[crypto] Calculate inverse of modulus on demand in bigint_montgomery()

Reduce the number of parameters passed to bigint_montgomery() by
calculating the inverse of the modulus modulo the element size on
demand.  Cache the result, since Montgomery reduction will be used
repeatedly with the same modulus value.

In all currently supported algorithms, the modulus is a public value
(or a fixed value defined by specification) and so this non-constant
timing does not leak any private information.

Signed-off-by: Michael Brown <mcb30@ipxe.org>

diff --git a/src/crypto/bigint.c b/src/crypto/bigint.c
index b357ea29f0bbf69912f160125d446cc5ad9188bc..3ef96d13ddd8ea83aae52fd9c65a0f85d4f46cad 100644 (file)
--- a/src/crypto/bigint.c
+++ b/src/crypto/bigint.c
@@ -354,23 +354,17 @@ void bigint_mod_invert_raw ( const bigint_element_t *invertend0,
  * Perform Montgomery reduction (REDC) of a big integer product
  *
  * @v modulus0         Element 0 of big integer modulus
- * @v modinv0          Element 0 of the inverse of the modulus modulo 2^k
  * @v mont0            Element 0 of big integer Montgomery product
  * @v result0          Element 0 of big integer to hold result
  * @v size             Number of elements in modulus and result
  *
- * Note that only the least significant element of the inverse modulo
- * 2^k is required, and that the Montgomery product will be
- * overwritten.
+ * Note that the Montgomery product will be overwritten.
  */
 void bigint_montgomery_raw ( const bigint_element_t *modulus0,
-                            const bigint_element_t *modinv0,
                             bigint_element_t *mont0,
                             bigint_element_t *result0, unsigned int size ) {
        const bigint_t ( size ) __attribute__ (( may_alias ))
                *modulus = ( ( const void * ) modulus0 );
-       const bigint_t ( 1 ) __attribute__ (( may_alias ))
-               *modinv = ( ( const void * ) modinv0 );
        union {
                bigint_t ( size * 2 ) full;
                struct {
@@ -380,7 +374,8 @@ void bigint_montgomery_raw ( const bigint_element_t *modulus0,
        } __attribute__ (( may_alias )) *mont = ( ( void * ) mont0 );
        bigint_t ( size ) __attribute__ (( may_alias ))
                *result = ( ( void * ) result0 );
-       bigint_element_t negmodinv = -modinv->element[0];
+       static bigint_t ( 1 ) cached;
+       static bigint_t ( 1 ) negmodinv;
        bigint_element_t multiple;
        bigint_element_t carry;
        unsigned int i;
@@ -391,11 +386,18 @@ void bigint_montgomery_raw ( const bigint_element_t *modulus0,
        /* Sanity checks */
        assert ( bigint_bit_is_set ( modulus, 0 ) );
 
+       /* Calculate inverse (or use cached version) */
+       if ( cached.element[0] != modulus->element[0] ) {
+               bigint_mod_invert ( modulus, &negmodinv );
+               negmodinv.element[0] = -negmodinv.element[0];
+               cached.element[0] = modulus->element[0];
+       }
+
        /* Perform multiprecision Montgomery reduction */
        for ( i = 0 ; i < size ; i++ ) {
 
                /* Determine scalar multiple for this round */
-               multiple = ( mont->low.element[i] * negmodinv );
+               multiple = ( mont->low.element[i] * negmodinv.element[0] );
 
                /* Multiply value to make it divisible by 2^(width*i) */
                carry = 0;
@@ -467,7 +469,6 @@ void bigint_mod_exp_raw ( const bigint_element_t *base0,
                } product;
        } *temp = tmp;
        const uint8_t one[1] = { 1 };
-       bigint_t ( 1 ) modinv;
        bigint_element_t submask;
        unsigned int subsize;
        unsigned int scale;
@@ -494,9 +495,6 @@ void bigint_mod_exp_raw ( const bigint_element_t *base0,
        if ( ! submask )
                submask = ~submask;
 
-       /* Calculate inverse of (scaled) modulus N modulo element size */
-       bigint_mod_invert ( &temp->modulus, &modinv );
-
        /* Calculate (R^2 mod N) via direct reduction of (R^2 - N) */
        memset ( &temp->product.full, 0, sizeof ( temp->product.full ) );
        bigint_subtract ( &temp->padded_modulus, &temp->product.full );
@@ -504,12 +502,11 @@ void bigint_mod_exp_raw ( const bigint_element_t *base0,
        bigint_copy ( &temp->product.low, &temp->stash );
 
        /* Initialise result = Montgomery(1, R^2 mod N) */
-       bigint_montgomery ( &temp->modulus, &modinv,
-                           &temp->product.full, result );
+       bigint_montgomery ( &temp->modulus, &temp->product.full, result );
 
        /* Convert base into Montgomery form */
        bigint_multiply ( base, &temp->stash, &temp->product.full );
-       bigint_montgomery ( &temp->modulus, &modinv, &temp->product.full,
+       bigint_montgomery ( &temp->modulus, &temp->product.full,
                            &temp->stash );
 
        /* Calculate x1 = base^exponent modulo N */
@@ -518,13 +515,13 @@ void bigint_mod_exp_raw ( const bigint_element_t *base0,
 
                /* Square (and reduce) */
                bigint_multiply ( result, result, &temp->product.full );
-               bigint_montgomery ( &temp->modulus, &modinv,
-                                   &temp->product.full, result );
+               bigint_montgomery ( &temp->modulus, &temp->product.full,
+                                   result );
 
