+ * \param y         Second integer.
+ *
+ * \return          1 if \p x is less than \p y, 0 otherwise
+ */
+static unsigned ct_lt_mpi_uint( const mbedtls_mpi_uint x,
+        const mbedtls_mpi_uint y )
+{
+    mbedtls_mpi_uint ret;
+    mbedtls_mpi_uint cond;
+
+    /*
+     * Check if the most significant bits (MSB) of the operands are different.
+     */
+    cond = ( x ^ y );
+    /*
+     * If the MSB are the same then the difference x-y will be negative (and
+     * have its MSB set to 1 during conversion to unsigned) if and only if x<y.
+     */
+    ret = ( x - y ) & ~cond;
+    /*
+     * If the MSB are different, then the operand with the MSB of 1 is the
+     * bigger. (That is if y has MSB of 1, then x<y is true and it is false if
+     * the MSB of y is 0.)
+     */
+    ret |= y & cond;
+
+
+    ret = ret >> ( biL - 1 );
+
+    return (unsigned) ret;
+}
+
+/*
+ * Compare signed values in constant time
+ */
+int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y,
+        unsigned *ret )
+{
+    size_t i;
+    /* The value of any of these variables is either 0 or 1 at all times. */
+    unsigned cond, done, X_is_negative, Y_is_negative;
+
+    MPI_VALIDATE_RET( X != NULL );
+    MPI_VALIDATE_RET( Y != NULL );
+    MPI_VALIDATE_RET( ret != NULL );
+
+    if( X->n != Y->n )
+        return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
+
+    /*
+     * Set sign_N to 1 if N >= 0, 0 if N < 0.
+     * We know that N->s == 1 if N >= 0 and N->s == -1 if N < 0.
+     */
+    X_is_negative = ( X->s & 2 ) >> 1;
+    Y_is_negative = ( Y->s & 2 ) >> 1;
+
+    /*
+     * If the signs are different, then the positive operand is the bigger.
+     * That is if X is negative (X_is_negative == 1), then X < Y is true and it
+     * is false if X is positive (X_is_negative == 0).
+     */
+    cond = ( X_is_negative ^ Y_is_negative );
+    *ret = cond & X_is_negative;
+
+    /*
+     * This is a constant-time function. We might have the result, but we still
+     * need to go through the loop. Record if we have the result already.
+     */
+    done = cond;
+
+    for( i = X->n; i > 0; i-- )
+    {
+        /*
+         * If Y->p[i - 1] < X->p[i - 1] then X < Y is true if and only if both
+         * X and Y are negative.
+         *
+         * Again even if we can make a decision, we just mark the result and
+         * the fact that we are done and continue looping.
+         */
+        cond = ct_lt_mpi_uint( Y->p[i - 1], X->p[i - 1] );
+        *ret |= cond & ( 1 - done ) & X_is_negative;
+        done |= cond;
+
+        /*
+         * If X->p[i - 1] < Y->p[i - 1] then X < Y is true if and only if both
+         * X and Y are positive.
+         *
+         * Again even if we can make a decision, we just mark the result and
+         * the fact that we are done and continue looping.
+         */
+        cond = ct_lt_mpi_uint( X->p[i - 1], Y->p[i - 1] );
+        *ret |= cond & ( 1 - done ) & ( 1 - X_is_negative );
+        done |= cond;
+    }
+
+    return( 0 );
+}
+
 /*
  * Compare signed values
  */

library/ecp.c

@@ -2803,6 +2803,7 @@ int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp,
     {
         /* SEC1 3.2.1: Generate d such that 1 <= n < N */
         int count = 0;
+        unsigned cmp = 0;
 
         /*
          * Match the procedure given in RFC 6979 (deterministic ECDSA):
@@ -2827,9 +2828,14 @@ int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp,
              */
             if( ++count > 30 )
                 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
+
+            ret = mbedtls_mpi_lt_mpi_ct( d, &grp->N, &cmp );
+            if( ret != 0 )
+            {
+                goto cleanup;
+            }
         }
-        while( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
-               mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 );
+        while( mbedtls_mpi_cmp_int( d, 1 ) < 0 || cmp != 1 );
     }
 #endif /* ECP_SHORTWEIERSTRASS */
 

tests/suites/test_suite_mpi.data

@@ -175,6 +175,93 @@ mbedtls_mpi_cmp_mpi:10:"2":10:"-3":1
 Base test mbedtls_mpi_cmp_mpi (Mixed values) #6
 mbedtls_mpi_cmp_mpi:10:"-2":10:"31231231289798":-1
 
