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Simplify the final reduction in mpi_montmul

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There was some confusion during review about when A->p[n] could be
nonzero. In fact, there is no need to set A->p[n]: only the
intermediate result d might need to extend to n+1 limbs, not the final
result A. So never access A->p[n]. Rework the explanation of the
calculation in a way that should be easier to follow.

Signed-off-by: Gilles Peskine <Gilles.Peskine@arm.com>
This commit is contained in:
Gilles Peskine 2020-06-08 22:37:50 +02:00
parent c097e9ea45
commit 221626f2d3
1 changed files with 18 additions and 11 deletions
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29
library/bignum.c
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@ -2009,8 +2009,8 @@ static void mpi_montg_init( mbedtls_mpi_uint *mm, const mbedtls_mpi *N )
/** Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36)
*
* \param[in,out] A One of the numbers to multiply.
* It must have at least one more limb than N
* (A->n >= N->n + 1).
* It must have at least as many limbs as N
* (A->n >= N->n), and any limbs beyond n are ignored.
* On successful completion, A contains the result of
* the multiplication A * B * R^-1 mod N where
* R = (2^ciL)^n.
@ -2054,18 +2054,25 @@ static void mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi
*d++ = u0; d[n + 1] = 0;
}
memcpy( A->p, d, ( n + 1 ) * ciL );
/* At this point, d is either the desired result or the desired result
* plus N. We now potentially subtract N, avoiding leaking whether the
* subtraction is performed through side channels. */
/* If A >= N then A -= N. Do the subtraction unconditionally to prevent
* timing attacks. */
/* Set d to A + (2^biL)^n - N. */
/* Copy the n least significant limbs of d to A, so that
* A = d if d < N (recall that N has n limbs). */
memcpy( A->p, d, n * ciL );
/* If d >= N then we want to set A to N - d. To prevent timing attacks,
* do the calculation without using conditional tests. */
/* Set d to d0 + (2^biL)^n - N where d0 is the current value of d. */
d[n] += 1;
d[n] -= mpi_sub_hlp( n, d, N->p );
/* Now d - (2^biL)^n = A - N so d >= (2^biL)^n iff A >= N.
* So we want to copy the result of the subtraction iff d->p[n] != 0.
* Note that d->p[n] is either 0 or 1 since A - N <= N <= (2^biL)^n. */
mpi_safe_cond_assign( n + 1, A->p, d, (unsigned char) d[n] );
A->p[n] = 0;
/* If d0 < N then d < (2^biL)^n
* so d[n] == 0 and we want to keep A as it is.
* If d0 >= N then d >= (2^biL)^n, and d <= (2^biL)^n + N < 2 * (2^biL)^n
* so d[n] == 1 and we want to set A to the result of the subtraction
* which is d - (2^biL)^n, i.e. the n least significant limbs of d.
* This exactly corresponds to a conditional assignment. */
mpi_safe_cond_assign( n, A->p, d, (unsigned char) d[n] );
}
/*