                /* Multiply (and reduce) */
                bigint_multiply ( &temp->stash, result, &temp->product.full );
-               bigint_montgomery ( &temp->modulus, &modinv,
-                                   &temp->product.full, &temp->product.low );
+               bigint_montgomery ( &temp->modulus, &temp->product.full,
+                                   &temp->product.low );
 
                /* Conditionally swap the multiplied result */
                bigint_swap ( result, &temp->product.low,
@@ -533,8 +530,7 @@ void bigint_mod_exp_raw ( const bigint_element_t *base0,
 
        /* Convert back out of Montgomery form */
        bigint_grow ( result, &temp->product.full );
-       bigint_montgomery ( &temp->modulus, &modinv, &temp->product.full,
-                           result );
+       bigint_montgomery ( &temp->modulus, &temp->product.full, result );
 
        /* Handle even moduli via Garner's algorithm */
        if ( subsize ) {

diff --git a/src/include/ipxe/bigint.h b/src/include/ipxe/bigint.h
index 3058547a6c7db4ded82a0eaefb2a98e06f0799d4..90e212b54f2c8d730dbcbdca467ac27366a31026 100644 (file)
--- a/src/include/ipxe/bigint.h
+++ b/src/include/ipxe/bigint.h
@@ -257,16 +257,15 @@ FILE_LICENCE ( GPL2_OR_LATER_OR_UBDL );
  * Perform Montgomery reduction (REDC) of a big integer product
  *
  * @v modulus          Big integer modulus
- * @v modinv           Big integer inverse of the modulus modulo 2^k
  * @v mont             Big integer Montgomery product
  * @v result           Big integer to hold result
  *
  * Note that the Montgomery product will be overwritten.
  */
-#define bigint_montgomery( modulus, modinv, mont, result ) do {                \
+#define bigint_montgomery( modulus, mont, result ) do {                        \
        unsigned int size = bigint_size (modulus);                      \
-       bigint_montgomery_raw ( (modulus)->element, (modinv)->element,  \
-                               (mont)->element, (result)->element,     \
+       bigint_montgomery_raw ( (modulus)->element, (mont)->element,    \
+                               (result)->element,                      \
                                size );                                 \
        } while ( 0 )
 
@@ -377,7 +376,6 @@ void bigint_reduce_raw ( bigint_element_t *modulus0, bigint_element_t *value0,
 void bigint_mod_invert_raw ( const bigint_element_t *invertend0,
                             bigint_element_t *inverse0, unsigned int size );
 void bigint_montgomery_raw ( const bigint_element_t *modulus0,
-                            const bigint_element_t *modinv0,
                             bigint_element_t *mont0,
                             bigint_element_t *result0, unsigned int size );
 void bigint_mod_exp_raw ( const bigint_element_t *base0,

diff --git a/src/tests/bigint_test.c b/src/tests/bigint_test.c
index dc74740e621a83e79071c08fee1db94ee7b70057..07ba13bb4a8b161c3a1e630254d19d7bc1258372 100644 (file)
--- a/src/tests/bigint_test.c
+++ b/src/tests/bigint_test.c
@@ -207,20 +207,17 @@ void bigint_mod_invert_sample ( const bigint_element_t *invertend0,
 }
 
 void bigint_montgomery_sample ( const bigint_element_t *modulus0,
-                               const bigint_element_t *modinv0,
                                bigint_element_t *mont0,
                                bigint_element_t *result0,
                                unsigned int size ) {
        const bigint_t ( size ) __attribute__ (( may_alias ))
                *modulus = ( ( const void * ) modulus0 );
-       const bigint_t ( 1 ) __attribute__ (( may_alias ))
-               *modinv = ( ( const void * ) modinv0 );
        bigint_t ( 2 * size ) __attribute__ (( may_alias ))
                *mont = ( ( void * ) mont0 );
        bigint_t ( size ) __attribute__ (( may_alias ))
                *result = ( ( void * ) result0 );
 
-       bigint_montgomery ( modulus, modinv, mont, result );
+       bigint_montgomery ( modulus, mont, result );
 }
 
 void bigint_mod_exp_sample ( const bigint_element_t *base0,
@@ -631,7 +628,6 @@ void bigint_mod_exp_sample ( const bigint_element_t *base0,
        unsigned int size =                                             \
                bigint_required_size ( sizeof ( modulus_raw ) );        \
        bigint_t ( size ) modulus_temp;                                 \
-       bigint_t ( 1 ) modinv_temp;                                     \
        bigint_t ( 2 * size ) mont_temp;                                \
        bigint_t ( size ) result_temp;                                  \
        {} /* Fix emacs alignment */                                    \
@@ -641,13 +637,10 @@ void bigint_mod_exp_sample ( const bigint_element_t *base0,
        bigint_init ( &modulus_temp, modulus_raw,                       \
                      sizeof ( modulus_raw ) );                         \
        bigint_init ( &mont_temp, mont_raw, sizeof ( mont_raw ) );      \
-       bigint_mod_invert ( &modulus_temp, &modinv_temp );              \
        DBG ( "Montgomery:\n" );                                        \
        DBG_HDA ( 0, &modulus_temp, sizeof ( modulus_temp ) );          \
-       DBG_HDA ( 0, &modinv_temp, sizeof ( modinv_temp ) );            \
        DBG_HDA ( 0, &mont_temp, sizeof ( mont_temp ) );                \
-       bigint_montgomery ( &modulus_temp, &modinv_temp, &mont_temp,    \
-                           &result_temp );                             \
+       bigint_montgomery ( &modulus_temp, &mont_temp, &result_temp );  \
        DBG_HDA ( 0, &result_temp, sizeof ( result_temp ) );            \
        bigint_done ( &result_temp, result_raw,                         \
                      sizeof ( result_raw ) );                          \