+Base test mbedtls_mpi_lt_mpi_ct #1
+mbedtls_mpi_lt_mpi_ct:1:"2B5":1:"2B5":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct #2
+mbedtls_mpi_lt_mpi_ct:1:"2B5":1:"2B4":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct #3
+mbedtls_mpi_lt_mpi_ct:1:"2B5":1:"2B6":1:0
+
+Base test mbedtls_mpi_lt_mpi_ct (Negative values) #1
+mbedtls_mpi_lt_mpi_ct:1:"-2":1:"-2":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct (Negative values) #2
+mbedtls_mpi_lt_mpi_ct:1:"-2":1:"-3":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct (Negative values) #3
+mbedtls_mpi_lt_mpi_ct:1:"-2":1:"-1":1:0
+
+Base test mbedtls_mpi_lt_mpi_ct (Mixed values) #1
+mbedtls_mpi_lt_mpi_ct:1:"-3":1:"2":1:0
+
+Base test mbedtls_mpi_lt_mpi_ct (Mixed values) #2
+mbedtls_mpi_lt_mpi_ct:1:"2":1:"-3":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct (Mixed values) #3
+mbedtls_mpi_lt_mpi_ct:2:"-2":2:"1C67967269C6":1:0
+
+Base test mbedtls_mpi_lt_mpi_ct (X is longer in storage)
+mbedtls_mpi_lt_mpi_ct:3:"2B5":2:"2B5":0:MBEDTLS_ERR_MPI_BAD_INPUT_DATA
+
+Base test mbedtls_mpi_lt_mpi_ct (Y is longer in storage)
+mbedtls_mpi_lt_mpi_ct:3:"2B5":4:"2B5":0:MBEDTLS_ERR_MPI_BAD_INPUT_DATA
+
+Base test mbedtls_mpi_lt_mpi_ct (corner case - 64 bit) #1
+mbedtls_mpi_lt_mpi_ct:2:"7FFFFFFFFFFFFFFF":2:"FF":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct (corner case - 64 bit) #2
+mbedtls_mpi_lt_mpi_ct:2:"8000000000000000":2:"7FFFFFFFFFFFFFFF":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct (corner case - 64 bit) #3
+mbedtls_mpi_lt_mpi_ct:2:"8000000000000000":2:"1":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct (corner case - 64 bit) #4
+mbedtls_mpi_lt_mpi_ct:2:"8000000000000000":2:"0":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct (corner case - 64 bit) #5
+mbedtls_mpi_lt_mpi_ct:2:"FFFFFFFFFFFFFFFF":2:"FF":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct (corner case - 32 bit) #1
+mbedtls_mpi_lt_mpi_ct:1:"7FFFFFFF":1:"FF":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct (corner case - 32 bit) #2
+mbedtls_mpi_lt_mpi_ct:1:"80000000":1:"7FFFFFFF":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct (corner case - 32 bit) #3
+mbedtls_mpi_lt_mpi_ct:1:"80000000":1:"1":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct (corner case - 32 bit) #4
+mbedtls_mpi_lt_mpi_ct:1:"80000000":1:"0":0:0
+
+Base test mbedtls_mpi_lt_mpi_ct (corner case - 32 bit) #5
+mbedtls_mpi_lt_mpi_ct:1:"FFFFFFFF":1:"FF":0:0
+
+Multi-limb mbedtls_mpi_lt_mpi_ct (X<Y, zero vs non-zero MS limb)
+mbedtls_mpi_lt_mpi_ct:2:"0FFFFFFFFFFFFFFFF":2:"1FFFFFFFFFFFFFFFF":1:0
+
+Multi-limb mbedtls_mpi_lt_mpi_ct (X>Y, equal MS limbs)
+mbedtls_mpi_lt_mpi_ct:2:"-EEFFFFFFFFFFFFFFF1":2:"-EEFFFFFFFFFFFFFFFF":0:0
+
+Multi-limb mbedtls_mpi_lt_mpi_ct (X=Y)
+mbedtls_mpi_lt_mpi_ct:2:"EEFFFFFFFFFFFFFFFF":2:"EEFFFFFFFFFFFFFFFF":0:0
+
+Multi-limb mbedtls_mpi_lt_mpi_ct (X=-Y)
+mbedtls_mpi_lt_mpi_ct:2:"-EEFFFFFFFFFFFFFFFF":2:"EEFFFFFFFFFFFFFFFF":1:0
+
+Multi-limb mbedtls_mpi_lt_mpi_ct (Alternating limbs) #1
+mbedtls_mpi_lt_mpi_ct:2:"11FFFFFFFFFFFFFFFF":2:"FF1111111111111111":1:0
+
+Multi-limb mbedtls_mpi_lt_mpi_ct (Alternating limbs) #2
+mbedtls_mpi_lt_mpi_ct:2:"FF1111111111111111":2:"11FFFFFFFFFFFFFFFF":0:0
+
+Multi-limb mbedtls_mpi_lt_mpi_ct (Alternating limbs) #3
+mbedtls_mpi_lt_mpi_ct:2:"-11FFFFFFFFFFFFFFFF":2:"-FF1111111111111111":0:0
+
+Multi-limb mbedtls_mpi_lt_mpi_ct (Alternating limbs) #4
+mbedtls_mpi_lt_mpi_ct:2:"-FF1111111111111111":2:"-11FFFFFFFFFFFFFFFF":1:0
+
 Base test mbedtls_mpi_cmp_abs #1
 mbedtls_mpi_cmp_abs:10:"693":10:"693":0
 

tests/suites/test_suite_mpi.function

@@ -587,6 +587,31 @@ exit:
 }
 /* END_CASE */
 
+/* BEGIN_CASE */
+void mbedtls_mpi_lt_mpi_ct( int size_X, char * input_X,
+                            int size_Y, char * input_Y,
+                            int input_ret, int input_err )
+{
+    unsigned ret;
+    unsigned input_uret = input_ret;
+    mbedtls_mpi X, Y;
+    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y );
+
+    TEST_ASSERT( mbedtls_mpi_read_string( &X, 16, input_X ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &Y, 16, input_Y ) == 0 );
+
+    mbedtls_mpi_grow( &X, size_X );
+    mbedtls_mpi_grow( &Y, size_Y );
+
+    TEST_ASSERT( mbedtls_mpi_lt_mpi_ct( &X, &Y, &ret ) == input_err );
+    if( input_err == 0 )
+        TEST_ASSERT( ret == input_uret );
+
+exit:
+    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y );
+}
+/* END_CASE */
+
 /* BEGIN_CASE */
 void mbedtls_mpi_cmp_abs( int radix_X, char * input_X, int radix_Y,
                           char * input_Y, int input_A )