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rsa: clarify CRT computation

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Signed-off-by: Manuel Pégourié-Gonnard <[email protected]>
This commit is contained in:
Manuel Pégourié-Gonnard
2025-12-09 09:26:20 +01:00
parent ec5bc19996
commit d251d73d06
1 changed files with 11 additions and 13 deletions
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library/rsa.c
+11 -13
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@@ -1271,28 +1271,26 @@ cleanup:
/* /*
* Compute T such that T = TP mod P and T = TQ mod Q. * Compute T such that T = TP mod P and T = TQ mod Q.
* (This is the Chinese Remainder Theorem - CRT.) * (This is the Chinese Remainder Theorem - CRT.)
*
* WARNING: uses TP as a temporary, so its value is lost!
*/ */
static int rsa_apply_crt(mbedtls_mpi *T, static int rsa_apply_crt(mbedtls_mpi *T,
mbedtls_mpi *TP, const mbedtls_mpi *TP,
const mbedtls_mpi *TQ, const mbedtls_mpi *TQ,
const mbedtls_rsa_context *ctx) const mbedtls_rsa_context *ctx)
{ {
int ret; int ret;
/* /*
* T = (TP - TQ) * (Q^-1 mod P) mod P * Set T = ((TP - TQ) * (Q^-1 mod P) mod P) * Q + TQ
*
* That way we have both:
* mod P: T = (TP - TQ) * (Q^-1 * Q) + TQ = (TP - TQ) * 1 + TQ = TP
* mod Q: T = (...) * Q + TQ = TQ
*/ */
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(T, TP, TQ)); MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(T, TP, TQ)); // T = TP - TQ
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(TP, T, &ctx->QP)); MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(T, T, &ctx->QP)); // T *= Q^-1 mod P
MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(T, TP, &ctx->P)); MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(T, T, &ctx->P)); // T %= P
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(T, T, &ctx->Q)); // T *= Q
/* MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(T, T, TQ)); // T += TQ
* T = TQ + T * Q
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(TP, T, &ctx->Q));
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(T, TQ, TP));
cleanup: cleanup:
return ret; return ret;